task stringclasses 2
values | metadata dict | prompt stringlengths 355 2.05k | answer stringclasses 105
values |
|---|---|---|---|
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 137,
"_task": "bayesian_association",
"_time": 1.892298698425293,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.32, 0.68 ;\n}\nprobability ( X_1 ) {\n table 0.82, 0.18 ;\n}\nprobability ( X_2 ) {\n table 0.02, 0.98 ;\n}\n",
"cot": "Result: P(X_1) = {0: 0.82, 1: 0.18}\nResult: P(X_1) = {0: 0.82, 1: 0.18}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.32, '1': 0.68}
P(X_1) = {'0': 0.82, '1': 0.18}
P(X_2) = {'0': 0.02, '1': 0.98}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.82, 1: 0.18} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 108,
"_level": 0,
"_prompt_tokens": 277,
"_task": "bayesian_intervention",
"_time": 1.4605143070220947,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.76, 0.24 ;\n}\nprobability ( X_1 ) {\n table 0.99, 0.01 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.28, 0.72;\n ( 0, 1 ) 0.6, 0.4;\n ( 1, 0 ) 0.88, 0.12;\n ( 1, 1 ) 0.58, 0.42;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=1), X_0=0)\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=1.\nResult: P(X_1) = {0: 0.99, 1: 0.01}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1. Observing/Knowing that the state X_0 is equal to 0",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.76, '1': 0.24}
P(X_2|X_0=0, X_1=0) = {'0': 0.28, '1': 0.72}
P(X_2|X_0=0, X_1=1) = {'0': 0.6, '1': 0.4}
P(X_2|X_0=1, X_1=0) = {'0': 0.88, '1': 0.12}
P(X_2|X_0=1, X_1=1) = {'0': 0.58, '1': 0.42}
P(X_1) = {'0': 0.99, '1': 0.01}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1. Observing/Knowing that the state X_0 is equal to 0
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.99, 1: 0.01} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 156,
"_task": "bayesian_association",
"_time": 1.4566493034362793,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.72, 0.28 ;\n}\nprobability ( X_1 ) {\n table 0.59, 0.41 ;\n}\nprobability ( X_2 ) {\n table 0.27, 0.73 ;\n}\n",
"cot": "Result: P(X_1) = {0: 0.59, 1: 0.41}\nResult: P(X_1) = {0: 0.59, 1: 0.41}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 1, and the state X_2 is equal to 0",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.72, '1': 0.28}
P(X_1) = {'0': 0.59, '1': 0.41}
P(X_2) = {'0': 0.27, '1': 0.73}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 1, and the state X_2 is equal to 0
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.59, 1: 0.41} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 81,
"_level": 0,
"_prompt_tokens": 160,
"_task": "bayesian_intervention",
"_time": 1.5368854999542236,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.69, 0.31 ;\n}\nprobability ( X_1 ) {\n table 0.94, 0.06 ;\n}\nprobability ( X_2 ) {\n table 0.4, 0.6 ;\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=0), X_0=0)\nSurgery: P(X_2)= Point Mass at X_2=0.\nResult: P(X_1) = {0: 0.94, 1: 0.06}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_0 is equal to 0",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.69, '1': 0.31}
P(X_1) = {'0': 0.94, '1': 0.06}
P(X_2) = {'0': 0.4, '1': 0.6}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_0 is equal to 0
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.94, 1: 0.06} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 205,
"_level": 0,
"_prompt_tokens": 254,
"_task": "bayesian_association",
"_time": 1.4630367755889893,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.03, 0.97 ;\n}\nprobability ( X_1 ) {\n table 0.72, 0.28 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.62, 0.38;\n ( 0, 1 ) 0.91, 0.09;\n ( 1, 0 ) 0.5, 0.5;\n ( 1, 1 ) 0.52, 0.48;\n\n}\n",
"cot": "Elim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.51, 1: 0.49}\nResult: P(X_2) = {0: 0.51, 1: 0.49}\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.51, 1: 0.49}\nResult: P(X_2) = {0: 0.51, 1: 0.49}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.03, '1': 0.97}
P(X_2|X_0=0, X_1=0) = {'0': 0.62, '1': 0.38}
P(X_2|X_0=0, X_1=1) = {'0': 0.91, '1': 0.09}
P(X_2|X_0=1, X_1=0) = {'0': 0.5, '1': 0.5}
P(X_2|X_0=1, X_1=1) = {'0': 0.52, '1': 0.48}
P(X_1) = {'0': 0.72, '1': 0.28}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.51, 1: 0.49} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 108,
"_level": 0,
"_prompt_tokens": 277,
"_task": "bayesian_intervention",
"_time": 1.5590705871582031,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.78, 0.22 ;\n}\nprobability ( X_1 ) {\n table 0.47, 0.53 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.66, 0.34;\n ( 0, 1 ) 0.4, 0.6;\n ( 1, 0 ) 0.68, 0.32;\n ( 1, 1 ) 0.36, 0.64;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_2=1), X_1=1)\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=1.\nResult: P(X_0) = {0: 0.78, 1: 0.22}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1. Observing/Knowing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.78, '1': 0.22}
P(X_2|X_0=0, X_1=0) = {'0': 0.66, '1': 0.34}
P(X_2|X_0=0, X_1=1) = {'0': 0.4, '1': 0.6}
P(X_2|X_0=1, X_1=0) = {'0': 0.68, '1': 0.32}
P(X_2|X_0=1, X_1=1) = {'0': 0.36, '1': 0.64}
P(X_1) = {'0': 0.47, '1': 0.53}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1. Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.78, 1: 0.22} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 75,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_association",
"_time": 1.469942331314087,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.39, 0.61 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.33, 0.67;\n ( 1 ) 0.53, 0.47;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.65, 0.35;\n ( 1 ) 0.14, 0.86;\n\n}\n",
"cot": "Result: P(X_1 | X_0=1) = {0: 0.53, 1: 0.47}\nResult: P(X_1 | X_0=1) = {0: 0.53, 1: 0.47}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.39, '1': 0.61}
P(X_1|X_0=0) = {'0': 0.33, '1': 0.67}
P(X_1|X_0=1) = {'0': 0.53, '1': 0.47}
P(X_2|X_0=0) = {'0': 0.65, '1': 0.35}
P(X_2|X_0=1) = {'0': 0.14, '1': 0.86}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.53, 1: 0.47} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 109,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.4507777690887451,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.64, 0.36 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.37, 0.63;\n ( 1 ) 0.34, 0.66;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.57, 0.43;\n ( 1 ) 0.4, 0.6;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=0), X_0=1)\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0'] -> X_2; P(X_2)= Point Mass at X_2=0.\nResult: P(X_1 | X_0=1) = {0: 0.34, 1: 0.66}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.64, '1': 0.36}
P(X_1|X_0=0) = {'0': 0.37, '1': 0.63}
P(X_1|X_0=1) = {'0': 0.34, '1': 0.66}
P(X_2|X_0=0) = {'0': 0.57, '1': 0.43}
P(X_2|X_0=1) = {'0': 0.4, '1': 0.6}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.34, 1: 0.66} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 137,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_association",
"_time": 1.4945213794708252,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.59, 0.41 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.71, 0.29;\n ( 1 ) 0.42, 0.58;\n\n}\nprobability ( X_2 ) {\n table 0.17, 0.83 ;\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_1) = {0: 0.59, 1: 0.41}\nResult: P(X_1) = {0: 0.59, 1: 0.41}\nElim order: ['X_0']\nSum out X_0 -> P(X_1) = {0: 0.59, 1: 0.41}\nResult: P(X_1) = {0: 0.59, 1: 0.41}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.59, '1': 0.41}
P(X_1|X_0=0) = {'0': 0.71, '1': 0.29}
P(X_1|X_0=1) = {'0': 0.42, '1': 0.58}
P(X_2) = {'0': 0.17, '1': 0.83}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.59, 1: 0.41} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 163,
"_level": 0,
"_prompt_tokens": 261,
"_task": "bayesian_intervention",
"_time": 1.4967918395996094,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.6, 0.4 ;\n}\nprobability ( X_1 ) {\n table 0.24, 0.76 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.47, 0.53;\n ( 0, 1 ) 0.4, 0.6;\n ( 1, 0 ) 0.68, 0.32;\n ( 1, 1 ) 0.61, 0.39;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=0))\nSurgery: P(X_0)= Point Mass at X_0=0.\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | do(X_0=0)) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2 | do(X_0=0)) = {0: 0.42, 1: 0.58}\nResult: P(X_2 | do(X_0=0)) = {0: 0.42, 1: 0.58}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.6, '1': 0.4}
P(X_2|X_0=0, X_1=0) = {'0': 0.47, '1': 0.53}
P(X_2|X_0=0, X_1=1) = {'0': 0.4, '1': 0.6}
P(X_2|X_0=1, X_1=0) = {'0': 0.68, '1': 0.32}
P(X_2|X_0=1, X_1=1) = {'0': 0.61, '1': 0.39}
P(X_1) = {'0': 0.24, '1': 0.76}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.42, 1: 0.58} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.5172131061553955,
"bif_description": "// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.7, 0.3 ;\n}\nprobability ( X_1 ) {\n table 0.5, 0.5 ;\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.94, 0.06;\n ( 1 ) 0.56, 0.44;\n\n}\n",
"cot": "Result: P(X_1) = {0: 0.5, 1: 0.5}\nResult: P(X_1) = {0: 0.5, 1: 0.5}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_1",
"X_2",
"X_0"
]
} | System:
P(X_1) = {'0': 0.5, '1': 0.5}
P(X_2|X_1=0) = {'0': 0.94, '1': 0.06}
P(X_2|X_1=1) = {'0': 0.56, '1': 0.44}
P(X_0) = {'0': 0.7, '1': 0.3}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.5, 1: 0.5} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 166,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_intervention",
"_time": 1.4749128818511963,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.38, 0.62 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.45, 0.55;\n ( 1 ) 0.87, 0.13;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.16, 0.84;\n ( 1 ) 0.5, 0.5;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=0))\nSurgery: P(X_0)= Point Mass at X_0=0.\nElim order: ['X_0', 'X_1']\nSum out X_0 -> P(X_1 | do(X_0=0)) = {0: 0.45, 1: 0.55}\nSum out X_1 -> P(X_2 | do(X_0=0)) = {0: 0.35, 1: 0.65}\nResult: P(X_2 | do(X_0=0)) = {0: 0.35, 1: 0.65}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.38, '1': 0.62}
P(X_1|X_0=0) = {'0': 0.45, '1': 0.55}
P(X_1|X_0=1) = {'0': 0.87, '1': 0.13}
P(X_2|X_1=0) = {'0': 0.16, '1': 0.84}
P(X_2|X_1=1) = {'0': 0.5, '1': 0.5}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.35, 1: 0.65} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 137,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.451801061630249,
