Independence Testing for Bounded Degree Bayesian Network

Arnab Bhattacharyya; Clément L. Canonne; Joy Qiping Yang

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arXiv · 2204.08690

Independence Testing for Bounded Degree Bayesian Network

Arnab Bhattacharyya·Clément L. Canonne·Joy Qiping Yang

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Abstract

We study the following independence testing problem: given access to samples from a distribution $P$ over $\{0,1\}^n$, decide whether $P$ is a product distribution or whether it is $\varepsilon$-far in total variation distance from any product distribution. For arbitrary distributions, this problem requires $\exp(n)$ samples. We show in this work that if $P$ has a sparse structure, then in fact only linearly many samples are required. Specifically, if $P$ is Markov with respect to a Bayesian network whose underlying DAG has in-degree bounded by $d$, then $\tilde{\Theta}(2^{d/2}\cdot n/\varepsilon^2)$ samples are necessary and sufficient for independence testing.

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BibTeX RIS

Arnab Bhattacharyya, Clément L. Canonne, Joy Qiping Yang. 2022-04-19. Independence Testing for Bounded Degree Bayesian Network. https://arxiv.org/abs/2204.08690

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