Measures of distinguishability between stochastic processes

Quantifying how distinguishable two stochastic processes are is at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this article, we suggest a set of requirement...

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Main Authors: Yang, Chengran, Binder, Felix C., Gu, Mile, Elliott, Thomas J.
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2021
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Online Access:https://hdl.handle.net/10356/146526
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1465262023-02-28T19:54:47Z Measures of distinguishability between stochastic processes Yang, Chengran Binder, Felix C. Gu, Mile Elliott, Thomas J. School of Physical and Mathematical Sciences Complexity Institute Science::Physics Stochastic Processes Information Theory Quantifying how distinguishable two stochastic processes are is at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this article, we suggest a set of requirements for a well-behaved measure of process distinguishability. Moreover, we propose a family of measures, called divergence rates, that satisfy all of these requirements. Focusing on a particular member of this family—the coemission divergence rate—we show that it can be computed efficiently, behaves qualitatively similar to other commonly used measures in their regimes of applicability, and remains well behaved in scenarios where other measures break down. Ministry of Education (MOE) National Research Foundation (NRF) Published version This research is supported by the National Research Foundation (NRF). Singapore, under its NRFF Fellow programme (Award No. NRF-NRFF2016-02), the Lee Kuan Yew Endowment Fund (Postdoctoral Fellowship), Singapore Ministry of Education Tier 1 Grants No. MOE2017-T1-002-043 and No FQXi-RFP-1809 from the Foundational Questions Institute and Fetzer Franklin Fund (a donor-advised fund of Silicon Valley Community Foundation). F.C.B. acknowledges funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska Curie Grant Agreement No. 801110 and the Austrian Federal Ministry of Education, Science, and Research (BMBWF). T.J.E., C.Y., and F.C.B. thank the Centre for Quantum Technologies for their hospitality. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore. 2021-02-23T06:53:07Z 2021-02-23T06:53:07Z 2020 Journal Article Yang, C., Binder, F. C., Gu, M., & Elliott, T. J. (2020). Measures of distinguishability between stochastic processes. Physical Review E, 101(6), 062137-. doi:10.1103/physreve.101.062137 2470-0045 https://hdl.handle.net/10356/146526 10.1103/PhysRevE.101.062137 32688504 2-s2.0-85088351861 6 101 en NRF-NRFF2016-02 MOE2017-T1-002-043 Physical Review E © 2020 American Physical Society (APS). All rights reserved. This paper was published in Physical Review E and is made available with permission of American Physical Society (APS). application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Physics
Stochastic Processes
Information Theory
spellingShingle Science::Physics
Stochastic Processes
Information Theory
Yang, Chengran
Binder, Felix C.
Gu, Mile
Elliott, Thomas J.
Measures of distinguishability between stochastic processes
description Quantifying how distinguishable two stochastic processes are is at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this article, we suggest a set of requirements for a well-behaved measure of process distinguishability. Moreover, we propose a family of measures, called divergence rates, that satisfy all of these requirements. Focusing on a particular member of this family—the coemission divergence rate—we show that it can be computed efficiently, behaves qualitatively similar to other commonly used measures in their regimes of applicability, and remains well behaved in scenarios where other measures break down.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Yang, Chengran
Binder, Felix C.
Gu, Mile
Elliott, Thomas J.
format Article
author Yang, Chengran
Binder, Felix C.
Gu, Mile
Elliott, Thomas J.
author_sort Yang, Chengran
title Measures of distinguishability between stochastic processes
title_short Measures of distinguishability between stochastic processes
title_full Measures of distinguishability between stochastic processes
title_fullStr Measures of distinguishability between stochastic processes
title_full_unstemmed Measures of distinguishability between stochastic processes
title_sort measures of distinguishability between stochastic processes
publishDate 2021
url https://hdl.handle.net/10356/146526
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