Kernel Selection is Model Selection: A Unified Complexity-Penalized Approach for MMD Two-Sample Tests
The Maximum Mean Discrepancy (MMD) is a cornerstone statistic for nonparametric two-sample testing, but its test power is dictated entirely by the chosen kernel. Because any fixed kernel inherently fails to distinguish certain distributions, the kernel must be dynamically optimized. However, data-driven optimization violates the foundational i.i.d. assumption, forcing a strict trade-off in existing frameworks. Ratio criteria ignore this dependence, inducing overfitting and variance collapse on rich kernel classes. Conversely, aggregation methods bypass the dependence using finite grids, but this strategy cannot scale to continuous search spaces like deep kernels. To break this dichotomy, ...
| Authors | Yijin Ni, Xiaoming Huo |
|---|---|
| Primary category | stat.ML |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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