"bif_description": "// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.57, 0.43 ;\n}\nprobability ( X_1 ) {\n table 0.53, 0.47 ;\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.42, 0.58;\n ( 1 ) 0.62, 0.38;\n\n}\n",
"cot": "Elim order: ['X_1']\nSum out X_1 -> P(X_2) = {0: 0.51, 1: 0.49}\nResult: P(X_2) = {0: 0.51, 1: 0.49}\nElim order: ['X_1']\nSum out X_1 -> P(X_2) = {0: 0.51, 1: 0.49}\nResult: P(X_2) = {0: 0.51, 1: 0.49}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_1",
"X_2",
"X_0"
]
} | System:
P(X_1) = {'0': 0.53, '1': 0.47}
P(X_2|X_1=0) = {'0': 0.42, '1': 0.58}
P(X_2|X_1=1) = {'0': 0.62, '1': 0.38}
P(X_0) = {'0': 0.57, '1': 0.43}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.51, 1: 0.49} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 75,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_intervention",
"_time": 1.5351448059082031,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.63, 0.37 ;\n}\nprobability ( X_1 ) {\n table 0.5, 0.5 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.21, 0.79;\n ( 1 ) 0.65, 0.35;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1))\nSurgery: P(X_1)= Point Mass at X_1=1.\nResult: P(X_0) = {0: 0.63, 1: 0.37}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.63, '1': 0.37}
P(X_2|X_0=0) = {'0': 0.21, '1': 0.79}
P(X_2|X_0=1) = {'0': 0.65, '1': 0.35}
P(X_1) = {'0': 0.5, '1': 0.5}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.63, 1: 0.37} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 137,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.4519500732421875,
"bif_description": "// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.09, 0.91 ;\n}\nprobability ( X_1 ) {\n table 0.53, 0.47 ;\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.78, 0.22;\n ( 1 ) 0.23, 0.77;\n\n}\n",
"cot": "Elim order: ['X_1']\nSum out X_1 -> P(X_2) = {0: 0.52, 1: 0.48}\nResult: P(X_2) = {0: 0.52, 1: 0.48}\nElim order: ['X_1']\nSum out X_1 -> P(X_2) = {0: 0.52, 1: 0.48}\nResult: P(X_2) = {0: 0.52, 1: 0.48}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_1",
"X_2",
"X_0"
]
} | System:
P(X_1) = {'0': 0.53, '1': 0.47}
P(X_2|X_1=0) = {'0': 0.78, '1': 0.22}
P(X_2|X_1=1) = {'0': 0.23, '1': 0.77}
P(X_0) = {'0': 0.09, '1': 0.91}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.52, 1: 0.48} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 75,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_intervention",
"_time": 1.4967172145843506,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.66, 0.34 ;\n}\nprobability ( X_1 ) {\n table 0.84, 0.16 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.25, 0.75;\n ( 1 ) 0.92, 0.08;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=0))\nSurgery: P(X_1)= Point Mass at X_1=0.\nResult: P(X_0) = {0: 0.66, 1: 0.34}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.66, '1': 0.34}
P(X_2|X_0=0) = {'0': 0.25, '1': 0.75}
P(X_2|X_0=1) = {'0': 0.92, '1': 0.08}
P(X_1) = {'0': 0.84, '1': 0.16}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.66, 1: 0.34} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.4616541862487793,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.93, 0.07 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.37, 0.63;\n ( 1 ) 0.55, 0.45;\n\n}\nprobability ( X_2 ) {\n table 0.57, 0.43 ;\n}\n",
"cot": "Result: P(X_2) = {0: 0.57, 1: 0.43}\nResult: P(X_2) = {0: 0.57, 1: 0.43}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.93, '1': 0.07}
P(X_1|X_0=0) = {'0': 0.37, '1': 0.63}
P(X_1|X_0=1) = {'0': 0.55, '1': 0.45}
P(X_2) = {'0': 0.57, '1': 0.43}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.57, 1: 0.43} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 112,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_intervention",
"_time": 1.4781944751739502,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.52, 0.48 ;\n}\nprobability ( X_1 ) {\n table 0.54, 0.46 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.62, 0.38;\n ( 1 ) 0.48, 0.52;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=1))\nSurgery: P(X_1)= Point Mass at X_1=1.\nElim order: ['X_0']\nSum out X_0 -> P(X_2) = {0: 0.55, 1: 0.45}\nResult: P(X_2) = {0: 0.55, 1: 0.45}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.52, '1': 0.48}
P(X_2|X_0=0) = {'0': 0.62, '1': 0.38}
P(X_2|X_0=1) = {'0': 0.48, '1': 0.52}
P(X_1) = {'0': 0.54, '1': 0.46}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.55, 1: 0.45} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 87,
"_level": 0,
"_prompt_tokens": 273,
"_task": "bayesian_association",
"_time": 1.5904970169067383,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.95, 0.05 ;\n}\nprobability ( X_1 ) {\n table 0.5, 0.5 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.34, 0.66;\n ( 0, 1 ) 0.06, 0.94;\n ( 1, 0 ) 0.78, 0.22;\n ( 1, 1 ) 0.63, 0.37;\n\n}\n",
"cot": "Result: P(X_2 | X_0=1, X_1=1) = {0: 0.63, 1: 0.37}\nResult: P(X_2 | X_0=1, X_1=1) = {0: 0.63, 1: 0.37}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.95, '1': 0.05}
P(X_2|X_0=0, X_1=0) = {'0': 0.34, '1': 0.66}
P(X_2|X_0=0, X_1=1) = {'0': 0.06, '1': 0.94}
P(X_2|X_0=1, X_1=0) = {'0': 0.78, '1': 0.22}
P(X_2|X_0=1, X_1=1) = {'0': 0.63, '1': 0.37}
P(X_1) = {'0': 0.5, '1': 0.5}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.63, 1: 0.37} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_intervention",
"_time": 1.5145950317382812,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.76, 0.24 ;\n}\nprobability ( X_1 ) {\n table 0.73, 0.27 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.7, 0.3;\n ( 1 ) 0.48, 0.52;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=1))\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0'] -> X_2; P(X_2)= Point Mass at X_2=1.\nResult: P(X_1) = {0: 0.73, 1: 0.27}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.76, '1': 0.24}
P(X_2|X_0=0) = {'0': 0.7, '1': 0.3}
P(X_2|X_0=1) = {'0': 0.48, '1': 0.52}
P(X_1) = {'0': 0.73, '1': 0.27}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.73, 1: 0.27} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.4566090106964111,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.32, 0.68 ;\n}\nprobability ( X_1 ) {\n table 0.59, 0.41 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.5, 0.5;\n ( 1 ) 0.57, 0.43;\n\n}\n",
"cot": "Result: P(X_0) = {0: 0.32, 1: 0.68}\nResult: P(X_0) = {0: 0.32, 1: 0.68}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.32, '1': 0.68}
P(X_2|X_0=0) = {'0': 0.5, '1': 0.5}
P(X_2|X_0=1) = {'0': 0.57, '1': 0.43}
P(X_1) = {'0': 0.59, '1': 0.41}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.32, 1: 0.68} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_intervention",
"_time": 1.5201406478881836,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.05, 0.95 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.36, 0.64;\n ( 1 ) 0.19, 0.81;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.65, 0.35;\n ( 1 ) 0.55, 0.45;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_2=1))\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_1'] -> X_2; P(X_2)= Point Mass at X_2=1.\nResult: P(X_0) = {0: 0.05, 1: 0.95}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.05, '1': 0.95}
P(X_1|X_0=0) = {'0': 0.36, '1': 0.64}
P(X_1|X_0=1) = {'0': 0.19, '1': 0.81}
P(X_2|X_1=0) = {'0': 0.65, '1': 0.35}
P(X_2|X_1=1) = {'0': 0.55, '1': 0.45}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.05, 1: 0.95} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_association",
"_time": 1.455700397491455,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.02, 0.98 ;\n}\nprobability ( X_1 ) {\n table 0.55, 0.45 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.44, 0.56;\n ( 1 ) 0.48, 0.52;\n\n}\n",
"cot": "Result: P(X_1) = {0: 0.55, 1: 0.45}\nResult: P(X_1) = {0: 0.55, 1: 0.45}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 0",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.02, '1': 0.98}
P(X_2|X_0=0) = {'0': 0.44, '1': 0.56}
P(X_2|X_0=1) = {'0': 0.48, '1': 0.52}
P(X_1) = {'0': 0.55, '1': 0.45}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 0
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.55, 1: 0.45} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 81,
"_level": 0,
"_prompt_tokens": 160,
"_task": "bayesian_intervention",
"_time": 1.5111091136932373,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.2, 0.8 ;\n}\nprobability ( X_1 ) {\n table 0.79, 0.21 ;\n}\nprobability ( X_2 ) {\n table 0.42, 0.58 ;\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_2=0), X_1=0)\nSurgery: P(X_2)= Point Mass at X_2=0.\nResult: P(X_0) = {0: 0.2, 1: 0.8}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.2, '1': 0.8}
P(X_1) = {'0': 0.79, '1': 0.21}
P(X_2) = {'0': 0.42, '1': 0.58}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.2, 1: 0.8} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 156,
"_task": "bayesian_association",
"_time": 1.4520039558410645,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.22, 0.78 ;\n}\nprobability ( X_1 ) {\n table 0.6, 0.4 ;\n}\nprobability ( X_2 ) {\n table 0.37, 0.63 ;\n}\n",
"cot": "Result: P(X_2) = {0: 0.37, 1: 0.63}\nResult: P(X_2) = {0: 0.37, 1: 0.63}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 0, and the state X_1 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.22, '1': 0.78}
P(X_1) = {'0': 0.6, '1': 0.4}
P(X_2) = {'0': 0.37, '1': 0.63}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 0, and the state X_1 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.37, 1: 0.63} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 163,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.4569575786590576,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.83, 0.17 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.51, 0.49;\n ( 1 ) 0.44, 0.56;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.58, 0.42;\n ( 0, 1 ) 0.22, 0.78;\n ( 1, 0 ) 0.63, 0.37;\n ( 1, 1 ) 0.67, 0.33;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=1))\nSurgery: P(X_0)= Point Mass at X_0=1.\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | do(X_0=1)) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2 | do(X_0=1)) = {0: 0.65, 1: 0.35}\nResult: P(X_2 | do(X_0=1)) = {0: 0.65, 1: 0.35}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.83, '1': 0.17}
P(X_1|X_0=0) = {'0': 0.51, '1': 0.49}
P(X_1|X_0=1) = {'0': 0.44, '1': 0.56}
P(X_2|X_0=0, X_1=0) = {'0': 0.58, '1': 0.42}
