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Fitting feature-dependent Markov chains

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  • Shane Barratt

    (Stanford University)

  • Stephen Boyd

    (Stanford University)

Abstract

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.

Suggested Citation

  • Shane Barratt & Stephen Boyd, 2023. "Fitting feature-dependent Markov chains," Journal of Global Optimization, Springer, vol. 87(2), pages 329-346, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01198-0
    DOI: 10.1007/s10898-022-01198-0
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    References listed on IDEAS

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    1. J.Robert Beck & Stephen G. Pauker, 1983. "The Markov Process in Medical Prognosis," Medical Decision Making, , vol. 3(4), pages 419-458, December.
    2. Frank A. Sonnenberg & J. Robert Beck, 1993. "Markov Models in Medical Decision Making," Medical Decision Making, , vol. 13(4), pages 322-338, December.
    3. Gordon Woo, 2002. "Quantitative Terrorism Risk Assessment," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 4(1), pages 7-14, April.
    4. Isabelle Deltour & Sylvia Richardson & Jean-Yves Le Hesran, 1999. "Stochastic Algorithms for Markov Models Estimation with Intermittent Missing Data," Biometrics, The International Biometric Society, vol. 55(2), pages 565-573, June.
    5. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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