Random Fourier signature features

Toth, Csaba, Oberhauser, Harald and Szabo, Zoltan ORCID: 0000-0001-6183-7603 (2024) Random Fourier signature features. SIAM Journal on Mathematics of Data Science. ISSN 2577-0187 (In Press)

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Abstract

Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to compute the signature kernel scale quadratically in terms of the length and the number of the sequences. To mitigate this severe computational bottleneck, we develop a random Fourier feature-based acceleration of the signature kernel acting on the inherently non-Euclidean domain of sequences. We show uniform approximation guarantees for the proposed unbiased estimator of the signature kernel, while keeping its computation linear in the sequence length and number. In addition, combined with recent advances on tensor projections, we derive two even more scalable time series features with favourable concentration properties and computational complexity both in time and memory. Our empirical results show that the reduction in computational cost comes at a negligible price in terms of accuracy on moderate-sized datasets, and it enables one to scale to large datasets up to a million time series.

Item Type:	Article
Additional Information:	© 2024 SIAM
Divisions:	Statistics
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics
Date Deposited:	04 Sep 2024 11:12
Last Modified:	12 Dec 2024 04:27
URI:	http://eprints.lse.ac.uk/id/eprint/125341

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