Revisiting Classifier Two-Sample Tests

TL;DR

This paper explores classifier-based two-sample tests (C2ST), demonstrating their theoretical properties, competitive performance, and novel applications in evaluating generative models and causal discovery.

Contribution

It provides a comprehensive analysis of C2ST, compares it with existing methods, and introduces new uses in evaluating generative models and causal inference.

Findings

C2ST learns data representations effectively.

C2ST has a simple null distribution and interpretable test statistics.

C2ST performs competitively against state-of-the-art two-sample tests.

Abstract

The goal of two-sample tests is to assess whether two samples, $S_P \sim P^n$ and $S_Q \sim Q^m$, are drawn from the same distribution. Perhaps intriguingly, one relatively unexplored method to build two-sample tests is the use of binary classifiers. In particular, construct a dataset by pairing the $n$ examples in $S_P$ with a positive label, and by pairing the $m$ examples in $S_Q$ with a negative label. If the null hypothesis "$P = Q$" is true, then the classification accuracy of a binary classifier on a held-out subset of this dataset should remain near chance-level. As we will show, such Classifier Two-Sample Tests (C2ST) learn a suitable representation of the data on the fly, return test statistics in interpretable units, have a simple null distribution, and their predictive uncertainty allow to interpret where $P$ and $Q$ differ. The goal of this paper is to establish the properties, performance, and uses of C2ST. First, we analyze their main theoretical properties. Second, we compare their performance against a variety of state-of-the-art alternatives. Third, we propose their use to evaluate the sample quality of generative models with intractable likelihoods, such as Generative Adversarial Networks (GANs). Fourth, we showcase the novel application of GANs together with C2ST for causal discovery.