Skip to main content

Estimation of Markov Chain via Rank-Constrained Likelihood

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

To refer to this page use:
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).
Publication Date: 1-Jan-2018
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
Version: Author's manuscript

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.