P(X_2|X_0=0, X_1=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=1, X_1=0) = {'0': 0.63, '1': 0.37}
P(X_2|X_0=1, X_1=1) = {'0': 0.67, '1': 0.33}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.65, 1: 0.35} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 161,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_association",
"_time": 1.471294641494751,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.63, 0.37 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.58, 0.42;\n ( 1 ) 0.68, 0.32;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.92, 0.08;\n ( 0, 1 ) 0.47, 0.53;\n ( 1, 0 ) 0.26, 0.74;\n ( 1, 1 ) 0.67, 0.33;\n\n}\n",
"cot": "Elim order: ['X_1']\nSum out X_1 -> P(X_2 | X_0=0) = {0: 0.73, 1: 0.27}\nResult: P(X_2 | X_0=0) = {0: 0.73, 1: 0.27}\nElim order: ['X_1']\nSum out X_1 -> P(X_2 | X_0=0) = {0: 0.73, 1: 0.27}\nResult: P(X_2 | X_0=0) = {0: 0.73, 1: 0.27}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.63, '1': 0.37}
P(X_1|X_0=0) = {'0': 0.58, '1': 0.42}
P(X_1|X_0=1) = {'0': 0.68, '1': 0.32}
P(X_2|X_0=0, X_1=0) = {'0': 0.92, '1': 0.08}
P(X_2|X_0=0, X_1=1) = {'0': 0.47, '1': 0.53}
P(X_2|X_0=1, X_1=0) = {'0': 0.26, '1': 0.74}
P(X_2|X_0=1, X_1=1) = {'0': 0.67, '1': 0.33}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.73, 1: 0.27} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 81,
"_level": 0,
"_prompt_tokens": 195,
"_task": "bayesian_intervention",
"_time": 1.4275445938110352,
"bif_description": "// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.58, 0.42 ;\n}\nprobability ( X_1 ) {\n table 0.55, 0.45 ;\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.65, 0.35;\n ( 1 ) 0.75, 0.25;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1), X_2=1)\nSurgery: P(X_1)= Point Mass at X_1=1.\nResult: P(X_0) = {0: 0.58, 1: 0.42}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_1",
"X_2",
"X_0"
]
} | System:
P(X_1) = {'0': 0.55, '1': 0.45}
P(X_2|X_1=0) = {'0': 0.65, '1': 0.35}
P(X_2|X_1=1) = {'0': 0.75, '1': 0.25}
P(X_0) = {'0': 0.58, '1': 0.42}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.58, 1: 0.42} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.514634132385254,
"bif_description": "// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.5, 0.5 ;\n}\nprobability ( X_1 ) {\n table 0.37, 0.63 ;\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.11, 0.89;\n ( 1 ) 0.87, 0.13;\n\n}\n",
"cot": "Result: P(X_1) = {0: 0.37, 1: 0.63}\nResult: P(X_1) = {0: 0.37, 1: 0.63}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_1",
"X_2",
"X_0"
]
} | System:
P(X_1) = {'0': 0.37, '1': 0.63}
P(X_2|X_1=0) = {'0': 0.11, '1': 0.89}
P(X_2|X_1=1) = {'0': 0.87, '1': 0.13}
P(X_0) = {'0': 0.5, '1': 0.5}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.37, 1: 0.63} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 102,
"_level": 0,
"_prompt_tokens": 261,
"_task": "bayesian_intervention",
"_time": 1.4985151290893555,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.64, 0.36 ;\n}\nprobability ( X_1 ) {\n table 0.18, 0.82 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.35, 0.65;\n ( 0, 1 ) 0.92, 0.08;\n ( 1, 0 ) 0.5, 0.5;\n ( 1, 1 ) 0.42, 0.58;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_2=0))\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=0.\nResult: P(X_0) = {0: 0.64, 1: 0.36}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.64, '1': 0.36}
P(X_2|X_0=0, X_1=0) = {'0': 0.35, '1': 0.65}
P(X_2|X_0=0, X_1=1) = {'0': 0.92, '1': 0.08}
P(X_2|X_0=1, X_1=0) = {'0': 0.5, '1': 0.5}
P(X_2|X_0=1, X_1=1) = {'0': 0.42, '1': 0.58}
P(X_1) = {'0': 0.18, '1': 0.82}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.64, 1: 0.36} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 89,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_association",
"_time": 1.4500200748443604,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.25, 0.75 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.54, 0.46;\n ( 1 ) 0.77, 0.23;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.64, 0.36;\n ( 1 ) 0.73, 0.27;\n\n}\n",
"cot": "Normalize (sum=0.71) -> P(X_0 | X_1=0) = {0: 0.19, 1: 0.81}\nNormalize (sum=0.71) -> P(X_0 | X_1=0) = {0: 0.19, 1: 0.81}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.25, '1': 0.75}
P(X_1|X_0=0) = {'0': 0.54, '1': 0.46}
P(X_1|X_0=1) = {'0': 0.77, '1': 0.23}
P(X_2|X_0=0) = {'0': 0.64, '1': 0.36}
P(X_2|X_0=1) = {'0': 0.73, '1': 0.27}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.19, 1: 0.81} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 109,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.5588388442993164,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.84, 0.16 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.49, 0.51;\n ( 1 ) 0.37, 0.63;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.48, 0.52;\n ( 1 ) 0.12, 0.88;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=0), X_0=1)\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nResult: P(X_2 | X_0=1) = {0: 0.12, 1: 0.88}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.84, '1': 0.16}
P(X_1|X_0=0) = {'0': 0.49, '1': 0.51}
P(X_1|X_0=1) = {'0': 0.37, '1': 0.63}
P(X_2|X_0=0) = {'0': 0.48, '1': 0.52}
P(X_2|X_0=1) = {'0': 0.12, '1': 0.88}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.12, 1: 0.88} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 175,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_association",
"_time": 1.483293056488037,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.56, 0.44 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.39, 0.61;\n ( 1 ) 0.22, 0.78;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.97, 0.03;\n ( 0, 1 ) 0.52, 0.48;\n ( 1, 0 ) 0.2, 0.8;\n ( 1, 1 ) 0.44, 0.56;\n\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_1=0, X_2) = {0: 0.23, 1: 0.08}\nNormalize (sum=0.32) -> P(X_2 | X_1=0) = {0: 0.73, 1: 0.27}\nElim order: ['X_0']\nSum out X_0 -> P(X_1=0, X_2) = {0: 0.23, 1: 0.08}\nNormalize (sum=0.32) -> P(X_2 | X_1=0) = {0: 0.73, 1: 0.27}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.56, '1': 0.44}
P(X_1|X_0=0) = {'0': 0.39, '1': 0.61}
P(X_1|X_0=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=0, X_1=0) = {'0': 0.97, '1': 0.03}
P(X_2|X_0=0, X_1=1) = {'0': 0.52, '1': 0.48}
P(X_2|X_0=1, X_1=0) = {'0': 0.2, '1': 0.8}
P(X_2|X_0=1, X_1=1) = {'0': 0.44, '1': 0.56}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.73, 1: 0.27} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 116,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.5258755683898926,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.33, 0.67 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.61, 0.39;\n ( 1 ) 0.97, 0.03;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.37, 0.63;\n ( 1 ) 0.57, 0.43;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=0), X_2=1)\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nNormalize (sum=0.5) -> P(X_0 | X_2=1) = {0: 0.42, 1: 0.58}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.33, '1': 0.67}
P(X_1|X_0=0) = {'0': 0.61, '1': 0.39}
P(X_1|X_0=1) = {'0': 0.97, '1': 0.03}
P(X_2|X_0=0) = {'0': 0.37, '1': 0.63}
P(X_2|X_0=1) = {'0': 0.57, '1': 0.43}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.42, 1: 0.58} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 101,
"_level": 0,
"_prompt_tokens": 226,
"_task": "bayesian_association",
"_time": 1.5065197944641113,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.48, 0.52 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.01, 0.99;\n ( 1 ) 0.91, 0.09;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.64, 0.36;\n ( 1 ) 0.53, 0.47;\n\n}\n",
"cot": "Normalize (sum=0.33) -> P(X_0 | X_1=1, X_2=0) = {0: 0.92, 1: 0.08}\nNormalize (sum=0.33) -> P(X_0 | X_1=1, X_2=0) = {0: 0.92, 1: 0.08}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 0, and the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.48, '1': 0.52}
P(X_1|X_0=0) = {'0': 0.01, '1': 0.99}
P(X_1|X_0=1) = {'0': 0.91, '1': 0.09}
P(X_2|X_0=0) = {'0': 0.64, '1': 0.36}
P(X_2|X_0=1) = {'0': 0.53, '1': 0.47}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 0, and the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.92, 1: 0.08} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 81,
"_level": 0,
"_prompt_tokens": 160,
"_task": "bayesian_intervention",
"_time": 1.4795513153076172,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.5, 0.5 ;\n}\nprobability ( X_1 ) {\n table 0.63, 0.37 ;\n}\nprobability ( X_2 ) {\n table 0.51, 0.49 ;\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_2=0), X_1=1)\nSurgery: P(X_2)= Point Mass at X_2=0.\nResult: P(X_0) = {0: 0.5, 1: 0.5}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.5, '1': 0.5}
P(X_1) = {'0': 0.63, '1': 0.37}
P(X_2) = {'0': 0.51, '1': 0.49}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.5, 1: 0.5} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 137,
"_task": "bayesian_association",
"_time": 1.514655351638794,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.32, 0.68 ;\n}\nprobability ( X_1 ) {\n table 0.97, 0.03 ;\n}\nprobability ( X_2 ) {\n table 0.52, 0.48 ;\n}\n",
"cot": "Result: P(X_0) = {0: 0.32, 1: 0.68}\nResult: P(X_0) = {0: 0.32, 1: 0.68}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.32, '1': 0.68}
P(X_1) = {'0': 0.97, '1': 0.03}
P(X_2) = {'0': 0.52, '1': 0.48}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.32, 1: 0.68} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 103,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.4499902725219727,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.31, 0.69 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.07, 0.93;\n ( 1 ) 0.74, 0.26;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.72, 0.28;\n ( 1 ) 0.59, 0.41;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1), X_2=1)\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=1.\nResult: P(X_0) = {0: 0.31, 1: 0.69}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.31, '1': 0.69}
P(X_1|X_0=0) = {'0': 0.07, '1': 0.93}
P(X_1|X_0=1) = {'0': 0.74, '1': 0.26}
P(X_2|X_1=0) = {'0': 0.72, '1': 0.28}
P(X_2|X_1=1) = {'0': 0.59, '1': 0.41}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.31, 1: 0.69} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_association",
"_time": 1.4583497047424316,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.51, 0.49 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.68, 0.32;\n ( 1 ) 0.38, 0.62;\n\n}\nprobability ( X_2 ) {\n table 0.47, 0.53 ;\n}\n",
