Journal article

Signature moments to characterize laws of stochastic processes

Abstract:: The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic processes and study the topology it induces on the space of laws of stochastic processes. This metric can be kernelized using the signature kernel which allows to efficiently compute it. As an application, we provide a non-parametric two-sample hypothesis test for laws of stochastic processes.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Chevyrev, I., & Oberhauser, H. (2022). Signature moments to characterize laws of stochastic processes. Journal of Machine Learning Research, 23(176), 1−42.

MLA Style

Chevyrev, I., and H. Oberhauser. “Signature Moments to Characterize Laws of Stochastic Processes.” Journal of Machine Learning Research, vol. 23, no. 176, Journal of Machine Learning Research, 2022, p. 1−42.

Chicago Style

Chevyrev, I, and H Oberhauser. 2022. “Signature Moments to Characterize Laws of Stochastic Processes.” Journal of Machine Learning Research 23 (176): 1−42.
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Publication website:: https://jmlr.org/papers/v23/20-1466.html

Authors

+ Chevyrev, I More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: St John's College
Role:: Author
ORCID:: 0000-0002-5630-9694

+ Oberhauser, H More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: St Hugh's College
Role:: Author
ORCID:: 0000-0003-2644-8906

Publisher:: Journal of Machine Learning Research
Journal:: Journal of Machine Learning Research More from this journal
Volume:: 23
Issue:: 176
Pages:: 1−42
Publication date:: 2022-06-22
Acceptance date:: 2022-06-05
EISSN:: 1533-7928
ISSN:: 1532-4435

Language:: English
Keywords:: math.ST

stat.ML

stat.TH

62M99 (Primary) 60G35, 62M07 (Secondary)

math.PR

FFR
Pubs id:: 936933
Local pid:: pubs:936933
Deposit date:: 2022-11-03

Terms of use

Copyright holder:: Chevyrev and Oberhauser
Copyright date:: 2022
Rights statement:: © 2022 Ilya Chevyrev and Harald Oberhauser. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v23/20-1466.html.

Licence:: CC Attribution (CC BY)

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