Minimax Testing of Identity to a Reference Ergodic Markov Chain

Geoffrey Wolfer; Aryeh Kontorovich

Minimax Testing of Identity to a Reference Ergodic Markov Chain

Geoffrey Wolfer
, Aryeh Kontorovich

Research output: Contribution to journal › Conference article › peer-review

12 Scopus citations

Abstract

We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or ε-far from a given reference chain. We obtain nearly matching (up to logarithmic factors) upper and lower sample complexity bounds for our notion of distance, which is based on total variation. Perhaps surprisingly, we discover that the sample complexity depends solely on the properties of the known reference chain and does not involve the unknown chain at all, which is not even assumed to be ergodic.

Original language	English
Pages (from-to)	191-201
Number of pages	11
Journal	Proceedings of Machine Learning Research
Volume	108
State	Published - 1 Jan 2020
Event	23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020 - Virtual, Online Duration: 26 Aug 2020 → 28 Aug 2020

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

Cite this

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abstract = "We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or ε-far from a given reference chain. We obtain nearly matching (up to logarithmic factors) upper and lower sample complexity bounds for our notion of distance, which is based on total variation. Perhaps surprisingly, we discover that the sample complexity depends solely on the properties of the known reference chain and does not involve the unknown chain at all, which is not even assumed to be ergodic.",

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AU - Kontorovich, Aryeh

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N2 - We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or ε-far from a given reference chain. We obtain nearly matching (up to logarithmic factors) upper and lower sample complexity bounds for our notion of distance, which is based on total variation. Perhaps surprisingly, we discover that the sample complexity depends solely on the properties of the known reference chain and does not involve the unknown chain at all, which is not even assumed to be ergodic.

AB - We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or ε-far from a given reference chain. We obtain nearly matching (up to logarithmic factors) upper and lower sample complexity bounds for our notion of distance, which is based on total variation. Perhaps surprisingly, we discover that the sample complexity depends solely on the properties of the known reference chain and does not involve the unknown chain at all, which is not even assumed to be ergodic.

UR - https://www.scopus.com/pages/publications/85107853532

M3 - Conference article

AN - SCOPUS:85107853532

SN - 2640-3498

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JO - Proceedings of Machine Learning Research

JF - Proceedings of Machine Learning Research

T2 - 23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020

Y2 - 26 August 2020 through 28 August 2020

ER -

Minimax Testing of Identity to a Reference Ergodic Markov Chain

Abstract

ASJC Scopus subject areas

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