Learning Deep Kernels for Non-Parametric Two-Sample Tests

TL;DR

This paper introduces deep neural network parameterized kernels for two-sample tests, enhancing adaptability and performance in high-dimensional, complex data scenarios, with proven consistency and superior empirical results.

Contribution

It presents a novel class of deep kernel-based two-sample tests that adapt to distribution complexity and proves their consistency, outperforming prior methods.

Findings

Deep kernels outperform traditional kernels in high-dimensional tests.

The proposed method is consistent and adaptable to distribution variations.

Experimental results show superior performance on benchmark and real-world data.

Abstract

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two sample tests is available at https://github.com/fengliu90/DK-for-TST.