Testing Hypotheses by Regularized Maximum Mean Discrepancy
This addresses a fundamental problem in statistics and machine learning for data analysis, offering incremental improvements in kernel-based hypothesis testing.
The paper tackles the problem of determining if two data samples come from different distributions by introducing Regularized Maximum Mean Discrepancy (RMMD), a kernel-based measure that improves performance with small sample sizes and excels in multiple comparison tests with power control, achieving outstanding results on datasets like EEG, MNIST, Berkley Covertype, and Flare-Solar.
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Maximum Mean Discrepancy (RMMD), our novel measure for kernel-based hypothesis testing, yields substantial improvements even when sample sizes are small, and excels at hypothesis tests involving multiple comparisons with power control. We derive asymptotic distributions under the null and alternative hypotheses, and assess power control. Outstanding results are obtained on: challenging EEG data, MNIST, the Berkley Covertype, and the Flare-Solar dataset.