A label efficient two-sample test
Weizhi Li, Gautam Dasarathy, Karthikeyan Natesan Ramamurthy, Visar Berisha
Abstract
Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are easily measured whereas sample labels are unknown and costly to obtain. Accordingly, we devise a three-stage framework in service of performing an effective two-sample test with only a small number of sample label queries: first, a classifier is trained with samples uniformly labeled to model the posterior probabilities of the labels; second, a novel query scheme dubbed bimodal query is used to query labels of samples from both classes, and last, the classical Friedman-Rafsky (FR) two-sample test is performed on the queried samples. Theoretical analysis and extensive experiments performed on several datasets demonstrate that the proposed test controls the Type I error and has decreased Type II error relative to uniform querying and certainty-based querying. Source code for our algorithms and experimental results is available at https://github.com/wayne0908/Label-Efficient-Two-Sample.
BibTeX
@InProceedings{pmlr-v180-li22f,
title = {A label efficient two-sample test},
author = {Li, Weizhi and Dasarathy, Gautam and Ramamurthy, Karthikeyan Natesan and Berisha, Visar},
booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
pages = {1168--1177},
year = {2022},
editor = {Cussens, James and Zhang, Kun},
volume = {180},
series = {Proceedings of Machine Learning Research},
month = {01--05 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v180/li22f/li22f.pdf},
url = {https://proceedings.mlr.press/v180/li22f.html},
abstract = {Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). We consider a new setting for this problem where sample features are easily measured whereas sample labels are unknown and costly to obtain. Accordingly, we devise a three-stage framework in service of performing an effective two-sample test with only a small number of sample label queries: first, a classifier is trained with samples uniformly labeled to model the posterior probabilities of the labels; second, a novel query scheme dubbed bimodal query is used to query labels of samples from both classes, and last, the classical Friedman-Rafsky (FR) two-sample test is performed on the queried samples. Theoretical analysis and extensive experiments performed on several datasets demonstrate that the proposed test controls the Type I error and has decreased Type II error relative to uniform querying and certainty-based querying. Source code for our algorithms and experimental results is available at https://github.com/wayne0908/Label-Efficient-Two-Sample.}
}