Near-Optimal Closeness Testing of Discrete Histogram Distributions release_vapi4nljgrhvfnobyyq4vpovuu

by Ilias Diakonikolas, Daniel M. Kane, Vladimir Nikishkin

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2017  

Abstract

We investigate the problem of testing the equivalence between two discrete histograms. A k-histogram over [n] is a probability distribution that is piecewise constant over some set of k intervals over [n]. Histograms have been extensively studied in computer science and statistics. Given a set of samples from two k-histogram distributions p, q over [n], we want to distinguish (with high probability) between the cases that p = q and p-q_1 ≥ϵ. The main contribution of this paper is a new algorithm for this testing problem and a nearly matching information-theoretic lower bound. Specifically, the sample complexity of our algorithm matches our lower bound up to a logarithmic factor, improving on previous work by polynomial factors in the relevant parameters. Our algorithmic approach applies in a more general setting and yields improved sample upper bounds for testing closeness of other structured distributions as well.
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Date   2017-03-06
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arXiv  1703.01913v1
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