ArticleIEEE transactions on information theory2020
Spectral State Compression of Markov Processes.
Article in IEEE transactions on information theory, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- SM-TCN: Multi-Resolution Sparse Convolution Network for Efficient High-Dimensional Time Series Forecast.Sensors (Basel, Switzerland) · 2025Article
- Detection and evaluation of clusters within sequential data.Data mining and knowledge discovery · 2025Article
- Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration.IEEE transactions on information theory · 2022Article
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2 authors.
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Abstract
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study the rank and features of Markov processes, as well as properties like representability, aggregability, and lumpability. We develop spectral methods for estimating the transition matrix of a low-rank Markov model, estimating the leading subspace spanned by Markov features, and recovering latent structures like state aggregation and lumpable partition of the state space. We prove statistical upper bounds for the estimation errors and nearly matching minimax lower bounds. Numerical studies are performed on synthetic data and a dataset of New York City taxi trips.
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