State Compression of Markov Processes via Empirical Low-Rank Estimation.

Model reduction is a central problem in analyzing complex systems andhigh-dimensional data. We study the state compression of finite-state Markovprocess from its empirical trajectories. We adopt a low-rank model which ismotivated by the state aggregation of controlled systems. A spectral method isproposed for estimating the frequency and transition matrices, estimating thecompressed state spaces, and recovering the state aggregation structure ifthere is any. We provide upper bounds for the estimation and recovery errorsand matching minimax lower bounds.