Fitting feature-dependent Markov chains

We describe a method for fitting a Markov chain, with a state transition matrix that depends on a feature vector, to data that can include missing values. Our model consists of separate logistic regressions for each row of the transition matrix. We fit the parameters in the model by maximizing the l...

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Bibliographic Details
Published in:Journal of global optimization 2023-11, Vol.87 (2-4), p.329-346
Main Authors: Barratt, Shane, Boyd, Stephen
Format: Article
Language:English
Subjects:
Analysis
Computer Science
Markov processes
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
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Description
Summary:We describe a method for fitting a Markov chain, with a state transition matrix that depends on a feature vector, to data that can include missing values. Our model consists of separate logistic regressions for each row of the transition matrix. We fit the parameters in the model by maximizing the log-likelihood of the data minus a regularizer. When there are missing values, the log-likelihood becomes intractable, and we resort to the expectation-maximization (EM) heuristic. We illustrate the method on several examples, and describe our efficient Python open-source implementation.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01198-0