Using Markov Blankets for Causal Structure Learning

1. Using Markov Blankets for Causal Structure Learning Jean-Philippe Pellet Andre Ellisseeff Presented by Na Dai

2. Motivation • Why structure learning? • What are Markov blankets? • Relationship between feature selection and Markov blankets?

3. Previous work • Score-based approaches • Constraint-based approaches • Hybrid approaches

4. Central Ideas • Building up local structures from Markov blankets. • Generating global graph structure from local structure. • How to generate Markov blankets?

5. Background • Feature selection • Conditional independence • Strong relevance • Weak relevance • Irrelevance • Feature selection task

6. Background • Causal structure learning • Goal: learn the full structure of the network • D-separation: 1) A --> C --> B 2) A <-- C <-- B 3) A <-- C --> B 4) A --> C <-- B

7. Background • Perfect map • Causal Markov condition • Faithfulness condition

8. Background • Causal sufficiency assumption • V-structure

9. Causal Network Construction • Properties of Markov blankets

10. Recovering Local Structure • Remove possible spouse links • Find d-separation set • Orient the arcs

11. Algorithm 1

12. Example of Local Causal Structure

13. Potential Improvements • Two passes becomes one pass • Combine spouse link detection and edge orientation. • If can find S to make X and Y conditionally independent, then X and Y are spouse. • If Z \in Mb(X) and Mb(Y) is not in S is a mutual child, the direction between X, Y, Z is determined. • Transform the problem to identify d-separation set.

14. Algorithm 2

15. Generic Algorithm based on Feature Selection • Find the conjectured Markov blanket of each variable with feature selection. • Build the moral graph. • Remove spouse links and orient V-structure. • Propagate orientation constraints.

16. Algorithm 3

17. Algorithm 4

18. Algorithms for Causal Feature Selection • RFE based approach • TC and TCbw algorithm

19. Conclusion • Causal discovery is close to feature selection • Three steps to build up the causal structure from Markov blankets. More efficient, and even better than previous methods.