TY - JOUR
T1 - Identity Testing of Reversible Markov Chains
AU - Fried, Sela
AU - Wolfer, Geoffrey
N1 - Funding Information:
Acknowledgments Sela Fried is supported by the
Funding Information:
Sela Fried is supported by the Israel Science Foundation (ISF) through grant no. 1456/18 and by the European Research Council through grant no. 949707. Geoffrey Wolfer is supported by the Japan Society for the Promotion of Science. We thank the referees for their careful reading and valuable comments that helped us improve the presentation of this paper.
Publisher Copyright:
Copyright © 2022 by the author(s)
PY - 2022/1/1
Y1 - 2022/1/1
N2 - We consider the problem of identity testing of Markov chain transition matrices based on a single trajectory of observations under the distance notion introduced by Daskalakis et al. (2018a) and further analyzed by Cherapanamjeri and Bartlett (2019). Both works made the restrictive assumption that the Markov chains under consideration are symmetric. In this work we relax the symmetry assumption and show that it is possible to perform identity testing under the much weaker assumption of reversibility, provided that the stationary distributions of the reference and of the unknown Markov chains are close under a distance notion related to the separation distance. Additionally, we provide intuition on the distance notion of Daskalakis et al. (2018a) by showing how it behaves under several natural operations. In particular, we address some of their open questions.
AB - We consider the problem of identity testing of Markov chain transition matrices based on a single trajectory of observations under the distance notion introduced by Daskalakis et al. (2018a) and further analyzed by Cherapanamjeri and Bartlett (2019). Both works made the restrictive assumption that the Markov chains under consideration are symmetric. In this work we relax the symmetry assumption and show that it is possible to perform identity testing under the much weaker assumption of reversibility, provided that the stationary distributions of the reference and of the unknown Markov chains are close under a distance notion related to the separation distance. Additionally, we provide intuition on the distance notion of Daskalakis et al. (2018a) by showing how it behaves under several natural operations. In particular, we address some of their open questions.
UR - http://www.scopus.com/inward/record.url?scp=85143360659&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85143360659
SN - 2640-3498
VL - 151
SP - 798
EP - 817
JO - Proceedings of Machine Learning Research
JF - Proceedings of Machine Learning Research
T2 - 25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022
Y2 - 28 March 2022 through 30 March 2022
ER -