Two-sample Testing Using Deep Learning

Matthias Kirchler; Shahryar Khorasani; Marius Kloft; Christoph Lippert

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arXiv · 1910.06239

Two-sample Testing Using Deep Learning

Matthias Kirchler·Shahryar Khorasani·Marius Kloft·Christoph Lippert

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Abstract

We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are consistent and asymptotically control the type-1 error rate. Their test statistics can be evaluated in linear time (in the sample size). Suitable data representations are obtained in a data-driven way, by solving a supervised or unsupervised transfer-learning task on an auxiliary (potentially distinct) data set. If no auxiliary data is available, we split the data into two chunks: one for learning representations and one for computing the test statistic. In experiments on audio samples, natural images and three-dimensional neuroimaging data our tests yield significant decreases in type-2 error rate (up to 35 percentage points) compared to state-of-the-art two-sample tests such as kernel-methods and classifier two-sample tests.

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BibTeX RIS

Matthias Kirchler, Shahryar Khorasani, Marius Kloft, Christoph Lippert. 2019-10-14. Two-sample Testing Using Deep Learning. https://arxiv.org/abs/1910.06239

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