eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-01-06
69:1
69:41
10.4230/LIPIcs.ITCS.2020.69
article
Testing Properties of Multiple Distributions with Few Samples
Aliakbarpour, Maryam
1
Silwal, Sandeep
1
Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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 (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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol151-itcs2020/LIPIcs.ITCS.2020.69/LIPIcs.ITCS.2020.69.pdf
Hypothesis Testing
Property Testing
Distribution Testing
Identity Testing
Closeness Testing
Multiple Sources