Deep-testing: the case of dependence detection

• URL: http://arxiv.org/abs/2604.26558v1
• Date: Wed, 29 Apr 2026 11:45:32 GMT
• Title: Deep-testing: the case of dependence detection
• Abstract summary: We propose a novel procedure called deep-testing, which approaches the classical inferential problem of hypothesis testing through deep learning.<n>Test statistic is a classification map learned by a deep neural network from simulated data satisfying the null and alternative hypotheses.<n>As a proof of concept, we apply deep-testing to the problem of independence testing, arguably one of the most important problems in statistics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an image of a handwritten digit from another, can it also distinguish an "image of a sample" (such as a scatter plot) generated under a given statistical model from one generated outside that model? Motivated by this idea, we propose a novel procedure called deep-testing, which approaches the classical inferential problem of hypothesis testing through deep learning. More specifically, the test statistic is a classification map learned by a deep neural network from simulated data satisfying the null and alternative hypotheses, leveraging its strong discriminating power to construct a highly powerful test. As a proof of concept, we apply deep-testing to the problem of independence testing, arguably one of the most important problems in statistics. In a large-scale simulation study, deep-testing achieves the highest overall power against nineteen competing methods across a broad range of complex dependence structures, confirming the viability of the proposed approach.

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