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

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

Previous work Score-based approaches Constraint-based approaches Hybrid approaches

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

Background Feature selection – Conditional independence – Strong relevance – Weak relevance – Irrelevance – Feature selection task

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

Background Perfect map Causal Markov condition Faithfulness condition

Background Causal sufficiency assumption V-structure

Causal Network Construction Properties of Markov blankets

Recovering Local Structure Remove possible spouse links – Find d-separation set Orient the arcs

Algorithm 1

Example of Local Causal Structure

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.

Algorithm 2

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.

Algorithm 3

Algorithm 4

Algorithms for Causal Feature Selection RFE based approach TC and TC bw algorithm

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.