Near-Optimal Degree Testing for Bayes Nets

Vipul Arora, Arnab Bhattacharyya, Clement Louis Canonne, Qiping Yang

Abstract: 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 Θ~(2n/2/ε2). 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 χ2 divergence, which are of independent interest.