%0 Journal Article %1 aliakbarpour2019testing %A Aliakbarpour, Maryam %A Silwal, Sandeep %D 2019 %K distributed hypothesis-testing readings %T Testing Properties of Multiple Distributions with Few Samples %U http://arxiv.org/abs/1911.07324 %X 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, $p_1, p_2, łdots, p_s$, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the $p_i$'s are uniform or $\epsilon$-far from being uniform in $\ell_1$-distance (2) Identity Testing: Testing whether all the $p_i$'s are equal to an explicitly given distribution $q$ or $\epsilon$-far from $q$ in $\ell_1$-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 $\epsilon$-far from $q$ in $\ell_1$-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.

@article{aliakbarpour2019testing, abstract = {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, $p_1, p_2, \ldots, p_s$, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the $p_i$'s are uniform or $\epsilon$-far from being uniform in $\ell_1$-distance (2) Identity Testing: Testing whether all the $p_i$'s are equal to an explicitly given distribution $q$ or $\epsilon$-far from $q$ in $\ell_1$-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 $\epsilon$-far from $q$ in $\ell_1$-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems.}, added-at = {2020-03-09T18:30:40.000+0100}, author = {Aliakbarpour, Maryam and Silwal, Sandeep}, biburl = {https://www.bibsonomy.org/bibtex/223ea18fd9be805717bd8ac7d6dd76602/kirk86}, description = {[1911.07324] Testing Properties of Multiple Distributions with Few Samples}, interhash = {b148a60ee99ca46e1bb49cd66ac958b7}, intrahash = {23ea18fd9be805717bd8ac7d6dd76602}, keywords = {distributed hypothesis-testing readings}, note = {cite arxiv:1911.07324Comment: ITCS 2020}, timestamp = {2020-03-09T18:30:40.000+0100}, title = {Testing Properties of Multiple Distributions with Few Samples}, url = {http://arxiv.org/abs/1911.07324}, year = 2019 }