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arXiv · 2304.06733

Near-Optimal Degree Testing for Bayes Nets

Vipul Arora·Arnab Bhattacharyya·Clément L. Canonne·Joy Qiping Yang
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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 $\tilde{\Theta}(2^{n/2}/\varepsilon^2)$. 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 $\chi^2$ divergence, which are of independent interest.

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BibTeXRIS

Vipul Arora, Arnab Bhattacharyya, Clément L. Canonne, Joy Qiping Yang. 2023-04-13. Near-Optimal Degree Testing for Bayes Nets. https://arxiv.org/abs/2304.06733

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