Learning Causal Structure of Time Series using Best Order Score Search

Irene Gema Castillo Mansilla, Urmi Ninad
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:182-209, 2026.

Abstract

Causal structure learning from observational data is central to many scientific and policy domains, but the time series setting common to many disciplines poses several challenges due to temporal dependence. In this paper we focus on score-based causal discovery for multivariate time series and introduce TS-BOSS, a time series extension of the recently proposed Best Order Score Search (BOSS) (Andrews et al., 2023). TS-BOSS performs a permutation-based search over dynamic Bayesian network structures while leveraging grow–shrink trees to cache intermediate score computations, preserving the scalability and strong empirical performance of BOSS in the static setting. We provide theoretical guarantees establishing the soundness of TS-BOSS under suitable assumptions, and we present an intermediate result that extends classical subgraph minimality results for permutation-based methods to the dynamic (time series) setting. This result paves the way for time series extensions of sparsest permutation-based causal discovery algorithms under suitable stationarity assumptions. We present experimental results on synthetic data that highlight the high accuracy of TS-BOSS.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-castillo-mansilla26a, title = {Learning Causal Structure of Time Series using Best Order Score Search}, author = {Castillo Mansilla, Irene Gema and Ninad, Urmi}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {182--209}, 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/castillo-mansilla26a/castillo-mansilla26a.pdf}, url = {https://proceedings.mlr.press/v343/castillo-mansilla26a.html}, abstract = {Causal structure learning from observational data is central to many scientific and policy domains, but the time series setting common to many disciplines poses several challenges due to temporal dependence. In this paper we focus on score-based causal discovery for multivariate time series and introduce TS-BOSS, a time series extension of the recently proposed Best Order Score Search (BOSS) (Andrews et al., 2023). TS-BOSS performs a permutation-based search over dynamic Bayesian network structures while leveraging grow–shrink trees to cache intermediate score computations, preserving the scalability and strong empirical performance of BOSS in the static setting. We provide theoretical guarantees establishing the soundness of TS-BOSS under suitable assumptions, and we present an intermediate result that extends classical subgraph minimality results for permutation-based methods to the dynamic (time series) setting. This result paves the way for time series extensions of sparsest permutation-based causal discovery algorithms under suitable stationarity assumptions. We present experimental results on synthetic data that highlight the high accuracy of TS-BOSS.} }
Endnote
%0 Conference Paper %T Learning Causal Structure of Time Series using Best Order Score Search %A Irene Gema Castillo Mansilla %A Urmi Ninad %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-castillo-mansilla26a %I PMLR %P 182--209 %U https://proceedings.mlr.press/v343/castillo-mansilla26a.html %V 343 %X Causal structure learning from observational data is central to many scientific and policy domains, but the time series setting common to many disciplines poses several challenges due to temporal dependence. In this paper we focus on score-based causal discovery for multivariate time series and introduce TS-BOSS, a time series extension of the recently proposed Best Order Score Search (BOSS) (Andrews et al., 2023). TS-BOSS performs a permutation-based search over dynamic Bayesian network structures while leveraging grow–shrink trees to cache intermediate score computations, preserving the scalability and strong empirical performance of BOSS in the static setting. We provide theoretical guarantees establishing the soundness of TS-BOSS under suitable assumptions, and we present an intermediate result that extends classical subgraph minimality results for permutation-based methods to the dynamic (time series) setting. This result paves the way for time series extensions of sparsest permutation-based causal discovery algorithms under suitable stationarity assumptions. We present experimental results on synthetic data that highlight the high accuracy of TS-BOSS.
APA
Castillo Mansilla, I.G. & Ninad, U.. (2026). Learning Causal Structure of Time Series using Best Order Score Search. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:182-209 Available from https://proceedings.mlr.press/v343/castillo-mansilla26a.html.

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