"cot": "Result: P(X_2) = {0: 0.47, 1: 0.53}\nResult: P(X_2) = {0: 0.47, 1: 0.53}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.51, '1': 0.49}
P(X_1|X_0=0) = {'0': 0.68, '1': 0.32}
P(X_1|X_0=1) = {'0': 0.38, '1': 0.62}
P(X_2) = {'0': 0.47, '1': 0.53}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.47, 1: 0.53} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.5,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 103,
"_level": 0,
"_prompt_tokens": 195,
"_task": "bayesian_intervention",
"_time": 1.4374792575836182,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.78, 0.22 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.45, 0.55;\n ( 1 ) 0.32, 0.68;\n\n}\nprobability ( X_2 ) {\n table 0.76, 0.24 ;\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=0), X_2=1)\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nResult: P(X_0) = {0: 0.78, 1: 0.22}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.78, '1': 0.22}
P(X_1|X_0=0) = {'0': 0.45, '1': 0.55}
P(X_1|X_0=1) = {'0': 0.32, '1': 0.68}
P(X_2) = {'0': 0.76, '1': 0.24}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.78, 1: 0.22} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 101,
"_level": 0,
"_prompt_tokens": 226,
"_task": "bayesian_association",
"_time": 1.4221315383911133,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.47, 0.53 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.09, 0.91;\n ( 1 ) 0.28, 0.72;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.37, 0.63;\n ( 1 ) 0.21, 0.79;\n\n}\n",
"cot": "Normalize (sum=0.75) -> P(X_1 | X_0=1, X_2=1) = {0: 0.24, 1: 0.76}\nNormalize (sum=0.75) -> P(X_1 | X_0=1, X_2=1) = {0: 0.24, 1: 0.76}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 1, and the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.47, '1': 0.53}
P(X_1|X_0=0) = {'0': 0.09, '1': 0.91}
P(X_1|X_0=1) = {'0': 0.28, '1': 0.72}
P(X_2|X_1=0) = {'0': 0.37, '1': 0.63}
P(X_2|X_1=1) = {'0': 0.21, '1': 0.79}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 1, and the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.24, 1: 0.76} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 144,
"_level": 0,
"_prompt_tokens": 277,
"_task": "bayesian_intervention",
"_time": 1.412781000137329,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.24, 0.76 ;\n}\nprobability ( X_1 ) {\n table 0.59, 0.41 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.48, 0.52;\n ( 0, 1 ) 0.25, 0.75;\n ( 1, 0 ) 0.63, 0.37;\n ( 1, 1 ) 0.55, 0.45;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=0), X_1=1)\nSurgery: P(X_0)= Point Mass at X_0=0.\nElim order: ['X_0']\nSum out X_0 -> P(X_2 | X_1=1, do(X_0=0)) = {0: 0.25, 1: 0.75}\nResult: P(X_2 | X_1=1, do(X_0=0)) = {0: 0.25, 1: 0.75}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 0. Observing/Knowing that the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.24, '1': 0.76}
P(X_2|X_0=0, X_1=0) = {'0': 0.48, '1': 0.52}
P(X_2|X_0=0, X_1=1) = {'0': 0.25, '1': 0.75}
P(X_2|X_0=1, X_1=0) = {'0': 0.63, '1': 0.37}
P(X_2|X_0=1, X_1=1) = {'0': 0.55, '1': 0.45}
P(X_1) = {'0': 0.59, '1': 0.41}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 0. Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.25, 1: 0.75} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 156,
"_task": "bayesian_association",
"_time": 1.4200267791748047,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.81, 0.19 ;\n}\nprobability ( X_1 ) {\n table 0.52, 0.48 ;\n}\nprobability ( X_2 ) {\n table 1.0, 0.0 ;\n}\n",
"cot": "Result: P(X_0) = {0: 0.81, 1: 0.19}\nResult: P(X_0) = {0: 0.81, 1: 0.19}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 0, and the state X_2 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.81, '1': 0.19}
P(X_1) = {'0': 0.52, '1': 0.48}
P(X_2) = {'0': 1.0, '1': 0.0}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 0, and the state X_2 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.81, 1: 0.19} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 151,
"_level": 0,
"_prompt_tokens": 277,
"_task": "bayesian_intervention",
"_time": 1.4360313415527344,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.5, 0.5 ;\n}\nprobability ( X_1 ) {\n table 0.43, 0.57 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.28, 0.72;\n ( 0, 1 ) 0.76, 0.24;\n ( 1, 0 ) 0.96, 0.04;\n ( 1, 1 ) 0.64, 0.36;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1), X_2=0)\nSurgery: P(X_1)= Point Mass at X_1=1.\nElim order: ['X_1']\nSum out X_1 -> P(X_2=0 | X_0, do(X_1=1)) = {0: 0.76, 1: 0.64}\nNormalize (sum=0.7) -> P(X_0 | X_2=0, do(X_1=1)) = {0: 0.54, 1: 0.46}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_2 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.5, '1': 0.5}
P(X_2|X_0=0, X_1=0) = {'0': 0.28, '1': 0.72}
P(X_2|X_0=0, X_1=1) = {'0': 0.76, '1': 0.24}
P(X_2|X_0=1, X_1=0) = {'0': 0.96, '1': 0.04}
P(X_2|X_0=1, X_1=1) = {'0': 0.64, '1': 0.36}
P(X_1) = {'0': 0.43, '1': 0.57}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_2 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.54, 1: 0.46} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 89,
"_level": 0,
"_prompt_tokens": 226,
"_task": "bayesian_association",
"_time": 1.41493558883667,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.97, 0.03 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.57, 0.43;\n ( 1 ) 0.98, 0.02;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.45, 0.55;\n ( 1 ) 0.05, 0.95;\n\n}\n",
"cot": "Normalize (sum=0.58) -> P(X_0 | X_1=0) = {0: 0.95, 1: 0.05}\nNormalize (sum=0.58) -> P(X_0 | X_1=0) = {0: 0.95, 1: 0.05}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 0, and the state X_2 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.97, '1': 0.03}
P(X_1|X_0=0) = {'0': 0.57, '1': 0.43}
P(X_1|X_0=1) = {'0': 0.98, '1': 0.02}
P(X_2|X_1=0) = {'0': 0.45, '1': 0.55}
P(X_2|X_1=1) = {'0': 0.05, '1': 0.95}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 0, and the state X_2 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.95, 1: 0.05} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.3874702453613281,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.85, 0.15 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.02, 0.98;\n ( 1 ) 0.56, 0.44;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.21, 0.79;\n ( 0, 1 ) 0.21, 0.79;\n ( 1, 0 ) 0.54, 0.46;\n ( 1, 1 ) 0.64, 0.36;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=0))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nResult: P(X_0) = {0: 0.85, 1: 0.15}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.85, '1': 0.15}
P(X_1|X_0=0) = {'0': 0.02, '1': 0.98}
P(X_1|X_0=1) = {'0': 0.56, '1': 0.44}
P(X_2|X_0=0, X_1=0) = {'0': 0.21, '1': 0.79}
P(X_2|X_0=0, X_1=1) = {'0': 0.21, '1': 0.79}
P(X_2|X_0=1, X_1=0) = {'0': 0.54, '1': 0.46}
P(X_2|X_0=1, X_1=1) = {'0': 0.64, '1': 0.36}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.85, 1: 0.15} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.4671366214752197,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.87, 0.13 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.98, 0.02;\n ( 1 ) 0.77, 0.23;\n\n}\nprobability ( X_2 ) {\n table 0.98, 0.02 ;\n}\n",
"cot": "Result: P(X_2) = {0: 0.98, 1: 0.02}\nResult: P(X_2) = {0: 0.98, 1: 0.02}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.87, '1': 0.13}
P(X_1|X_0=0) = {'0': 0.98, '1': 0.02}
P(X_1|X_0=1) = {'0': 0.77, '1': 0.23}
P(X_2) = {'0': 0.98, '1': 0.02}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.98, 1: 0.02} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.409942865371704,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.91, 0.09 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.56, 0.44;\n ( 1 ) 0.55, 0.45;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.68, 0.32;\n ( 0, 1 ) 0.21, 0.79;\n ( 1, 0 ) 0.68, 0.32;\n ( 1, 1 ) 0.42, 0.58;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=1.\nResult: P(X_0) = {0: 0.91, 1: 0.09}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.91, '1': 0.09}
P(X_1|X_0=0) = {'0': 0.56, '1': 0.44}
P(X_1|X_0=1) = {'0': 0.55, '1': 0.45}
P(X_2|X_0=0, X_1=0) = {'0': 0.68, '1': 0.32}
P(X_2|X_0=0, X_1=1) = {'0': 0.21, '1': 0.79}
P(X_2|X_0=1, X_1=0) = {'0': 0.68, '1': 0.32}
P(X_2|X_0=1, X_1=1) = {'0': 0.42, '1': 0.58}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.91, 1: 0.09} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 101,
"_level": 0,
"_prompt_tokens": 226,
"_task": "bayesian_association",
"_time": 1.4418978691101074,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.75, 0.25 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.2, 0.8;\n ( 1 ) 0.29, 0.71;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.78, 0.22;\n ( 1 ) 0.72, 0.28;\n\n}\n",
"cot": "Normalize (sum=0.18) -> P(X_0 | X_1=1, X_2=1) = {0: 0.73, 1: 0.27}\nNormalize (sum=0.18) -> P(X_0 | X_1=1, X_2=1) = {0: 0.73, 1: 0.27}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1, and the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.75, '1': 0.25}
P(X_1|X_0=0) = {'0': 0.2, '1': 0.8}
P(X_1|X_0=1) = {'0': 0.29, '1': 0.71}
P(X_2|X_0=0) = {'0': 0.78, '1': 0.22}
P(X_2|X_0=1) = {'0': 0.72, '1': 0.28}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1, and the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.73, 1: 0.27} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 144,
"_level": 0,
"_prompt_tokens": 277,
"_task": "bayesian_intervention",
"_time": 1.320075511932373,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.18, 0.82 ;\n}\nprobability ( X_1 ) {\n table 0.6, 0.4 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.28, 0.72;\n ( 0, 1 ) 0.42, 0.58;\n ( 1, 0 ) 0.82, 0.18;\n ( 1, 1 ) 0.8, 0.2;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=1), X_0=1)\nSurgery: P(X_1)= Point Mass at X_1=1.\nElim order: ['X_1']\nSum out X_1 -> P(X_2 | X_0=1, do(X_1=1)) = {0: 0.8, 1: 0.2}\nResult: P(X_2 | X_0=1, do(X_1=1)) = {0: 0.8, 1: 0.2}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.18, '1': 0.82}
P(X_2|X_0=0, X_1=0) = {'0': 0.28, '1': 0.72}
P(X_2|X_0=0, X_1=1) = {'0': 0.42, '1': 0.58}
P(X_2|X_0=1, X_1=0) = {'0': 0.82, '1': 0.18}
P(X_2|X_0=1, X_1=1) = {'0': 0.8, '1': 0.2}
P(X_1) = {'0': 0.6, '1': 0.4}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.8, 1: 0.2} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 254,
"_task": "bayesian_association",
"_time": 1.3293626308441162,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.55, 0.45 ;\n}\nprobability ( X_1 ) {\n table 0.62, 0.38 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.38, 0.62;\n ( 0, 1 ) 0.7, 0.3;\n ( 1, 0 ) 0.49, 0.51;\n ( 1, 1 ) 0.52, 0.48;\n\n}\n",
