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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...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publication website:
https://jmlr.org/papers/v23/20-1466.html

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St John's College
Role:
Author
ORCID:
0000-0002-5630-9694
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:
Pubs id:
936933
Local pid:
pubs:936933
Deposit date:
2022-11-03

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