Signature moments to characterize laws of stochastic processes
Statistics Theory
2022-09-16 v2 Probability
Machine Learning
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1810.10971,
title = {Signature moments to characterize laws of stochastic processes},
author = {Ilya Chevyrev and Harald Oberhauser},
journal= {arXiv preprint arXiv:1810.10971},
year = {2022}
}
Comments
42 pages. Restructured the text, changed experiments in final section. To appear in Journal of Machine Learning Research