"cot": "Result: P(X_1) = {0: 0.62, 1: 0.38}\nResult: P(X_1) = {0: 0.62, 1: 0.38}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.55, '1': 0.45}
P(X_2|X_0=0, X_1=0) = {'0': 0.38, '1': 0.62}
P(X_2|X_0=0, X_1=1) = {'0': 0.7, '1': 0.3}
P(X_2|X_0=1, X_1=0) = {'0': 0.49, '1': 0.51}
P(X_2|X_0=1, X_1=1) = {'0': 0.52, '1': 0.48}
P(X_1) = {'0': 0.62, '1': 0.38}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.62, 1: 0.38} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 126,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.4181938171386719,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.41, 0.59 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.52, 0.48;\n ( 1 ) 0.42, 0.58;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.44, 0.56;\n ( 0, 1 ) 0.19, 0.81;\n ( 1, 0 ) 0.88, 0.12;\n ( 1, 1 ) 0.07, 0.93;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_0=1))\nSurgery: P(X_0)= Point Mass at X_0=1.\nElim order: ['X_0']\nSum out X_0 -> P(X_1 | do(X_0=1)) = {0: 0.42, 1: 0.58}\nResult: P(X_1 | do(X_0=1)) = {0: 0.42, 1: 0.58}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.41, '1': 0.59}
P(X_1|X_0=0) = {'0': 0.52, '1': 0.48}
P(X_1|X_0=1) = {'0': 0.42, '1': 0.58}
P(X_2|X_0=0, X_1=0) = {'0': 0.44, '1': 0.56}
P(X_2|X_0=0, X_1=1) = {'0': 0.19, '1': 0.81}
P(X_2|X_0=1, X_1=0) = {'0': 0.88, '1': 0.12}
P(X_2|X_0=1, X_1=1) = {'0': 0.07, '1': 0.93}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.42, 1: 0.58} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 205,
"_level": 0,
"_prompt_tokens": 289,
"_task": "bayesian_association",
"_time": 1.3394780158996582,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.44, 0.56 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.53, 0.47;\n ( 1 ) 0.55, 0.45;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.27, 0.73;\n ( 0, 1 ) 0.41, 0.59;\n ( 1, 0 ) 0.27, 0.73;\n ( 1, 1 ) 0.57, 0.43;\n\n}\n",
"cot": "Elim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.37, 1: 0.63}\nResult: P(X_2) = {0: 0.37, 1: 0.63}\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.37, 1: 0.63}\nResult: P(X_2) = {0: 0.37, 1: 0.63}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.44, '1': 0.56}
P(X_1|X_0=0) = {'0': 0.53, '1': 0.47}
P(X_1|X_0=1) = {'0': 0.55, '1': 0.45}
P(X_2|X_0=0, X_1=0) = {'0': 0.27, '1': 0.73}
P(X_2|X_0=0, X_1=1) = {'0': 0.41, '1': 0.59}
P(X_2|X_0=1, X_1=0) = {'0': 0.27, '1': 0.73}
P(X_2|X_0=1, X_1=1) = {'0': 0.57, '1': 0.43}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.37, 1: 0.63} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 126,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.353822946548462,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.08, 0.92 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.61, 0.39;\n ( 1 ) 0.66, 0.34;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.76, 0.24;\n ( 0, 1 ) 0.72, 0.28;\n ( 1, 0 ) 0.15, 0.85;\n ( 1, 1 ) 0.84, 0.16;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_0=1))\nSurgery: P(X_0)= Point Mass at X_0=1.\nElim order: ['X_0']\nSum out X_0 -> P(X_1 | do(X_0=1)) = {0: 0.66, 1: 0.34}\nResult: P(X_1 | do(X_0=1)) = {0: 0.66, 1: 0.34}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.08, '1': 0.92}
P(X_1|X_0=0) = {'0': 0.61, '1': 0.39}
P(X_1|X_0=1) = {'0': 0.66, '1': 0.34}
P(X_2|X_0=0, X_1=0) = {'0': 0.76, '1': 0.24}
P(X_2|X_0=0, X_1=1) = {'0': 0.72, '1': 0.28}
P(X_2|X_0=1, X_1=0) = {'0': 0.15, '1': 0.85}
P(X_2|X_0=1, X_1=1) = {'0': 0.84, '1': 0.16}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.66, 1: 0.34} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 87,
"_level": 0,
"_prompt_tokens": 308,
"_task": "bayesian_association",
"_time": 1.3416125774383545,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.6, 0.4 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.81, 0.19;\n ( 1 ) 0.38, 0.62;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.28, 0.72;\n ( 0, 1 ) 0.82, 0.18;\n ( 1, 0 ) 0.58, 0.42;\n ( 1, 1 ) 0.34, 0.66;\n\n}\n",
"cot": "Result: P(X_2 | X_0=0, X_1=1) = {0: 0.82, 1: 0.18}\nResult: P(X_2 | X_0=0, X_1=1) = {0: 0.82, 1: 0.18}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=0) = {'0': 0.81, '1': 0.19}
P(X_1|X_0=1) = {'0': 0.38, '1': 0.62}
P(X_2|X_0=0, X_1=0) = {'0': 0.28, '1': 0.72}
P(X_2|X_0=0, X_1=1) = {'0': 0.82, '1': 0.18}
P(X_2|X_0=1, X_1=0) = {'0': 0.58, '1': 0.42}
P(X_2|X_0=1, X_1=1) = {'0': 0.34, '1': 0.66}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.82, 1: 0.18} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 132,
"_level": 0,
"_prompt_tokens": 195,
"_task": "bayesian_intervention",
"_time": 1.3097269535064697,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.89, 0.11 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.8, 0.2;\n ( 1 ) 0.94, 0.06;\n\n}\nprobability ( X_2 ) {\n table 0.63, 0.37 ;\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_0=1), X_2=1)\nSurgery: P(X_0)= Point Mass at X_0=1.\nElim order: ['X_0']\nSum out X_0 -> P(X_1 | do(X_0=1)) = {0: 0.94, 1: 0.06}\nResult: P(X_1 | do(X_0=1)) = {0: 0.94, 1: 0.06}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 1. Observing/Knowing that the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.89, '1': 0.11}
P(X_1|X_0=0) = {'0': 0.8, '1': 0.2}
P(X_1|X_0=1) = {'0': 0.94, '1': 0.06}
P(X_2) = {'0': 0.63, '1': 0.37}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 1. Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.94, 1: 0.06} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 75,
"_level": 0,
"_prompt_tokens": 191,
"_task": "bayesian_association",
"_time": 1.3236851692199707,
"bif_description": "// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.57, 0.43 ;\n}\nprobability ( X_1 ) {\n table 0.68, 0.32 ;\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.25, 0.75;\n ( 1 ) 0.51, 0.49;\n\n}\n",
"cot": "Result: P(X_2 | X_1=1) = {0: 0.51, 1: 0.49}\nResult: P(X_2 | X_1=1) = {0: 0.51, 1: 0.49}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_1",
"X_2",
"X_0"
]
} | System:
P(X_1) = {'0': 0.68, '1': 0.32}
P(X_2|X_1=0) = {'0': 0.25, '1': 0.75}
P(X_2|X_1=1) = {'0': 0.51, '1': 0.49}
P(X_0) = {'0': 0.57, '1': 0.43}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.51, 1: 0.49} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 139,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.281278371810913,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.45, 0.55 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.57, 0.43;\n ( 1 ) 0.71, 0.29;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.24, 0.76;\n ( 0, 1 ) 0.62, 0.38;\n ( 1, 0 ) 0.5, 0.5;\n ( 1, 1 ) 0.14, 0.86;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=1))\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=1.\nElim order: ['X_0']\nSum out X_0 -> P(X_1) = {0: 0.65, 1: 0.35}\nResult: P(X_1) = {0: 0.65, 1: 0.35}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.45, '1': 0.55}
P(X_1|X_0=0) = {'0': 0.57, '1': 0.43}
P(X_1|X_0=1) = {'0': 0.71, '1': 0.29}
P(X_2|X_0=0, X_1=0) = {'0': 0.24, '1': 0.76}
P(X_2|X_0=0, X_1=1) = {'0': 0.62, '1': 0.38}
P(X_2|X_0=1, X_1=0) = {'0': 0.5, '1': 0.5}
P(X_2|X_0=1, X_1=1) = {'0': 0.14, '1': 0.86}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.65, 1: 0.35} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 87,
"_level": 0,
"_prompt_tokens": 308,
"_task": "bayesian_association",
"_time": 1.3730511665344238,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.59, 0.41 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.12, 0.88;\n ( 1 ) 0.6, 0.4;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.76, 0.24;\n ( 0, 1 ) 0.85, 0.15;\n ( 1, 0 ) 0.39, 0.61;\n ( 1, 1 ) 0.4, 0.6;\n\n}\n",
"cot": "Result: P(X_2 | X_0=0, X_1=1) = {0: 0.85, 1: 0.15}\nResult: P(X_2 | X_0=0, X_1=1) = {0: 0.85, 1: 0.15}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.59, '1': 0.41}
P(X_1|X_0=0) = {'0': 0.12, '1': 0.88}
P(X_1|X_0=1) = {'0': 0.6, '1': 0.4}
P(X_2|X_0=0, X_1=0) = {'0': 0.76, '1': 0.24}
P(X_2|X_0=0, X_1=1) = {'0': 0.85, '1': 0.15}
P(X_2|X_0=1, X_1=0) = {'0': 0.39, '1': 0.61}
P(X_2|X_0=1, X_1=1) = {'0': 0.4, '1': 0.6}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1, and the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.85, 1: 0.15} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 163,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.3359830379486084,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.47, 0.53 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.49, 0.51;\n ( 1 ) 0.18, 0.82;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.71, 0.29;\n ( 0, 1 ) 0.93, 0.07;\n ( 1, 0 ) 0.44, 0.56;\n ( 1, 1 ) 0.95, 0.05;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=1))\nSurgery: P(X_0)= Point Mass at X_0=1.\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | do(X_0=1)) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2 | do(X_0=1)) = {0: 0.86, 1: 0.14}\nResult: P(X_2 | do(X_0=1)) = {0: 0.86, 1: 0.14}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.47, '1': 0.53}
P(X_1|X_0=0) = {'0': 0.49, '1': 0.51}
P(X_1|X_0=1) = {'0': 0.18, '1': 0.82}
P(X_2|X_0=0, X_1=0) = {'0': 0.71, '1': 0.29}
P(X_2|X_0=0, X_1=1) = {'0': 0.93, '1': 0.07}
P(X_2|X_0=1, X_1=0) = {'0': 0.44, '1': 0.56}
P(X_2|X_0=1, X_1=1) = {'0': 0.95, '1': 0.05}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.86, 1: 0.14} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 175,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_association",
"_time": 1.3316311836242676,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.01, 0.99 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.6, 0.4;\n ( 1 ) 0.53, 0.47;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.64, 0.36;\n ( 1 ) 0.45, 0.55;\n\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_1=1, X_2) = {0: 0.21, 1: 0.26}\nNormalize (sum=0.47) -> P(X_2 | X_1=1) = {0: 0.45, 1: 0.55}\nElim order: ['X_0']\nSum out X_0 -> P(X_1=1, X_2) = {0: 0.21, 1: 0.26}\nNormalize (sum=0.47) -> P(X_2 | X_1=1) = {0: 0.45, 1: 0.55}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.01, '1': 0.99}
P(X_1|X_0=0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=1) = {'0': 0.53, '1': 0.47}
P(X_2|X_0=0) = {'0': 0.64, '1': 0.36}
