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A new algorithm for inference in HMM's with lower span complexity

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  • Pereira, Diogo
  • Nunes, Cláudia
  • Rodrigues, Rui

Abstract

The maximum likelihood problem for Hidden Markov Models is usually numerically solved by the Baum-Welch algorithm, which uses the Expectation-Maximization algorithm to find the estimates of the parameters. This algorithm has a recursion depth equal to the data sample size and cannot be computed in parallel, which limits the use of modern GPUs to speed up computation time. A new algorithm is proposed that provides the same estimates as the Baum-Welch algorithm, requiring about the same number of iterations, but is designed in such a way that it can be parallelized. As a consequence, it leads to a significant reduction in the computation time. This reduction is illustrated by means of numerical examples, where we consider simulated data as well as real datasets.

Suggested Citation

  • Pereira, Diogo & Nunes, Cláudia & Rodrigues, Rui, 2024. "A new algorithm for inference in HMM's with lower span complexity," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:csdana:v:195:y:2024:i:c:s0167947324000392
    DOI: 10.1016/j.csda.2024.107955
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    References listed on IDEAS

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    1. Turner, Rolf, 2008. "Direct maximization of the likelihood of a hidden Markov model," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4147-4160, May.
    2. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    3. Stoner, Oliver & Economou, Theo, 2020. "An advanced hidden Markov model for hourly rainfall time series," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
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