2019/11/17 by Maryam Aliakbarpour, Aliakbarpour, Maryam, Sandeep Silwal +1
Computer Science · #Complexity and Algorithms in Graphs #Machine Learning and Algorithms #Cryptography and Data Security
paper · pdf · doi:10.48550/arxiv.1911.07324
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, p1, p2, …, ps, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the pi's are uniform or ε-far from being uniform in ℓ1-distance (2) Identity Testing: Testing whether all the pi's are equal to an explicitly given distribution q or ε-far from q in ℓ1-distance, and (3) Closeness Testing: Testing whether all the pi's are equal to a distribution q which we have sample access to, or ε-far from q in ℓ1-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.