Identification of Conditional Causal Effects under Markov - PowerPoint PPT Presentation

Identification of Conditional Causal Effects under Markov Equivalence Amin Jaber, Jiji Zhang, Elias Bareinboim jaber0@purdue.edu , jijizhang@ln.edu.hk , eb@cs.columbia.edu 33rd Conference on Neural Information Processing Systems (NeurIPS) 
 1 Vancouver, Canada — December, 2019

Motivating Example - What’s the e ff ect of exercise on cholesterol? 1 2 2

Solution: Causal Diagram Motivating Example Age - What’s the e ff ect of exercise on cholesterol? 1 2 Exercise Cholesterol 2

Solution: Causal Diagram Motivating Example Age - What’s the e ff ect of exercise on cholesterol? 1 2 Exercise Cholesterol Correlation ✕ More exercise → Higher cholesterol 2

Solution: Causal Diagram Motivating Example Age - What’s the e ff ect of exercise on cholesterol? 1 2 Exercise Cholesterol ✓ Correlation ✕ Causation More exercise → Higher cholesterol More exercise → Lower cholesterol 2 (for each age group)

What is Causal Identification? 3

What is Causal Identification? Query 1 Q= P x ( y | z ) 3

What is Causal Identification? Query 1 Q= P x ( y | z ) Diagram 2 X Z Y 3

What is Causal Identification? Query 1 Q= P x ( y | z ) Diagram 2 X Z Y Data 3 P ( x , z , y ) 3

What is Causal Identification? Based on the current knowledge about the problem (2) and the available data (3), is the research question (1) identifiable? Query 1 Q= P x ( y | z ) Diagram 2 X Z Y Data 3 P ( x , z , y ) 3

What is Causal Identification? Based on the current knowledge about the problem (2) and the available data (3), is the research question (1) identifiable? Query 1 computable Q= P x ( y | z ) Diagram 2 X Z Y Data 3 P ( x , z , y ) 3

What is Causal Identification? Based on the current knowledge about the problem (2) and the available data (3), is the research question (1) identifiable? Query 1 Q= P x ( y | z ) Causal Solution Diagram Inference 2 yes / no? Engine X Z Y Data 3 P ( x , z , y ) 3

What is Causal Identification? Based on the current knowledge about the problem (2) and the available data (3), is the research question (1) identifiable? Query 1 Q= P x ( y | z ) Causal Solution Diagram Inference 2 yes / no? Engine X Z Y P x ( y | z ) = P ( y | z , x ) Data 3 P ( x , z , y ) 3

What is Causal Identification? Based on the current knowledge about the problem (2) and the available data (3), is the research question (1) identifiable? Query 1 Q= P x ( y | z ) Causal Solution Diagram Inference 2 yes / no? Engine X Z Y P x ( y | z ) = P ( y | z , x ) Causation Association Data 3 (Query) (Data) P ( x , z , y ) 👎 3

What is Causal Identification? Based on the current knowledge about the problem (2) and the available data (3), is the research question (1) identifiable? Query 1 Q= P x ( y | z ) Causal Solution Diagram Inference 2 yes / no? Engine X Z Y P x ( y | z ) = P ( y | z , x ) Causation Association Data 3 (Query) (Data) P ( x , z , y ) 👎 Great, but… 3

Can a causal diagram be learned from data? 4

Can a causal diagram be learned from data? Answer: In general, no! 4

Can a causal diagram be learned from data? 1 X Z Y 2 X Z Y 3 X Z Y 4

Can a causal diagram be learned from data? 1 X Z Y P ( x , z , y ) Non-causal 2 X Z Y Probability Distribution 3 X Z Y 4

Can a causal diagram be learned from data? 1 X Z Y P ( x , z , y ) Non-causal 2 X Z Y Probability Distribution 3 X Z Y Diagrams impose the same constraints over the observational distribution . 4

Can a causal diagram be learned from data? 1 X Z Y P ( x , z , y ) Non-causal 2 X Z Y Probability Distribution 3 X Z Y Diagrams impose the same constraints over the observational distribution . 4 Markov Equivalence Class

Can a causal diagram be learned from data? 1 X Z Y Summary Graph Partial Ancestral P ( x , z , y ) Graph (PAG) Non-causal 2 X Z X Z Y Y Probability Distribution 3 X Z Y Diagrams impose the same constraints over the observational distribution . 4 Markov Equivalence Class

Data-Driven Causal Identification Query 1 Q= P x ( y | z ) Relaxed 3 Diagram CI Engine X Z Y ? Causal Learning Data 2 P ( x , z , y ) 5

Data-Driven Causal Identification Query 1 Q= P x ( y | z ) Relaxed 3 Diagram CI Engine X Z Y Causal Learning Data 2 P ( x , z , y ) 5

Data-Driven Causal Identification • Research question: Based on the qualitative causal diagram (3) learned from data (2), is the causal effect (1) computable? Query 1 Q= P x ( y | z ) Relaxed 3 Diagram Solution CI Engine yes / no? X Z Y Causal Learning Data 2 P ( x , z , y ) 5

Data-Driven Causal Identification • Research question: Based on the qualitative causal diagram (3) learned from data (2), is the causal effect (1) computable? Query 1 Q= P x ( y | z ) Relaxed 3 Diagram Solution CI Engine yes / no? X Z Y Causal Learning Data 2 P ( x , z , y ) 5

Data-Driven Causal Identification • Research question: Based on the qualitative causal diagram (3) learned from data (2), is the causal effect (1) computable? Query 1 Q= P x ( y | z ) Relaxed 3 Diagram Solution CI Engine yes / no? P x ( y | z ) = P ( y | z , x ) 👎 X Z Y Causal Learning E ff ect is identifiable in every 
 diagram in the equivalence class, 
 Data 2 and with same expression! P ( x , z , y ) 5

Conclusions 6

Conclusions • We develop an algorithm to identify conditional causal e ff ects from an equivalence class of causal diagrams. 6

Conclusions • We develop an algorithm to identify conditional causal e ff ects from an equivalence class of causal diagrams. • This is the first general, entirely data-driven procedure for finding conditional causal e ff ects available in the literature. 6

Conclusions • We develop an algorithm to identify conditional causal e ff ects from an equivalence class of causal diagrams. • This is the first general, entirely data-driven procedure for finding conditional causal e ff ects available in the literature. • To know more about it -- stop by our poster #186. 6

Conclusions • We develop an algorithm to identify conditional causal e ff ects from an equivalence class of causal diagrams. • This is the first general, entirely data-driven procedure for finding conditional causal e ff ects available in the literature. • To know more about it -- stop by our poster #186. Thank you!  6