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Testing Poisson Binomial Distributions

Abstract

A Poisson Binomial distribution over nn variables is the distribution of the sum of nn independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution PP supported on {0,...,n}\{0,...,n\} to which we have sample access is a Poisson Binomial distribution, or far from all Poisson Binomial distributions. The sample complexity of our algorithm is O(n1/4)O(n^{1/4}) to which we provide a matching lower bound. We note that our sample complexity improves quadratically upon that of the naive "learn followed by tolerant-test" approach, while instance optimal identity testing [VV14] is not applicable since we are looking to simultaneously test against a whole family of distributions.

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