Learning Kernel Tests Without Data Splitting

Abstract

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.

24 (11+13) pages, 10 figures. Camera-Ready version. Accepted to the Thirty-fourth Conference on Neural Information Processing Systems (NeurIPS 2020)

References in corpus (8)

• Generative Moment Matching Networks
• Learning Deep Kernels for Non-Parametric Two-Sample Tests
• An Adaptive Test of Independence with Analytic Kernel Embeddings
• Informative Features for Model Comparison
• Kernel Stein Tests for Multiple Model Comparison
• Two-sample Testing Using Deep Learning
• Comparing distributions: ${\ell }_1$ geometry improves kernel two-sample testing
• Post Selection Inference with Kernels

Cited by in corpus (3)

• MMD Aggregated Two-Sample Test
• Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data
• A Witness Two-Sample Test