Distributionally Robust Skeleton Learning of Discrete Bayesian Networks

Yeshu Li, Brian D Ziebart

Keywords: structure learning, Bayesian network, robustness

TL;DR: We propose a distributionally robust method for skeleton learning of discrete Bayesian networks with tractable algorithms and out-of-sample exact recovery guarantees.

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.

Submission Number: 9344