Learning Deep Kernels for Non-Parametric Two-Sample Tests
This work addresses the need for more powerful and adaptive two-sample tests in high-dimensional and complex data scenarios, representing an incremental improvement over prior kernel-based methods.
The authors tackled the problem of determining whether two sets of samples come from the same distribution by proposing deep kernel-based two-sample tests, which adapt to distribution variations and achieve superior performance in experiments on benchmark and real-world data.
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.