Independence Testing for Bounded Degree Bayesian Network

• URL: http://arxiv.org/abs/2204.08690v1
• Date: Tue, 19 Apr 2022 06:16:14 GMT
• Title: Independence Testing for Bounded Degree Bayesian Network
• Authors: Arnab Bhattacharyya, Cl\'ement L. Canonne, and Joy Qiping Yang
• Abstract summary: We show that if $P$ has a sparse structure, then in fact only linearly many samples are required. We also show that if $P$ is Markov with respect to a Bayesian network whose underlying DAG has in-degree bounded by $d$, then $tildeTheta (2d/2cdot n/varepsilon2)$ samples are necessary.
• Score: 4.230271396864461
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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