Neural Autoregressive Flows for Markov Boundary Learning

TL;DR

This paper introduces a scalable, theoretically supported method for Markov boundary discovery using neural autoregressive networks and information-theoretic scoring, improving efficiency and accuracy in causal inference tasks.

Contribution

It presents a novel masked autoregressive network and a polynomial-time greedy search for reliable Markov boundary learning with theoretical guarantees.

Findings

Outperforms existing methods in real-world datasets

Scales efficiently to high-dimensional data

Accelerates causal discovery with learned boundaries

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.