Testing Properties of Multiple Distributions with Few Samples [article]

Maryam Aliakbarpour, Sandeep Silwal
2019 arXiv   pre-print
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
more » ... (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.
arXiv:1911.07324v1 fatcat:qzfz4buxcrhtzamw3o2netatpe