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Distributionally Robust Skeleton Learning of Discrete Bayesian Networks

arXiv 2311.06117 ↗First posted 10 Nov 2023cs.LG stat.MLcited by 0

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Abstract (arXiv)

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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References · 37

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
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25 more
  1. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  2. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 64
  3. 2018On Causal Discovery with Equal Variance Assumptioncited by 59
  4. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
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  7. 2016Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimizationcited by 33
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  11. 2022Reliable Causal Discovery with Improved Exact Search and Weaker Assumptionscited by 19
  12. 2017Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)cited by 18
  13. 2018Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimatorcited by 16
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  15. 2020Generalised Lipschitz Regularisation Equals Distributional Robustnesscited by 14
  16. 2015A hybrid algorithm for Bayesian network structure learning with application to multi-label learningcited by 12
  17. 2015Learning Directed Acyclic Graphs with Penalized Neighbourhood Regressioncited by 12
  18. 2014Parameterized Complexity Results for Exact Bayesian Network Structure Learningcited by 11
  19. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 11
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  24. 2022Distributionally Robust Causal Inference with Observational Datacited by 2
  25. 2020Robust Identifiability in Linear Structural Equation Models of Causal Inferencecited by 1

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