Nyström Kernel Stein Discrepancy

Kalinke, Florian, Szabo, Zoltan ORCID: 0000-0001-6183-7603 and Sriperumbudur, Bharath K. (2024) Nyström Kernel Stein Discrepancy. In: 28th International Conference on Artificial Intelligence and Statistics, 2025-05-03 - 2025-05-05, Splash Beach Resort in Mai Khao, Phuket, Thailand, THA. (In Press)

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Abstract

Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the kernel Stein discrepancy (KSD), which combines Stein's method with kernel techniques, gained considerable attention. Through the Stein operator, KSD allows the construction of powerful goodness-of-fit tests where it is sufficient to know the target distribution up to a multiplicative constant. However, the typical U- and V-statistic-based KSD estimators suffer from a quadratic runtime complexity, which hinders their application in large-scale settings. In this work, we propose a Nyström-based KSD acceleration -- with runtime O(mn+m³) for n samples and m≪n Nyström points -- , show its √n-consistency under the null with a classical sub-Gaussian assumption, and demonstrate its applicability for goodness-of-fit testing on a suite of benchmarks.

Item Type:	Conference or Workshop Item (Poster)
Additional Information:	© 2025 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	14 Jun 2024 09:48
Last Modified:	23 Jan 2025 15:51
URI:	http://eprints.lse.ac.uk/id/eprint/123872

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