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 <-- 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 dseparation 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.