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.

翻译：深度学习方法在分类和图像识别问题上已被证明极为有效。本文探讨这种成功能否迁移至假设检验领域：如果神经网络能够区分手写数字图像等对象，它是否也能区分在给定统计模型下生成的“样本图像”（如散点图）与在该模型外生成的图像？受这一想法启发，我们提出了一种名为深度测试的新方法，通过深度学习处理经典统计推断中的假设检验问题。具体而言，检验统计量是由深度神经网络从满足原假设和备择假设的模拟数据中学习到的分类映射，利用其强大的判别能力构建高功效检验。作为概念验证，我们将深度测试应用于独立性检验——这或许是统计学中最重要的课题之一。在大规模仿真研究中，面对复杂的依赖结构类型，深度测试在十九种对比方法中实现了最高总体功效，证实了所提方法的可行性。