Directional Kernel Mean Difference: A Fast Signed Statistic for Univariate Distribution Comparison

arXiv:2607.20119 · stat.ML, cs.LG · Submitted 2026-07-22 · Read on arXiv

Shijie Zhong, Jiangfeng Fu

stat.ML, cs.LG

Submitted: 2026-07-22

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Embeddings — 12× in this paper · explained in 2 episodes
• Monotonicity — 8× in this paper · explained in 2 episodes
• Directional Kernel Mean Difference — 7× in this paper
• Robustness — 7× in this paper · explained in 6 episodes
• Benchmark — 5× in this paper · explained in 2 episodes
• Consistency — 4× in this paper · explained in 3 episodes
• Maximum Mean Discrepancy — 4× in this paper
• Structural Properties — 4× in this paper · explained in 2 episodes
• Theoretical Guarantees — 4× in this paper · explained in 2 episodes
• Axioms — 2× in this paper · explained in 2 episodes
• Conditional Independence — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Maximum Mean Discrepancy (MMD) — 2× in this paper · explained in 3 episodes
• Causal Discovery — 1× in this paper · explained in 3 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Covariate Shift — 1× in this paper · explained in 3 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Hyperparameters — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 7 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Universality — 1× in this paper · explained in 2 episodes

Sources

• Equivalence of distance-based and RKHS-based statistics in hypothesis testing
• Kernel-based Conditional Independence Test and Application in Causal Discovery

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