Distributionally Robust Skeleton Learning of Discrete Bayesian Networks

TL;DR

This paper introduces a distributionally robust method for learning the skeletons of discrete Bayesian networks that effectively handles outliers and does not rely on strict assumptions, with proven guarantees and practical algorithms.

Contribution

It proposes a novel distributionally robust optimization approach for skeleton learning in discrete Bayesian networks, applicable to general categorical variables without faithfulness assumptions.

Findings

Non-asymptotic guarantees for structure learning.

Logarithmic sample complexity for bounded-degree graphs.

Validated effectiveness on synthetic and real datasets.

Abstract

We consider the problem of learning the exact skeleton of general discrete Bayesian networks from potentially corrupted data. Building on distributionally robust optimization and a regression approach, we propose to optimize the most adverse risk over a family of distributions within bounded Wasserstein distance or KL divergence to the empirical distribution. The worst-case risk accounts for the effect of outliers. The proposed approach applies for general categorical random variables without assuming faithfulness, an ordinal relationship or a specific form of conditional distribution. We present efficient algorithms and show the proposed methods are closely related to the standard regularized regression approach. Under mild assumptions, we derive non-asymptotic guarantees for successful structure learning with logarithmic sample complexities for bounded-degree graphs. Numerical study on synthetic and real datasets validates the effectiveness of our method. Code is available at https://github.com/DanielLeee/drslbn.