Testing Properties of Multiple Distributions with Few Samples
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We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from s distributions, p_1, p_2, ..., p_s, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the p_i's are uniform or ϵ-far from being uniform in ℓ_1-distance (2) Identity Testing: Testing whether all the p_i's are equal to an explicitly given distribution q or ϵ-far from q in ℓ_1-distance, and (3) Closeness Testing: Testing whether all the p_i's are equal to a distribution q which we have sample access to, or ϵ-far from q in ℓ_1-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.
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