using markov blankets for causal structure learning jean-philippe pellet andre ellisseeff presented...
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![Page 1: Using Markov Blankets for Causal Structure Learning Jean-Philippe Pellet Andre Ellisseeff Presented by Na Dai](https://reader038.vdocument.in/reader038/viewer/2022110207/56649d1f5503460f949f2b8e/html5/thumbnails/1.jpg)
Using Markov Blankets for Causal Structure Learning
Jean-Philippe PelletAndre Ellisseeff
Presented by Na Dai
![Page 2: Using Markov Blankets for Causal Structure Learning Jean-Philippe Pellet Andre Ellisseeff Presented by Na Dai](https://reader038.vdocument.in/reader038/viewer/2022110207/56649d1f5503460f949f2b8e/html5/thumbnails/2.jpg)
Motivation
• Why structure learning?• What are Markov blankets?• Relationship between feature selection and
Markov blankets?
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Previous work
• Score-based approaches• Constraint-based approaches• Hybrid approaches
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Central Ideas
• Building up local structures from Markov blankets.
• Generating global graph structure from local structure.
• How to generate Markov blankets?
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Background
• Feature selection– Conditional independence
– Strong relevance
– Weak relevance
– Irrelevance
– Feature selection task
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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
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Background
• Perfect map
• Causal Markov condition
• Faithfulness condition
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Background
• Causal sufficiency assumption
• V-structure
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Causal Network Construction
• Properties of Markov blankets
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Recovering Local Structure
• Remove possible spouse links– Find d-separation set
• Orient the arcs
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Algorithm 1
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Example of Local Causal Structure
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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.
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Algorithm 2
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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.
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Algorithm 3
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Algorithm 4
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Algorithms for Causal Feature Selection
• RFE based approach• TC and TCbw algorithm
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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.