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 εfar from being uniform in ℓ_1distance (2) Identity Testing: Testing whether all the p_i’s are equal to an explicitly given distribution q or εfar from q in ℓ_1distance, and (3) Closeness Testing: Testing whether all the p_i’s are equal to a distribution q which we have sample access to, or εfar from q in ℓ_1distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.
Testing Properties of Multiple Distributions with Few Samples.
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 εfar from being uniform in ℓ_1distance (2) Identity Testing: Testing whether all the p_i’s are equal to an explicitly given distribution q or εfar from q in ℓ_1distance, and (3) Closeness Testing: Testing whether all the p_i’s are equal to a distribution q which we have sample access to, or εfar from q in ℓ_1distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.
 Award ID(s):
 1741137
 Publication Date:
 NSFPAR ID:
 10220369
 Journal Name:
 11th Innovations in Theoretical Computer Science Conference, ITCS 2020
 Sponsoring Org:
 National Science Foundation
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