Applications of the Theory of Aggregated Markov Processes in Stochastic Learning Theory

2023/11/01 by Fangyuan Lin, Lin, Fangyuan
Computer Science · #60J20 #Applications (stat.AP) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2311.01476

openalex publication_date 2023/11/01 · openalex created_date 2023/11/07 · openalex updated_date 2026/07/28

Abstract

A stochastic process that arises by composing a function with a Markov process is called an aggregated Markov process (AMP). The purpose of composing a Markov process with a function can be a reduction of dimensions, e.g., a projection onto certain coordinates. The theory around AMP has been extensively studied e.g. by Dynkin, Cameron, Rogers and Pitman, and Kelly, all of whom provided sufficient conditions for an AMP to remain Markov. In another direction, Larget provided a canonical representation for AMP, which can be used to verify the equivalence of two AMPs. The purpose of this paper is to describe how the theory of AMP can be applied to stochastic learning theory as they learn a particular task.

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