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Structure learning for continuous time Bayesian networks via penalized likelihood

Author

Listed:
  • Tomasz Ca̧kała
  • Błażej Miasojedow
  • Wojciech Rejchel
  • Maryia Shpak

Abstract

Continuous time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, social science models or medicine. The literature on this topic is usually focused on a case when a dependence structure of a system is known and we are to determine conditional transition intensities (parameters of a network). In the paper, we study a structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes a dependence structure of a graph with high probability. We also investigate properties of the procedure in numerical studies.

Suggested Citation

  • Tomasz Ca̧kała & Błażej Miasojedow & Wojciech Rejchel & Maryia Shpak, 2024. "Structure learning for continuous time Bayesian networks via penalized likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(4), pages 1707-1729, December.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:4:p:1707-1729
    DOI: 10.1111/sjos.12747
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    References listed on IDEAS

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    1. Paul Fearnhead & Chris Sherlock, 2006. "An exact Gibbs sampler for the Markov‐modulated Poisson process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 767-784, November.
    2. Piotr Pokarowski & Wojciech Rejchel & Agnieszka Sołtys & Michał Frej & Jan Mielniczuk, 2022. "Improving Lasso for model selection and prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 831-863, June.
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