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28 March 2024
 
  » arxiv » 1706.6359

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Learning Markov Models from Closed Loop Data-sets
Jonathan Epperlein ; Robert Shorten ; Sergiy Zhuk ;
Date 20 Jun 2017
AbstractMany practical problems involve developing prediction and optimization tools to manage supply and demand issues. Almost always, these prediction tools are created with a view to affecting behavioural change, thus creating a feedback loop. Clearly, successful applications actuating behavioural change, affect the original model underpinning the predictor, leading to an inconsistency. This feedback loop is often not considered in standard so-called Big Data learning techniques which rely upon machine learning/statistical learning machinery. The objective of this paper is to develop mathematically sound tools for the design of predictor feedback systems. For this purpose we use the framework of Hidden Markov Models (HMMs). More specifically, we assume that we observe a time series which is a path (output) of a Markov chain ${R}$ modulated by another Markov chain ${S}$, i.e. the transition matrix of ${R}$ is unknown and depends on the current realisation of the state of ${S}$. The transition matrix of the latter is also unknown. In other words, at each time instant, ${S}$ selects a transition matrix for ${R}$ within a given set which consist of a number of known and uncertain matrices of a given dimension. The state of ${S}$, in turn, depends on the current state of ${R}$ thus introducing a feed-back loop. We propose a modification of classical Baum-Welsch algorithm, a variant of Expectation-Maximization family of methods, which estimates the transition matrices of ${S}$ and ${R}$. Experimental study shows that most of the time our method is identifying the "true" transition matrices which were used to generate the data. In all cases, the likelihoods of our estimates are at least as good as the likelihoods of the "true" matrices.
Source arXiv, 1706.6359
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