Work

A Unified View of Optimal Kernel Hypothesis Testing

Year: 2025

Type: preprint

Abstract: This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with two adaptive kernel selection methods (kernel pooling and aggregation), and under various testing constraints: computational efficiency, differential privacy, and robustness to data corruption. Intuition behind the derivation of the power results is provided in a unified way across the three frameworks, and open problems are highlighted.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2503.07084

Author: Schrab, Antonin

Institutions: University of London, Institut national de recherche en sciences et technologies du numérique, MODAL: MOdel for Data Analysis and Learning, Gatsby Computational Neuroscience Unit, University College London

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4414687703

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