Papers › Learning Deep Kernels for Non-Parametric Two-Sample Tests
Learning Deep Kernels for Non-Parametric Two-Sample Tests
Feng Liu, Wenkai Xu, Jie Lu, Guangquan Zhang, Arthur Gretton, Danica J. Sutherland
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.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Two-sample testing | Blob (9 modes, 40 for each) | MMD-D | Avg accuracy | 98.5 | #1 of 1 | Archive leaderboard | report |
| Two-sample testing | CIFAR-10 vs CIFAR-10.1 (1000 samples) | MMD-D | Avg accuracy | 74.4 | #1 of 1 | Archive leaderboard | report |
| Two-sample testing | HDGM (d=10, N=4000) | MMD-D | Avg accuracy | 65.9 | #1 of 1 | Archive leaderboard | report |
| Two-sample testing | HIGGS Data Set | MMD-D | Avg accuracy | 57.9 | #1 of 1 | Archive leaderboard | report |
| Two-sample testing | MNIST vs Fake MNIST | MMD-D | Avg accuracy | 91 | #1 of 1 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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