Robust Learning of Fixed-Structure Bayesian Networks in Nearly-Linear Time
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We study the problem of learning Bayesian networks where an ϵ-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/ϵ), where d is the number of variables in the Bayesian network and ϵ 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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