Distributionally Robust Skeleton Learning of Discrete Bayesian Networks
This provides a robust method for structure learning in Bayesian networks, which is incremental but addresses data corruption issues important for applications in fields like bioinformatics or finance.
The paper tackles the problem of learning the exact skeleton of discrete Bayesian networks from potentially corrupted data by using distributionally robust optimization to handle outliers, achieving non-asymptotic guarantees with logarithmic sample complexity for bounded-degree graphs.
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.