Telling Two Distributions Apart: a Tight Characterization
Data Structures and Algorithms
2011-10-17 v1
Abstract
We consider the problem of distinguishing between two arbitrary black-box distributions defined over the domain [n], given access to samples from both. It is known that in the worst case O(n^{2/3}) samples is both necessary and sufficient, provided that the distributions have L1 difference of at least {\epsilon}. However, it is also known that in many cases fewer samples suffice. We identify a new parameter, that provides an upper bound on how many samples needed, and present an efficient algorithm that requires the number of samples independent of the domain size. Also for a large subclass of distributions we provide a lower bound, that matches our upper bound up to a poly-logarithmic factor.
Cite
@article{arxiv.1110.3100,
title = {Telling Two Distributions Apart: a Tight Characterization},
author = {Eyal Even Dar and Mark Sandler},
journal= {arXiv preprint arXiv:1110.3100},
year = {2011}
}
Comments
17 pages