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Estimation of Markov Chain via Rank-Constrained Likelihood

Author(s): Li, Xudong; Wang, Mengdi; Zhang, Anru

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dc.contributor.authorLi, Xudong-
dc.contributor.authorWang, Mengdi-
dc.contributor.authorZhang, Anru-
dc.date.accessioned2020-02-24T20:24:02Z-
dc.date.available2020-02-24T20:24:02Z-
dc.date.issued2018-01-01en_US
dc.identifier.citationLi, X, Wang, M, Zhang, A. (2018). Estimation of Markov chain via rank-constrained likelihood. 35th International Conference on Machine Learning, ICML 2018, 7 (4729 - 4744).en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1t20r-
dc.description.abstractThis paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank- constrained likelihood maximization. Statistical upper bounds are provided for the Kullback- Leiber divergence and the ii risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments show that the proposed estimator achieves better empirical performance than other popular approaches. © Copyright 2018 by the author(s).en_US
dc.format.extent4729 - 4744en_US
dc.language.isoen_USen_US
dc.relation.ispartofProceedings of the 35th International Conference on Machine Learning, Stockholm, Sweden, PMLR 80, 2018en_US
dc.rightsAuthor's manuscripten_US
dc.titleEstimation of Markov Chain via Rank-Constrained Likelihooden_US
dc.typeJournal Articleen_US
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceedingen_US

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