Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation

Kun Deng and Dayu Huang

International Journal of Systems Science, 2015, vol. 46, issue 11, 2029-2047

Abstract: This paper is concerned with model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov chain. The Kullback–Leibler divergence rate is used to measure the similarity between two Markov chains; the nuclear norm is used to approximate the rank function. A nuclear-norm regularised optimisation problem is formulated to approximately find the optimal low-rank approximation. The proposed regularised problem is analysed and performance bounds are obtained through the convex analysis. An iterative fixed point algorithm is developed based on the proximal splitting technique to compute the optimal solutions. The effectiveness of this approach is illustrated via numerical examples.

Date: 2015
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DOI: 10.1080/00207721.2013.844284

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