### Abstract

Time granularity is an important factor in characterizing dynamical systems. Hybrid time Bayesian networks model the dynamics of systems that contain both irregularly-timed variables and variables whose evolution is naturally described by discrete time. The former observations are modeled as variables in continuous-time manner and the latter are modeled by discrete-time random variables. We address the problem of learning parameters of hybrid time models from complete data where all the states are known at any time point, and from incomplete trajectories, where continuous-time variables are observed only at some time points. We show that for the complete case, the parameters can be estimated straightforwardly. When some continuous-time variables are (partially) unobserved, it becomes infeasible to learn the parameters in closed form. In that case, we propose to use Markov chain Monte Carlo sampling to estimate the posterior distribution over the parameters. We tested the approach on a number of hybrid time models where continuous-time variables are completely or partially observed, showing that close estimation of the original parameters can be recovered. A medical example is used to illustrate the learning parameters of hybrid time Bayesian networks.

Original language | English |
---|---|

Title of host publication | Proceedings of the Eighth International Conference on Probabilistic Graphical Models |

Subtitle of host publication | Volume 52 of the JMLR Workshop and Conference Proceedings: PGM 2016, Lugano, 6–9 September 201 |

Editors | Alessandro Antonucci, Giorgio Corani, Cassio Polpo de Campos |

Publisher | PMLR |

Pages | 287-298 |

Number of pages | 12 |

Volume | 52 |

Publication status | Published - 2016 |

Event | International Conference on Probabilistic Graphical Models 2016 - Università della Svizzera Italiana (USI), Lugano, Switzerland Duration: 6 Sep 2016 → 9 Sep 2016 Conference number: 8 https://www2.idsia.ch/cms/pgm/ |

### Conference

Conference | International Conference on Probabilistic Graphical Models 2016 |
---|---|

Abbreviated title | PGM 2016 |

Country | Switzerland |

City | Lugano |

Period | 6/09/16 → 9/09/16 |

Internet address |

## Fingerprint Dive into the research topics of 'Learning Parameters of Hybrid Time Bayesian Networks'. Together they form a unique fingerprint.

## Cite this

Liu, M., Hommersom, A., Heijden, M. V. D., & Lucas, P. J. F. (2016). Learning Parameters of Hybrid Time Bayesian Networks. In A. Antonucci, G. Corani, & C. P. de Campos (Eds.),

*Proceedings of the Eighth International Conference on Probabilistic Graphical Models: Volume 52 of the JMLR Workshop and Conference Proceedings: PGM 2016, Lugano, 6–9 September 201*(Vol. 52, pp. 287-298). PMLR. http://proceedings.mlr.press/v52/liu16.pdf