Directional Kernel Mean Difference: A Fast Signed Statistic for Univariate Distribution Comparison
We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts. Unlike the squared Maximum Mean Discrepancy (MMD), which discards directional information by squaring the RKHS distance, DKMD integrates the difference of kernel mean embeddings against a fixed odd weighting function. This construction yields three structural properties: antisymmetry, immunity to symmetric distributional differences, and directional monotonicity under stochastic dominance. We derive a data-driven Riemann estimator that ensures asymptotic consistency with the continuous formulation, strictly preserving ...
| Authors | Shijie Zhong, Jiangfeng Fu |
|---|---|
| Primary category | stat.ML |
| Published | 22 July 2026 |
| Last updated at source | 22 July 2026 |
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