Using Markov Blankets for Causal Structure Learning

Jean-Philippe PelletAndre 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 <-- C --> 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 TCbw 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.