Robust Learning of Fixed-Structure Bayesian Networks in Nearly-Linear Time
Authors: Yu Cheng,Honghao Lin

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.