Testing Bayesian Networks

TL;DR

This paper develops the first efficient algorithms for testing whether high-dimensional Bayesian networks are identical or close, providing optimal sample complexity bounds and advancing the understanding of distribution testing in graphical models.

Contribution

It introduces the first non-trivial, efficient testing algorithms for identity and closeness testing of Bayesian networks, along with matching lower bounds.

Findings

Algorithms with sublinear sample complexity for high-dimensional Bayesian networks.

Sample-optimal testing algorithms up to constant factors.

Information-theoretic lower bounds established for these testing problems.

Abstract

This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a directed acyclic graph, where we associate a random variable with each node. The value at any particular node is conditionally independent of all the other non-descendant nodes once its parents are fixed. Specifically, we study the properties of identity testing and closeness testing of Bayesian networks. Our main contribution is the first non-trivial efficient testing algorithms for these problems and corresponding information-theoretic lower bounds. For a wide range of parameter settings, our testing algorithms have sample complexity sublinear in the dimension and are sample-optimal, up to constant factors.