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|Abstract:||This 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).|
|Citation:||Li, 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).|
|Pages:||4729 - 4744|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Proceedings of the 35th International Conference on Machine Learning, Stockholm, Sweden, PMLR 80, 2018|
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