Independence Testing for Bounded Degree Bayesian Network
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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 ε-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 Θ̃(2^d/2· n/ε^2) samples are necessary and sufficient for independence testing.
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