New Algorithm Discovers Markov Blankets Beyond Faithfulness

Loong Kuan Lee, Ragavi Krishnamoorthy, Nico Piatkowski· July 30, 2026 View original

Summary

This paper introduces a "k-order" relaxation of the faithfulness assumption, enabling the discovery of Markov blankets even when traditional methods fail due to higher-order dependencies like XOR relations. The proposed k-order Markov blanket (kOMB) algorithm empirically recovers Markov blankets under both true and empirical violations of faithfulness.

Many methods for discovering the Markov blanket (MB) of a variable rely on the faithfulness assumption, which states that conditional independencies in the data directly reflect separations in the graphical structure. However, this assumption often breaks down in the presence of higher-order dependencies, such as XOR relationships, or due to empirical violations in finite datasets. To address this, researchers propose a "k-order" relaxation of the faithfulness assumption, specifically designed to capture parity-type relationships involving k+2 variables. Building on this relaxation, they introduce a proof-of-concept algorithm called k-order Markov blanket (kOMB). Empirical evaluations demonstrate that kOMB successfully recovers the Markov blanket even when the faithfulness assumption is violated, offering a more robust approach to causal discovery and feature selection.

Why it matters

For data scientists and researchers, this advancement provides a more robust method for feature selection and causal discovery, particularly in datasets where complex, non-linear relationships violate traditional assumptions, leading to more accurate and reliable models.

How to implement this in your domain

  1. 1Review existing feature selection and causal discovery pipelines to identify potential limitations due to the faithfulness assumption.
  2. 2Explore the kOMB algorithm or similar methods that relax the faithfulness assumption for datasets with known higher-order dependencies.
  3. 3Experiment with kOMB in feature selection tasks to see if it improves model performance or interpretability compared to traditional methods.
  4. 4Contribute to or utilize open-source implementations of kOMB to integrate it into data analysis workflows.

Who benefits

Data ScienceHealthcareFinanceMarketingAI/ML Research

Key takeaways

  • Traditional Markov blanket discovery methods often fail when the faithfulness assumption is violated by higher-order dependencies.
  • A "k-order" relaxation of the faithfulness assumption is proposed to capture complex parity-type relationships.
  • The k-order Markov blanket (kOMB) algorithm can recover MBs even under true and empirical violations of faithfulness.
  • This method offers a more robust approach to causal discovery and feature selection.

Original post by Loong Kuan Lee, Ragavi Krishnamoorthy, Nico Piatkowski

"arXiv:2607.26357v1 Announce Type: new Abstract: The problem of learning the graphical Markov blanket (MB) of a variable from data has applications in many areas such as structure learning for Bayesian networks and Markov random fields, causal discovery, and feature selection. How…"

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Originally posted by Loong Kuan Lee, Ragavi Krishnamoorthy, Nico Piatkowski on X · view source

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