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About this paper
Antonin Schrab, Ilmun Kim, Mélisande Albert, Béatrice Laurent, Benjamin Guedj, Arthur Gretton
MMDAgg tests multiple kernel bandwidths with joint calibration, rather than selecting one using held-out data. It controls finite-sample false-positive rates and adapts over Sobolev balls up to an iterated-logarithmic penalty, under bounded-density, balanced-sample and kernel-family conditions. In an image-shift benchmark, its Laplace version reached average power 0.83 at 10,000 samples, versus 0.87 for AutoML, a benchmark-specific result.
Key insights
- It is possible to construct MMD-based two-sample tests that guarantee non-asymptotic control of the Type I error, crucial for reliability in practical applications with fixed sample sizes.
- Aggregating MMD tests over a diverse collection of kernel bandwidths and types allows the test to be minimax adaptive, achieving near-optimal performance across unknown distributional smoothness parameters.
- The proposed aggregation approach effectively selects optimal bandwidths and kernels without requiring data splitting, thereby maximizing the data available for testing and enhancing power.
Summary by alphaXiv.
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