The minimax rate of HSIC estimation for translation-invariant kernels

Kalinke, Florian and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2024) The minimax rate of HSIC estimation for translation-invariant kernels. In: Globerson, A., Mackey, L., Belgrave, D., Fan, A., Paquet, U., Tomczak, J. and Zhang, C., (eds.) Advances in Neural Information Processing Systems 37 (NeurIPS 2024). Neural Information Processing Systems Foundation. ISBN 9798331314385

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Abstract

Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of M ≥ 2 random variables. Probably the most widespread independence measure relying on kernels is the socalled Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on Rd for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is On−1/2 . Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nyström-based one) on Rd.

Item Type:	Book Section
Additional Information:	© 2025 The Author(s)
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics H Social Sciences > HA Statistics
Date Deposited:	26 Jun 2025 11:45
Last Modified:	26 Jun 2025 11:45
URI:	http://eprints.lse.ac.uk/id/eprint/128571

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