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

TL;DR

This paper introduces a nearly-linear time algorithm for robustly learning fixed-structure Bayesian networks with adversarial sample corruption, significantly improving speed and simplicity over prior methods.

Contribution

The work presents the first nearly-linear time algorithm for robust Bayesian network learning with a dimension-independent error guarantee, connecting it to robust mean estimation.

Findings

Achieves nearly-linear runtime in the number of nonzero entries.

Provides a dimension-independent error guarantee.

Simplifies previous algorithms significantly.

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.