P(X_2|X_0=1) = {'0': 0.45, '1': 0.55}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.45, 1: 0.55} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 189,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.353182315826416,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.53, 0.47 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.97, 0.03;\n ( 1 ) 0.29, 0.71;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.27, 0.73;\n ( 0, 1 ) 0.22, 0.78;\n ( 1, 0 ) 0.77, 0.23;\n ( 1, 1 ) 0.95, 0.05;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=0))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0, do(X_1=0)) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2 | do(X_1=0)) = {0: 0.5, 1: 0.5}\nResult: P(X_2 | do(X_1=0)) = {0: 0.5, 1: 0.5}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.53, '1': 0.47}
P(X_1|X_0=0) = {'0': 0.97, '1': 0.03}
P(X_1|X_0=1) = {'0': 0.29, '1': 0.71}
P(X_2|X_0=0, X_1=0) = {'0': 0.27, '1': 0.73}
P(X_2|X_0=0, X_1=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=1, X_1=0) = {'0': 0.77, '1': 0.23}
P(X_2|X_0=1, X_1=1) = {'0': 0.95, '1': 0.05}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.5, 1: 0.5} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 205,
"_level": 0,
"_prompt_tokens": 254,
"_task": "bayesian_association",
"_time": 1.3331048488616943,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.93, 0.07 ;\n}\nprobability ( X_1 ) {\n table 0.52, 0.48 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.33, 0.67;\n ( 0, 1 ) 0.21, 0.79;\n ( 1, 0 ) 0.24, 0.76;\n ( 1, 1 ) 0.59, 0.41;\n\n}\n",
"cot": "Elim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.28, 1: 0.72}\nResult: P(X_2) = {0: 0.28, 1: 0.72}\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.28, 1: 0.72}\nResult: P(X_2) = {0: 0.28, 1: 0.72}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.93, '1': 0.07}
P(X_2|X_0=0, X_1=0) = {'0': 0.33, '1': 0.67}
P(X_2|X_0=0, X_1=1) = {'0': 0.21, '1': 0.79}
P(X_2|X_0=1, X_1=0) = {'0': 0.24, '1': 0.76}
P(X_2|X_0=1, X_1=1) = {'0': 0.59, '1': 0.41}
P(X_1) = {'0': 0.52, '1': 0.48}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.28, 1: 0.72} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 126,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_intervention",
"_time": 1.3946819305419922,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.82, 0.18 ;\n}\nprobability ( X_1 ) {\n table 0.39, 0.61 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.11, 0.89;\n ( 1 ) 0.4, 0.6;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=0))\nSurgery: P(X_0)= Point Mass at X_0=0.\nElim order: ['X_0']\nSum out X_0 -> P(X_2 | do(X_0=0)) = {0: 0.11, 1: 0.89}\nResult: P(X_2 | do(X_0=0)) = {0: 0.11, 1: 0.89}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.82, '1': 0.18}
P(X_2|X_0=0) = {'0': 0.11, '1': 0.89}
P(X_2|X_0=1) = {'0': 0.4, '1': 0.6}
P(X_1) = {'0': 0.39, '1': 0.61}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.11, 1: 0.89} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 205,
"_level": 0,
"_prompt_tokens": 289,
"_task": "bayesian_association",
"_time": 1.2993595600128174,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.35, 0.65 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.6, 0.4;\n ( 1 ) 0.22, 0.78;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.48, 0.52;\n ( 0, 1 ) 0.25, 0.75;\n ( 1, 0 ) 0.87, 0.13;\n ( 1, 1 ) 0.73, 0.27;\n\n}\n",
"cot": "Elim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.63, 1: 0.37}\nResult: P(X_2) = {0: 0.63, 1: 0.37}\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2) = {0: 0.63, 1: 0.37}\nResult: P(X_2) = {0: 0.63, 1: 0.37}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.35, '1': 0.65}
P(X_1|X_0=0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=0, X_1=0) = {'0': 0.48, '1': 0.52}
P(X_2|X_0=0, X_1=1) = {'0': 0.25, '1': 0.75}
P(X_2|X_0=1, X_1=0) = {'0': 0.87, '1': 0.13}
P(X_2|X_0=1, X_1=1) = {'0': 0.73, '1': 0.27}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.63, 1: 0.37} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 151,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.310816764831543,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.49, 0.51 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.54, 0.46;\n ( 1 ) 0.14, 0.86;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.43, 0.57;\n ( 1 ) 0.31, 0.69;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=0), X_1=1)\nSurgery: P(X_0)= Point Mass at X_0=0.\nElim order: ['X_0']\nSum out X_0 -> P(X_1=1, X_2 | do(X_0=0)) = {0: 0.2, 1: 0.26}\nNormalize (sum=0.46) -> P(X_2 | X_1=1, do(X_0=0)) = {0: 0.43, 1: 0.57}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 0. Observing/Knowing that the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.49, '1': 0.51}
P(X_1|X_0=0) = {'0': 0.54, '1': 0.46}
P(X_1|X_0=1) = {'0': 0.14, '1': 0.86}
P(X_2|X_0=0) = {'0': 0.43, '1': 0.57}
P(X_2|X_0=1) = {'0': 0.31, '1': 0.69}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 0. Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.43, 1: 0.57} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 89,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_association",
"_time": 1.2945208549499512,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.6, 0.4 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.45, 0.55;\n ( 1 ) 0.22, 0.78;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.64, 0.36;\n ( 1 ) 0.49, 0.51;\n\n}\n",
"cot": "Normalize (sum=0.64) -> P(X_0 | X_1=1) = {0: 0.51, 1: 0.49}\nNormalize (sum=0.64) -> P(X_0 | X_1=1) = {0: 0.51, 1: 0.49}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=0) = {'0': 0.45, '1': 0.55}
P(X_1|X_0=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=0) = {'0': 0.64, '1': 0.36}
P(X_2|X_0=1) = {'0': 0.49, '1': 0.51}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.51, 1: 0.49} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.2959847450256348,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.46, 0.54 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.95, 0.05;\n ( 1 ) 0.71, 0.29;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.91, 0.09;\n ( 0, 1 ) 0.7, 0.3;\n ( 1, 0 ) 0.63, 0.37;\n ( 1, 1 ) 0.35, 0.65;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=1.\nResult: P(X_0) = {0: 0.46, 1: 0.54}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.46, '1': 0.54}
P(X_1|X_0=0) = {'0': 0.95, '1': 0.05}
P(X_1|X_0=1) = {'0': 0.71, '1': 0.29}
P(X_2|X_0=0, X_1=0) = {'0': 0.91, '1': 0.09}
P(X_2|X_0=0, X_1=1) = {'0': 0.7, '1': 0.3}
P(X_2|X_0=1, X_1=0) = {'0': 0.63, '1': 0.37}
P(X_2|X_0=1, X_1=1) = {'0': 0.35, '1': 0.65}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.46, 1: 0.54} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 175,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_association",
"_time": 1.372321605682373,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.54, 0.46 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.01, 0.99;\n ( 1 ) 0.4, 0.6;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.14, 0.86;\n ( 1 ) 0.47, 0.53;\n\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_1, X_2=0) = {0: 0.09, 1: 0.2}\nNormalize (sum=0.29) -> P(X_1 | X_2=0) = {0: 0.3, 1: 0.7}\nElim order: ['X_0']\nSum out X_0 -> P(X_1, X_2=0) = {0: 0.09, 1: 0.2}\nNormalize (sum=0.29) -> P(X_1 | X_2=0) = {0: 0.3, 1: 0.7}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 0",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.54, '1': 0.46}
P(X_1|X_0=0) = {'0': 0.01, '1': 0.99}
P(X_1|X_0=1) = {'0': 0.4, '1': 0.6}
P(X_2|X_0=0) = {'0': 0.14, '1': 0.86}
P(X_2|X_0=1) = {'0': 0.47, '1': 0.53}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 0
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.3, 1: 0.7} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 75,
"_level": 0,
"_prompt_tokens": 261,
"_task": "bayesian_intervention",
"_time": 1.272784948348999,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.12, 0.88 ;\n}\nprobability ( X_1 ) {\n table 0.55, 0.45 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.55, 0.45;\n ( 0, 1 ) 0.76, 0.24;\n ( 1, 0 ) 0.27, 0.73;\n ( 1, 1 ) 0.47, 0.53;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=0))\nSurgery: P(X_1)= Point Mass at X_1=0.\nResult: P(X_0) = {0: 0.12, 1: 0.88}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.12, '1': 0.88}
P(X_2|X_0=0, X_1=0) = {'0': 0.55, '1': 0.45}
P(X_2|X_0=0, X_1=1) = {'0': 0.76, '1': 0.24}
P(X_2|X_0=1, X_1=0) = {'0': 0.27, '1': 0.73}
P(X_2|X_0=1, X_1=1) = {'0': 0.47, '1': 0.53}
P(X_1) = {'0': 0.55, '1': 0.45}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.12, 1: 0.88} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 175,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_association",
"_time": 1.2807633876800537,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.14, 0.86 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.41, 0.59;\n ( 1 ) 0.39, 0.61;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.57, 0.43;\n ( 0, 1 ) 0.37, 0.63;\n ( 1, 0 ) 0.72, 0.28;\n ( 1, 1 ) 0.51, 0.49;\n\n}\n",
"cot": "Elim order: ['X_1']\nSum out X_1 -> P(X_2=1 | X_0) = {0: 0.55, 1: 0.41}\nNormalize (sum=0.43) -> P(X_0 | X_2=1) = {0: 0.18, 1: 0.82}\nElim order: ['X_1']\nSum out X_1 -> P(X_2=1 | X_0) = {0: 0.55, 1: 0.41}\nNormalize (sum=0.43) -> P(X_0 | X_2=1) = {0: 0.18, 1: 0.82}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.14, '1': 0.86}
P(X_1|X_0=0) = {'0': 0.41, '1': 0.59}
P(X_1|X_0=1) = {'0': 0.39, '1': 0.61}
P(X_2|X_0=0, X_1=0) = {'0': 0.57, '1': 0.43}
P(X_2|X_0=0, X_1=1) = {'0': 0.37, '1': 0.63}
P(X_2|X_0=1, X_1=0) = {'0': 0.72, '1': 0.28}
P(X_2|X_0=1, X_1=1) = {'0': 0.51, '1': 0.49}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.18, 1: 0.82} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 87,
"_level": 0,
"_prompt_tokens": 195,
"_task": "bayesian_intervention",
"_time": 1.2470557689666748,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.57, 0.43 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.77, 0.23;\n ( 1 ) 0.86, 0.14;\n\n}\nprobability ( X_2 ) {\n table 0.4, 0.6 ;\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=1), X_0=0)\nSurgery: P(X_2)= Point Mass at X_2=1.\nResult: P(X_1 | X_0=0) = {0: 0.77, 1: 0.23}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1. Observing/Knowing that the state X_0 is equal to 0",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.57, '1': 0.43}
P(X_1|X_0=0) = {'0': 0.77, '1': 0.23}
P(X_1|X_0=1) = {'0': 0.86, '1': 0.14}
P(X_2) = {'0': 0.4, '1': 0.6}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1. Observing/Knowing that the state X_0 is equal to 0
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.77, 1: 0.23} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 175,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_association",
