Kernelized cumulants: beyond kernel mean embeddings

Bonnier, Patric, Oberhauser, Harald and Szabo, Zoltan (2023) Kernelized cumulants: beyond kernel mean embeddings. In: Advances in Neural Information Processing Systems 36. Curran Associates, Inc..

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Abstract

In Rd, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert spaces (RKHS) using tools from tensor algebras and show that they are computationally tractable by a kernel trick. These kernelized cumulants provide a new set of all-purpose statistics; the classical maximum mean discrepancy and Hilbert-Schmidt independence criterion arise as the degree one objects in our general construction. We argue both theoretically and empirically (on synthetic, environmental, and traffic data analysis) that going beyond degree one has several advantages and can be achieved with the same computational complexity and minimal overhead in our experiments.

Item Type:	Book Section
Additional Information:	© 2023 The Author(s).
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	31 Oct 2023 10:18
Last Modified:	26 Apr 2024 15:48
URI:	http://eprints.lse.ac.uk/id/eprint/120569

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