2022/04/29 by Bernhard C. Geiger, Geiger, Bernhard C.
Computer Science · #60J10 #94A16 #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2204.13896
openalex publication_date 2022/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a smaller state space that is informativeabout certain quantities of interest. The second part considers Markov chain model reduction, which focuses on replacing the original Markov model by a simplified one that yields similar behavior as the original Markov model. We discuss the practical relevance of both approaches in the field of knowledge discovery and data mining by formulating problems of unsupervised machine learning as reduction problems of Markov chains. Finally, we briefly discuss the concept of lumpability, the phenomenon when a coarse graining yields a reduced Markov model.