Active Sequential Two-Sample Testing

• URL: http://arxiv.org/abs/2301.12616v4
• Date: Fri, 28 Jun 2024 03:57:21 GMT
• Title: Active Sequential Two-Sample Testing
• Authors: Weizhi Li, Prad Kadambi, Pouria Saidi, Karthikeyan Natesan Ramamurthy, Gautam Dasarathy, Visar Berisha,
• Abstract summary: We consider the two-sample testing problem in a new scenario where sample measurements are inexpensive to access. We devise the first emphactiveNIST-sample testing framework that not only sequentially but also emphactively queries. In practice, we introduce an instantiation of our framework and evaluate it using several experiments.
• Score: 18.99517340397671
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. To address the problem, we devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries}. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is provided by a probabilistic classification model. The classification model is adaptively updated and used to predict where the (unlabelled) features have a high dependency on labels; labeling the ``high-dependency'' features leads to the increased power of the proposed testing framework. In theory, we provide the proof that our framework produces an \emph{anytime-valid} $p$-value. In addition, we characterize the proposed framework's gain in testing power by analyzing the mutual information between the feature and label variables in asymptotic and finite-sample scenarios. In practice, we introduce an instantiation of our framework and evaluate it using several experiments; the experiments on the synthetic, MNIST, and application-specific datasets demonstrate that the testing power of the instantiated active sequential test significantly increases while the Type I error is under control.

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