"_time": 1.2654917240142822,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.62, 0.38 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.56, 0.44;\n ( 1 ) 0.04, 0.96;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.04, 0.96;\n ( 0, 1 ) 0.82, 0.18;\n ( 1, 0 ) 0.42, 0.58;\n ( 1, 1 ) 0.71, 0.29;\n\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_1, X_2=1) = {0: 0.34, 1: 0.15}\nNormalize (sum=0.5) -> P(X_1 | X_2=1) = {0: 0.69, 1: 0.31}\nElim order: ['X_0']\nSum out X_0 -> P(X_1, X_2=1) = {0: 0.34, 1: 0.15}\nNormalize (sum=0.5) -> P(X_1 | X_2=1) = {0: 0.69, 1: 0.31}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.62, '1': 0.38}
P(X_1|X_0=0) = {'0': 0.56, '1': 0.44}
P(X_1|X_0=1) = {'0': 0.04, '1': 0.96}
P(X_2|X_0=0, X_1=0) = {'0': 0.04, '1': 0.96}
P(X_2|X_0=0, X_1=1) = {'0': 0.82, '1': 0.18}
P(X_2|X_0=1, X_1=0) = {'0': 0.42, '1': 0.58}
P(X_2|X_0=1, X_1=1) = {'0': 0.71, '1': 0.29}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.69, 1: 0.31} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_intervention",
"_time": 1.353398323059082,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.09, 0.91 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.19, 0.81;\n ( 1 ) 0.58, 0.42;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.72, 0.28;\n ( 1 ) 0.83, 0.17;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=1))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=1.\nResult: P(X_0) = {0: 0.09, 1: 0.91}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.09, '1': 0.91}
P(X_1|X_0=0) = {'0': 0.19, '1': 0.81}
P(X_1|X_0=1) = {'0': 0.58, '1': 0.42}
P(X_2|X_1=0) = {'0': 0.72, '1': 0.28}
P(X_2|X_1=1) = {'0': 0.83, '1': 0.17}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.09, 1: 0.91} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 254,
"_task": "bayesian_association",
"_time": 1.2412662506103516,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.53, 0.47 ;\n}\nprobability ( X_1 ) {\n table 0.55, 0.45 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.63, 0.37;\n ( 0, 1 ) 0.5, 0.5;\n ( 1, 0 ) 0.05, 0.95;\n ( 1, 1 ) 0.21, 0.79;\n\n}\n",
"cot": "Result: P(X_1) = {0: 0.55, 1: 0.45}\nResult: P(X_1) = {0: 0.55, 1: 0.45}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.53, '1': 0.47}
P(X_2|X_0=0, X_1=0) = {'0': 0.63, '1': 0.37}
P(X_2|X_0=0, X_1=1) = {'0': 0.5, '1': 0.5}
P(X_2|X_0=1, X_1=0) = {'0': 0.05, '1': 0.95}
P(X_2|X_0=1, X_1=1) = {'0': 0.21, '1': 0.79}
P(X_1) = {'0': 0.55, '1': 0.45}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.55, 1: 0.45} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 109,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.2989048957824707,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.69, 0.31 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.48, 0.52;\n ( 1 ) 0.33, 0.67;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.41, 0.59;\n ( 1 ) 0.23, 0.77;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=1), X_0=1)\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=1.\nResult: P(X_2 | X_0=1) = {0: 0.23, 1: 0.77}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.69, '1': 0.31}
P(X_1|X_0=0) = {'0': 0.48, '1': 0.52}
P(X_1|X_0=1) = {'0': 0.33, '1': 0.67}
P(X_2|X_0=0) = {'0': 0.41, '1': 0.59}
P(X_2|X_0=1) = {'0': 0.23, '1': 0.77}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1. Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.23, 1: 0.77} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 289,
"_task": "bayesian_association",
"_time": 1.2666051387786865,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.67, 0.33 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.53, 0.47;\n ( 1 ) 0.54, 0.46;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 1.0, 0.0;\n ( 0, 1 ) 0.65, 0.35;\n ( 1, 0 ) 0.9, 0.1;\n ( 1, 1 ) 0.26, 0.74;\n\n}\n",
"cot": "Result: P(X_0) = {0: 0.67, 1: 0.33}\nResult: P(X_0) = {0: 0.67, 1: 0.33}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.67, '1': 0.33}
P(X_1|X_0=0) = {'0': 0.53, '1': 0.47}
P(X_1|X_0=1) = {'0': 0.54, '1': 0.46}
P(X_2|X_0=0, X_1=0) = {'0': 1.0, '1': 0.0}
P(X_2|X_0=0, X_1=1) = {'0': 0.65, '1': 0.35}
P(X_2|X_0=1, X_1=0) = {'0': 0.9, '1': 0.1}
P(X_2|X_0=1, X_1=1) = {'0': 0.26, '1': 0.74}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.67, 1: 0.33} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 108,
"_level": 0,
"_prompt_tokens": 277,
"_task": "bayesian_intervention",
"_time": 1.3498456478118896,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.65, 0.35 ;\n}\nprobability ( X_1 ) {\n table 0.02, 0.98 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.88, 0.12;\n ( 0, 1 ) 0.13, 0.87;\n ( 1, 0 ) 0.39, 0.61;\n ( 1, 1 ) 0.82, 0.18;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=0), X_0=1)\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=0.\nResult: P(X_1) = {0: 0.02, 1: 0.98}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.65, '1': 0.35}
P(X_2|X_0=0, X_1=0) = {'0': 0.88, '1': 0.12}
P(X_2|X_0=0, X_1=1) = {'0': 0.13, '1': 0.87}
P(X_2|X_0=1, X_1=0) = {'0': 0.39, '1': 0.61}
P(X_2|X_0=1, X_1=1) = {'0': 0.82, '1': 0.18}
P(X_1) = {'0': 0.02, '1': 0.98}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.02, 1: 0.98} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 137,
"_level": 0,
"_prompt_tokens": 179,
"_task": "bayesian_association",
"_time": 1.2593872547149658,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.22, 0.78 ;\n}\nprobability ( X_1 ) {\n table 0.15, 0.85 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.95, 0.05;\n ( 1 ) 0.54, 0.46;\n\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_2) = {0: 0.63, 1: 0.37}\nResult: P(X_2) = {0: 0.63, 1: 0.37}\nElim order: ['X_0']\nSum out X_0 -> P(X_2) = {0: 0.63, 1: 0.37}\nResult: P(X_2) = {0: 0.63, 1: 0.37}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=0) = {'0': 0.95, '1': 0.05}
P(X_2|X_0=1) = {'0': 0.54, '1': 0.46}
P(X_1) = {'0': 0.15, '1': 0.85}
Observed conditions:
Observing/Knowing that the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.63, 1: 0.37} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 166,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_intervention",
"_time": 1.2456748485565186,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.88, 0.12 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.5, 0.5;\n ( 1 ) 0.17, 0.83;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.55, 0.45;\n ( 1 ) 0.33, 0.67;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=0))\nSurgery: P(X_0)= Point Mass at X_0=0.\nElim order: ['X_0', 'X_1']\nSum out X_0 -> P(X_1 | do(X_0=0)) = {0: 0.5, 1: 0.5}\nSum out X_1 -> P(X_2 | do(X_0=0)) = {0: 0.44, 1: 0.56}\nResult: P(X_2 | do(X_0=0)) = {0: 0.44, 1: 0.56}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.88, '1': 0.12}
P(X_1|X_0=0) = {'0': 0.5, '1': 0.5}
P(X_1|X_0=1) = {'0': 0.17, '1': 0.83}
P(X_2|X_1=0) = {'0': 0.55, '1': 0.45}
P(X_2|X_1=1) = {'0': 0.33, '1': 0.67}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.44, 1: 0.56} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 289,
"_task": "bayesian_association",
"_time": 1.3564162254333496,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.8, 0.2 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.85, 0.15;\n ( 1 ) 0.99, 0.01;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.9, 0.1;\n ( 0, 1 ) 0.16, 0.84;\n ( 1, 0 ) 0.26, 0.74;\n ( 1, 1 ) 0.51, 0.49;\n\n}\n",
"cot": "Result: P(X_0) = {0: 0.8, 1: 0.2}\nResult: P(X_0) = {0: 0.8, 1: 0.2}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.8, '1': 0.2}
P(X_1|X_0=0) = {'0': 0.85, '1': 0.15}
P(X_1|X_0=1) = {'0': 0.99, '1': 0.01}
P(X_2|X_0=0, X_1=0) = {'0': 0.9, '1': 0.1}
P(X_2|X_0=0, X_1=1) = {'0': 0.16, '1': 0.84}
P(X_2|X_0=1, X_1=0) = {'0': 0.26, '1': 0.74}
P(X_2|X_0=1, X_1=1) = {'0': 0.51, '1': 0.49}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.8, 1: 0.2} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 163,
"_level": 0,
"_prompt_tokens": 261,
"_task": "bayesian_intervention",
"_time": 1.2847497463226318,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.52, 0.48 ;\n}\nprobability ( X_1 ) {\n table 0.41, 0.59 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.22, 0.78;\n ( 0, 1 ) 0.22, 0.78;\n ( 1, 0 ) 0.22, 0.78;\n ( 1, 1 ) 0.51, 0.49;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_0=1))\nSurgery: P(X_0)= Point Mass at X_0=1.\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | do(X_0=1)) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2 | do(X_0=1)) = {0: 0.39, 1: 0.61}\nResult: P(X_2 | do(X_0=1)) = {0: 0.39, 1: 0.61}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_0 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.52, '1': 0.48}
P(X_2|X_0=0, X_1=0) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=0, X_1=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=1, X_1=0) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=1, X_1=1) = {'0': 0.51, '1': 0.49}
P(X_1) = {'0': 0.41, '1': 0.59}
Observed conditions:
Doing/Imposing that the state X_0 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.39, 1: 0.61} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 254,
"_task": "bayesian_association",
"_time": 1.3583250045776367,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.33, 0.67 ;\n}\nprobability ( X_1 ) {\n table 0.92, 0.08 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.45, 0.55;\n ( 0, 1 ) 0.11, 0.89;\n ( 1, 0 ) 0.55, 0.45;\n ( 1, 1 ) 0.77, 0.23;\n\n}\n",
"cot": "Result: P(X_0) = {0: 0.33, 1: 0.67}\nResult: P(X_0) = {0: 0.33, 1: 0.67}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.33, '1': 0.67}
P(X_2|X_0=0, X_1=0) = {'0': 0.45, '1': 0.55}
P(X_2|X_0=0, X_1=1) = {'0': 0.11, '1': 0.89}
P(X_2|X_0=1, X_1=0) = {'0': 0.55, '1': 0.45}
P(X_2|X_0=1, X_1=1) = {'0': 0.77, '1': 0.23}
P(X_1) = {'0': 0.92, '1': 0.08}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.33, 1: 0.67} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 189,
"_level": 0,
"_prompt_tokens": 296,
"_task": "bayesian_intervention",
"_time": 1.2416698932647705,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.12, 0.88 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.68, 0.32;\n ( 1 ) 0.28, 0.72;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.33, 0.67;\n ( 0, 1 ) 0.44, 0.56;\n ( 1, 0 ) 0.48, 0.52;\n ( 1, 1 ) 0.68, 0.32;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=1))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=1.\nElim order: ['X_1', 'X_0']\nSum out X_1 -> P(X_2 | X_0, do(X_1=1)) = [Distribution over ['X_2', 'X_0']]\nSum out X_0 -> P(X_2 | do(X_1=1)) = {0: 0.65, 1: 0.35}\nResult: P(X_2 | do(X_1=1)) = {0: 0.65, 1: 0.35}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.12, '1': 0.88}
