Near-Optimal Degree Testing for Bayes Nets

04/13/2023

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by   Vipul Arora, et al.

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This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution P over {0,1}^n, given sample access to P. We show that the sample complexity of the problem is Θ̃(2^n/2/ε^2). Our algorithm relies on a testing-by-learning framework, previously used to obtain sample-optimal testers; in order to apply this framework, we develop new algorithms for “near-proper” learning of Bayes nets, and high-probability learning under χ^2 divergence, which are of independent interest.