Label efficient two-sample test

• URL: http://arxiv.org/abs/2111.08861v1
• Date: Wed, 17 Nov 2021 01:55:01 GMT
• Title: Label efficient two-sample test
• Authors: Weizhi Li, Gautam Dasarathy, Karthikeyan Natesan Ramamurthy, Visar Berisha
• Abstract summary: Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis) In this paper, we consider this important variation on the classical two-sample test problem and pose it as a problem of obtaining the labels of only a small number of samples in service of performing a two-sample test. We devise a label efficient three-stage framework: firstly, a classifier is trained with samples uniformly labeled to model the posterior probabilities of the labels; secondly, an innovative query scheme dubbed emphbimodal query is used to query labels
• Score: 39.0914588747459
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two-sample tests evaluate whether two samples are realizations of the same distribution (the null hypothesis) or two different distributions (the alternative hypothesis). In the traditional formulation of this problem, the statistician has access to both the measurements (feature variables) and the group variable (label variable). However, in several important applications, feature variables can be easily measured but the binary label variable is unknown and costly to obtain. In this paper, we consider this important variation on the classical two-sample test problem and pose it as a problem of obtaining the labels of only a small number of samples in service of performing a two-sample test. We devise a label efficient three-stage framework: firstly, a classifier is trained with samples uniformly labeled to model the posterior probabilities of the labels; secondly, an innovative query scheme dubbed \emph{bimodal query} is used to query labels of samples from both classes with maximum posterior probabilities, and lastly, the classical Friedman-Rafsky (FR) two-sample test is performed on the queried samples. Our theoretical analysis shows that bimodal query is optimal for the FR test under reasonable conditions and that the three-stage framework controls the Type I error. Extensive experiments performed on synthetic, benchmark, and application-specific datasets demonstrate that the three-stage framework has decreased Type II error over uniform querying and certainty-based querying with same number of labels while controlling the Type I error.

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