State Compression of Markov Processes via Empirical Low-Rank Estimation

02/08/2018

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by   Anru Zhang, et al.

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Model reduction is a central problem in analyzing complex systems and high-dimensional data. We study the state compression of finite-state Markov process from its empirical trajectories. We adopt a low-rank model which is motivated by the state aggregation of controlled systems. A spectral method is proposed for estimating the frequency and transition matrices, estimating the compressed state spaces, and recovering the state aggregation structure if there is any. We provide upper bounds for the estimation and recovery errors and matching minimax lower bounds.