Fast Constraint-Based Structure Learning for Continuous-Time Bayesian Networks

Alessandro Bregoli, Marco Midali, Marco Scutari, Fabio Stella, Alessio Zanga
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:112-126, 2026.

Abstract

Continuous-time Bayesian networks (CTBNs) are a class of probabilistic graphical models representing complex processes evolving over time. Applying Bayesian networks’ state-space factorisation to the time-space mathematical structure of continuous-time Markov processes (CTMPs) significantly reduces the number of parameters required to model them. However, learning the structure of a CTBN that correctly factorises the corresponding CTMP is difficult, as the set of candidate graphs grows exponentially with the size of the CTMP random vector. In this work, we present HITON-CTPC, a novel constraint-based algorithm to navigate the search space of CTBNs more efficiently. Specifically, we incorporate the key steps of the HITON-PC BN structure-learning algorithm into the CTPC CTBN algorithm, thereby enabling us to add heuristics for determining the order of conditional independence tests. We assessed the performance of the proposed solution through an extensive set of synthetic experiments spanning a wide range of state-space and time-space configurations. We observed that HITON-CTPC achieves competitive structural accuracy while significantly reducing execution time. Furthermore, we evaluated the new HITON-CTPC algorithm using the Beijing Multi-Site Air Quality data set (Chen, 2017) to assess its ability to reconstruct significant relationships in a real-world scenario.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-bregoli26a, title = {Fast Constraint-Based Structure Learning for Continuous-Time {Bayesian} Networks}, author = {Bregoli, Alessandro and Midali, Marco and Scutari, Marco and Stella, Fabio and Zanga, Alessio}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {112--126}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/bregoli26a/bregoli26a.pdf}, url = {https://proceedings.mlr.press/v343/bregoli26a.html}, abstract = {Continuous-time Bayesian networks (CTBNs) are a class of probabilistic graphical models representing complex processes evolving over time. Applying Bayesian networks’ state-space factorisation to the time-space mathematical structure of continuous-time Markov processes (CTMPs) significantly reduces the number of parameters required to model them. However, learning the structure of a CTBN that correctly factorises the corresponding CTMP is difficult, as the set of candidate graphs grows exponentially with the size of the CTMP random vector. In this work, we present HITON-CTPC, a novel constraint-based algorithm to navigate the search space of CTBNs more efficiently. Specifically, we incorporate the key steps of the HITON-PC BN structure-learning algorithm into the CTPC CTBN algorithm, thereby enabling us to add heuristics for determining the order of conditional independence tests. We assessed the performance of the proposed solution through an extensive set of synthetic experiments spanning a wide range of state-space and time-space configurations. We observed that HITON-CTPC achieves competitive structural accuracy while significantly reducing execution time. Furthermore, we evaluated the new HITON-CTPC algorithm using the Beijing Multi-Site Air Quality data set (Chen, 2017) to assess its ability to reconstruct significant relationships in a real-world scenario.} }
Endnote
%0 Conference Paper %T Fast Constraint-Based Structure Learning for Continuous-Time Bayesian Networks %A Alessandro Bregoli %A Marco Midali %A Marco Scutari %A Fabio Stella %A Alessio Zanga %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-bregoli26a %I PMLR %P 112--126 %U https://proceedings.mlr.press/v343/bregoli26a.html %V 343 %X Continuous-time Bayesian networks (CTBNs) are a class of probabilistic graphical models representing complex processes evolving over time. Applying Bayesian networks’ state-space factorisation to the time-space mathematical structure of continuous-time Markov processes (CTMPs) significantly reduces the number of parameters required to model them. However, learning the structure of a CTBN that correctly factorises the corresponding CTMP is difficult, as the set of candidate graphs grows exponentially with the size of the CTMP random vector. In this work, we present HITON-CTPC, a novel constraint-based algorithm to navigate the search space of CTBNs more efficiently. Specifically, we incorporate the key steps of the HITON-PC BN structure-learning algorithm into the CTPC CTBN algorithm, thereby enabling us to add heuristics for determining the order of conditional independence tests. We assessed the performance of the proposed solution through an extensive set of synthetic experiments spanning a wide range of state-space and time-space configurations. We observed that HITON-CTPC achieves competitive structural accuracy while significantly reducing execution time. Furthermore, we evaluated the new HITON-CTPC algorithm using the Beijing Multi-Site Air Quality data set (Chen, 2017) to assess its ability to reconstruct significant relationships in a real-world scenario.
APA
Bregoli, A., Midali, M., Scutari, M., Stella, F. & Zanga, A.. (2026). Fast Constraint-Based Structure Learning for Continuous-Time Bayesian Networks. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:112-126 Available from https://proceedings.mlr.press/v343/bregoli26a.html.

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