Learning Kernel Tests Without Data Splitting
This addresses a bottleneck in large-scale kernel tests for researchers and practitioners, offering a more powerful alternative to data-splitting methods, though it appears incremental as it builds on selective inference.
The paper tackles the problem of reduced test power in kernel-based statistical tests due to data splitting for hyperparameter tuning, and proposes a method that allows learning hyperparameters and testing on the full sample without splitting, resulting in empirically higher test power at the same significance level.
Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While data splitting results in a tractable null distribution, it suffers from a reduction in test power due to smaller test sample size. Inspired by the selective inference framework, we propose an approach that enables learning the hyperparameters and testing on the full sample without data splitting. Our approach can correctly calibrate the test in the presence of such dependency, and yield a test threshold in closed form. At the same significance level, our approach's test power is empirically larger than that of the data-splitting approach, regardless of its split proportion.