P(X_1|X_0=0) = {'0': 0.68, '1': 0.32}
P(X_1|X_0=1) = {'0': 0.28, '1': 0.72}
P(X_2|X_0=0, X_1=0) = {'0': 0.33, '1': 0.67}
P(X_2|X_0=0, X_1=1) = {'0': 0.44, '1': 0.56}
P(X_2|X_0=1, X_1=0) = {'0': 0.48, '1': 0.52}
P(X_2|X_0=1, X_1=1) = {'0': 0.68, '1': 0.32}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.65, 1: 0.35} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 87,
"_level": 0,
"_prompt_tokens": 273,
"_task": "bayesian_association",
"_time": 1.2760357856750488,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.16, 0.84 ;\n}\nprobability ( X_1 ) {\n table 0.53, 0.47 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.53, 0.47;\n ( 0, 1 ) 0.27, 0.73;\n ( 1, 0 ) 0.75, 0.25;\n ( 1, 1 ) 0.45, 0.55;\n\n}\n",
"cot": "Result: P(X_2 | X_0=1, X_1=1) = {0: 0.45, 1: 0.55}\nResult: P(X_2 | X_0=1, X_1=1) = {0: 0.45, 1: 0.55}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 1, and the state X_1 is equal to 1",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.16, '1': 0.84}
P(X_2|X_0=0, X_1=0) = {'0': 0.53, '1': 0.47}
P(X_2|X_0=0, X_1=1) = {'0': 0.27, '1': 0.73}
P(X_2|X_0=1, X_1=0) = {'0': 0.75, '1': 0.25}
P(X_2|X_0=1, X_1=1) = {'0': 0.45, '1': 0.55}
P(X_1) = {'0': 0.53, '1': 0.47}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 1, and the state X_1 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.45, 1: 0.55} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 121,
"_level": 0,
"_prompt_tokens": 312,
"_task": "bayesian_intervention",
"_time": 1.307042121887207,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.22, 0.78 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.5, 0.5;\n ( 1 ) 0.13, 0.87;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.35, 0.65;\n ( 0, 1 ) 0.38, 0.62;\n ( 1, 0 ) 0.53, 0.47;\n ( 1, 1 ) 0.14, 0.86;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_2=0), X_1=0)\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=0.\nNormalize (sum=0.21) -> P(X_0 | X_1=0) = {0: 0.52, 1: 0.48}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.22, '1': 0.78}
P(X_1|X_0=0) = {'0': 0.5, '1': 0.5}
P(X_1|X_0=1) = {'0': 0.13, '1': 0.87}
P(X_2|X_0=0, X_1=0) = {'0': 0.35, '1': 0.65}
P(X_2|X_0=0, X_1=1) = {'0': 0.38, '1': 0.62}
P(X_2|X_0=1, X_1=0) = {'0': 0.53, '1': 0.47}
P(X_2|X_0=1, X_1=1) = {'0': 0.14, '1': 0.86}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0. Observing/Knowing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.52, 1: 0.48} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 75,
"_level": 0,
"_prompt_tokens": 226,
"_task": "bayesian_association",
"_time": 1.2385146617889404,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.88, 0.12 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.09, 0.91;\n ( 1 ) 0.75, 0.25;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.26, 0.74;\n ( 1 ) 0.33, 0.67;\n\n}\n",
"cot": "Result: P(X_1 | X_0=1) = {0: 0.75, 1: 0.25}\nResult: P(X_1 | X_0=1) = {0: 0.75, 1: 0.25}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_2 is equal to 1, and the state X_0 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.88, '1': 0.12}
P(X_1|X_0=0) = {'0': 0.09, '1': 0.91}
P(X_1|X_0=1) = {'0': 0.75, '1': 0.25}
P(X_2|X_0=0) = {'0': 0.26, '1': 0.74}
P(X_2|X_0=1) = {'0': 0.33, '1': 0.67}
Observed conditions:
Observing/Knowing that the state X_2 is equal to 1, and the state X_0 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.75, 1: 0.25} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 134,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_intervention",
"_time": 1.3034136295318604,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.73, 0.27 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.79, 0.21;\n ( 1 ) 0.29, 0.71;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.67, 0.33;\n ( 1 ) 0.4, 0.6;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_1 | do(X_2=1))\nSurgery: Cut incoming edges to intervened node 'X_2': ['X_1'] -> X_2; P(X_2)= Point Mass at X_2=1.\nElim order: ['X_0']\nSum out X_0 -> P(X_1) = {0: 0.66, 1: 0.34}\nResult: P(X_1) = {0: 0.66, 1: 0.34}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.73, '1': 0.27}
P(X_1|X_0=0) = {'0': 0.79, '1': 0.21}
P(X_1|X_0=1) = {'0': 0.29, '1': 0.71}
P(X_2|X_1=0) = {'0': 0.67, '1': 0.33}
P(X_2|X_1=1) = {'0': 0.4, '1': 0.6}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.66, 1: 0.34} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 101,
"_level": 0,
"_prompt_tokens": 273,
"_task": "bayesian_association",
"_time": 1.2705867290496826,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.79, 0.21 ;\n}\nprobability ( X_1 ) {\n table 0.02, 0.98 ;\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.6, 0.4;\n ( 0, 1 ) 0.67, 0.33;\n ( 1, 0 ) 0.59, 0.41;\n ( 1, 1 ) 0.23, 0.77;\n\n}\n",
"cot": "Normalize (sum=0.76) -> P(X_1 | X_0=1, X_2=1) = {0: 0.01, 1: 0.99}\nNormalize (sum=0.76) -> P(X_1 | X_0=1, X_2=1) = {0: 0.01, 1: 0.99}",
"n_round": 2,
"scenario": "Observing/Knowing that the state X_0 is equal to 1, and the state X_2 is equal to 1",
"target": "X_1",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.79, '1': 0.21}
P(X_2|X_0=0, X_1=0) = {'0': 0.6, '1': 0.4}
P(X_2|X_0=0, X_1=1) = {'0': 0.67, '1': 0.33}
P(X_2|X_0=1, X_1=0) = {'0': 0.59, '1': 0.41}
P(X_2|X_0=1, X_1=1) = {'0': 0.23, '1': 0.77}
P(X_1) = {'0': 0.02, '1': 0.98}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 1, and the state X_2 is equal to 1
Task: Compute probability distribution for X_1 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.01, 1: 0.99} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 109,
"_level": 0,
"_prompt_tokens": 230,
"_task": "bayesian_intervention",
"_time": 1.2429628372192383,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.81, 0.19 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.07, 0.93;\n ( 1 ) 0.37, 0.63;\n\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.39, 0.61;\n ( 1 ) 0.56, 0.44;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_2 | do(X_1=0), X_0=0)\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nResult: P(X_2 | X_0=0) = {0: 0.39, 1: 0.61}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_0 is equal to 0",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.81, '1': 0.19}
P(X_1|X_0=0) = {'0': 0.07, '1': 0.93}
P(X_1|X_0=1) = {'0': 0.37, '1': 0.63}
P(X_2|X_0=0) = {'0': 0.39, '1': 0.61}
P(X_2|X_0=1) = {'0': 0.56, '1': 0.44}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0. Observing/Knowing that the state X_0 is equal to 0
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.39, 1: 0.61} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 137,
"_level": 0,
"_prompt_tokens": 172,
"_task": "bayesian_association",
"_time": 1.3093230724334717,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.2, 0.8 ;\n}\nprobability ( X_1 ) {\n table 0.19, 0.81 ;\n}\nprobability ( X_2 | X_0 ) {\n ( 0 ) 0.39, 0.61;\n ( 1 ) 0.95, 0.05;\n\n}\n",
"cot": "Elim order: ['X_0']\nSum out X_0 -> P(X_2) = {0: 0.84, 1: 0.16}\nResult: P(X_2) = {0: 0.84, 1: 0.16}\nElim order: ['X_0']\nSum out X_0 -> P(X_2) = {0: 0.84, 1: 0.16}\nResult: P(X_2) = {0: 0.84, 1: 0.16}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_2",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_2",
"X_1"
]
} | System:
P(X_0) = {'0': 0.2, '1': 0.8}
P(X_2|X_0=0) = {'0': 0.39, '1': 0.61}
P(X_2|X_0=1) = {'0': 0.95, '1': 0.05}
P(X_1) = {'0': 0.19, '1': 0.81}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.84, 1: 0.16} |
bayesian_intervention | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 97,
"_level": 0,
"_prompt_tokens": 214,
"_task": "bayesian_intervention",
"_time": 1.268449068069458,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.07, 0.93 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.56, 0.44;\n ( 1 ) 0.32, 0.68;\n\n}\nprobability ( X_2 | X_1 ) {\n ( 0 ) 0.51, 0.49;\n ( 1 ) 0.45, 0.55;\n\n}\n",
"cot": "Goal: Compute Causal Effect: P(X_0 | do(X_1=0))\nSurgery: Cut incoming edges to intervened node 'X_1': ['X_0'] -> X_1; P(X_1)= Point Mass at X_1=0.\nResult: P(X_0) = {0: 0.07, 1: 0.93}",
"n_round": 2,
"scenario": "Doing/Imposing that the state X_1 is equal to 0",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.07, '1': 0.93}
P(X_1|X_0=0) = {'0': 0.56, '1': 0.44}
P(X_1|X_0=1) = {'0': 0.32, '1': 0.68}
P(X_2|X_1=0) = {'0': 0.51, '1': 0.49}
P(X_2|X_1=1) = {'0': 0.45, '1': 0.55}
Observed conditions:
Doing/Imposing that the state X_1 is equal to 0
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.07, 1: 0.93} |
bayesian_association | {
"_config": {
"c": 1,
"concise_cot": true,
"cot_scientific_notation": false,
"cpt_relative_threshold": 0,
"edge_prob": 0.7,
"graph_generation_mode": "erdos",
"is_verbose": false,
"level": 0,
"max_domain_size": 2,
"n_nodes": 3,
"n_round": 2,
"seed": null,
"size": null
},
"_cot_tokens": 63,
"_level": 0,
"_prompt_tokens": 289,
"_task": "bayesian_association",
"_time": 1.338697910308838,
"bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: TabularCPD\n\nnetwork unknown {\n}\nvariable X_0 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_1 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nvariable X_2 {\n type discrete [ 2 ] { 0, 1 };\n property weight = None ;\n}\nprobability ( X_0 ) {\n table 0.36, 0.64 ;\n}\nprobability ( X_1 | X_0 ) {\n ( 0 ) 0.73, 0.27;\n ( 1 ) 0.24, 0.76;\n\n}\nprobability ( X_2 | X_0, X_1 ) {\n ( 0, 0 ) 0.78, 0.22;\n ( 0, 1 ) 0.22, 0.78;\n ( 1, 0 ) 0.51, 0.49;\n ( 1, 1 ) 0.94, 0.06;\n\n}\n",
"cot": "Result: P(X_0) = {0: 0.36, 1: 0.64}\nResult: P(X_0) = {0: 0.36, 1: 0.64}",
"n_round": 2,
"scenario": "Without further Observation/Knowledge of other variable.",
"target": "X_0",
"target_var_values": [
0,
1
],
"variables": [
"X_0",
"X_1",
"X_2"
]
} | System:
P(X_0) = {'0': 0.36, '1': 0.64}
P(X_1|X_0=0) = {'0': 0.73, '1': 0.27}
P(X_1|X_0=1) = {'0': 0.24, '1': 0.76}
P(X_2|X_0=0, X_1=0) = {'0': 0.78, '1': 0.22}
P(X_2|X_0=0, X_1=1) = {'0': 0.22, '1': 0.78}
P(X_2|X_0=1, X_1=0) = {'0': 0.51, '1': 0.49}
P(X_2|X_0=1, X_1=1) = {'0': 0.94, '1': 0.06}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability distribution for X_0 (possible values: [0, 1]).
Output: Python dict mapping each value to its probability, rounded to 2 decimals.
Example: {0: 0.12, 1: 0.88} | {0: 0.36, 1: 0.64} |
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