Distributionally Robust Skeleton Learning of Discrete Bayesian Networks

• URL: http://arxiv.org/abs/2311.06117v1
• Date: Fri, 10 Nov 2023 15:33:19 GMT
• Title: Distributionally Robust Skeleton Learning of Discrete Bayesian Networks
• Authors: Yeshu Li and Brian D. Ziebart
• Abstract summary: We consider the problem of learning the exact skeleton of general discrete Bayesian networks from potentially corrupted data. We propose to optimize the most adverse risk over a family of distributions within bounded Wasserstein distance or KL divergence to the empirical distribution. We present efficient algorithms and show the proposed methods are closely related to the standard regularized regression approach.
• Score: 9.46389554092506
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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