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Poster
Estimation of Markov Chain via Rank-constrained Likelihood
XUDONG LI · Mengdi Wang · Anru Zhang

Fri Jul 13 09:15 AM -- 12:00 PM (PDT) @ Hall B #50
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.