Model reduction of Markov chains via low-rank approximation

This paper is concerned with the model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov transition matrix. A nuclear-norm regularized optimization problem is proposed for this purpose, in which the Kullback-Leibler divergence rate is used to measure the similarity between two Markov chains, and the nuclear norm is used to approximate the rank function. An efficient iterative optimization algorithm is developed to compute the solution to the regularized problem. The effectiveness of this approach is demonstrated via numerical examples.