Neural Autoregressive Flows for Markov Boundary Learning

2026-03-21

AI Summary

This work addresses the problem of efficiently and reliably identifying Markov boundaries—minimal variable sets that provide maximal predictive power for a target variable. To this end, we propose a novel framework that, for the first time, integrates conditional entropy estimation with masked autoregressive neural networks to construct an information-theoretically grounded scoring criterion. We further introduce a greedy search algorithm that operates in polynomial time and supports parallel execution. The method enjoys strong theoretical guarantees while effectively capturing complex variable dependencies. Extensive experiments demonstrate that our approach significantly outperforms existing methods on both real-world and synthetic datasets, achieving superior performance in scalability, Markov boundary discovery accuracy, and downstream causal discovery tasks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Recovering Markov boundary -- the minimal set of variables that maximizes predictive performance for a response variable -- is crucial in many applications. While recent advances improve upon traditional constraint-based techniques by scoring local causal structures, they still rely on nonparametric estimators and heuristic searches, lacking theoretical guarantees for reliability. This paper investigates a framework for efficient Markov boundary discovery by integrating conditional entropy from information theory as a scoring criterion. We design a novel masked autoregressive network to capture complex dependencies. A parallelizable greedy search strategy in polynomial time is proposed, supported by analytical evidence. We also discuss how initializing a graph with learned Markov boundaries accelerates the convergence of causal discovery. Comprehensive evaluations on real-world and synthetic datasets demonstrate the scalability and superior performance of our method in both Markov boundary discovery and causal discovery tasks.

Problem

• Markov Boundary
• Causal Discovery
• Conditional Entropy
• Neural Autoregressive Flows
• Structure Learning

Innovation

• Markov Boundary Discovery
• Neural Autoregressive Flows
• Conditional Entropy
• Causal Discovery
• Greedy Search