Robust Learning of Fixed-Structure Bayesian Networks in Nearly-Linear Time

• URL: http://arxiv.org/abs/2105.05555v1
• Date: Wed, 12 May 2021 10:11:32 GMT
• Title: Robust Learning of Fixed-Structure Bayesian Networks in Nearly-Linear Time
• Authors: Yu Cheng and Honghao Lin
• Abstract summary: We study the problem of learning Bayesian networks where an $epsilon$-fraction of the samples are adversarially corrupted. We present the first nearly-linear time algorithm for this problem with a dimension-independent error guarantee.
• Score: 13.617081331738056
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of learning Bayesian networks where an $\epsilon$-fraction of the samples are adversarially corrupted. We focus on the fully-observable case where the underlying graph structure is known. In this work, we present the first nearly-linear time algorithm for this problem with a dimension-independent error guarantee. Previous robust algorithms with comparable error guarantees are slower by at least a factor of $(d/\epsilon)$, where $d$ is the number of variables in the Bayesian network and $\epsilon$ is the fraction of corrupted samples. Our algorithm and analysis are considerably simpler than those in previous work. We achieve this by establishing a direct connection between robust learning of Bayesian networks and robust mean estimation. As a subroutine in our algorithm, we develop a robust mean estimation algorithm whose runtime is nearly-linear in the number of nonzeros in the input samples, which may be of independent interest.

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