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Modern kernel-based two-sample tests have shown great success indistinguishing complex, high-dimensional distributions with appropriate learnedkernels. Previous work has demonstrated that this kernel learning proceduresucceeds, assuming a considerable number of observed samples from eachdistribution. In realistic scenarios with very limited numbers of data samples,however, it can be challenging to identify a kernel powerful enough todistinguish complex distributions. We address this issue by introducing theproblem of meta two-sample testing (M2ST), which aims to exploit (abundant)auxiliary data on related tasks to find an algorithm that can quickly identifya powerful test on new target tasks. We propose two specific algorithms forthis task: a generic scheme which improves over baselines and a more tailoredapproach which performs even better. We provide both theoretical justificationand empirical evidence that our proposed meta-testing schemes out-performlearning kernel-based tests directly from scarce observations, and identifywhen such schemes will be successful.

Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data