Estimation of Markov Chain via Rank-Constrained Likelihood

Xudong Li; Mengdi Wang; Anru Zhang

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arXiv · 1804.00795

Estimation of Markov Chain via Rank-Constrained Likelihood

Xudong Li·Mengdi Wang·Anru Zhang

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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 $\ell_2$ 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.

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BibTeX RIS

Xudong Li, Mengdi Wang, Anru Zhang. 2018-04-03. Estimation of Markov Chain via Rank-Constrained Likelihood. https://arxiv.org/abs/1804.00795

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