Learning Causal Structure of Time Series using Best Order Score Search

2026-03-05

AI Summary

This work addresses the challenge of learning causal structures from observational time series data, where temporal dependencies complicate inference. The authors propose TS-BOSS, an extension of the static BOSS framework to dynamic settings, which performs permutation-based structure search over dynamic Bayesian networks and leverages a grow-shrink tree to cache intermediate scores for computational efficiency. TS-BOSS establishes, for the first time, theoretical guarantees for permutation-based causal discovery in the time series context and generalizes the subgraph minimality result to this setting. Empirical evaluations demonstrate that TS-BOSS achieves significantly higher adjacency recall—particularly on highly autocorrelated synthetic data—while maintaining precision, highlighting its superior performance and scalability.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Topic discovery and tracking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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. Our experiments on synthetic data show that TS-BOSS is especially effective in high auto-correlation regimes, where it consistently achieves higher adjacency recall at comparable precision than standard constraint-based methods. Overall, TS-BOSS offers a high-performing, scalable approach for time series causal discovery and our results provide a principled bridge for extending sparsity-based, permutation-driven causal learning theory to dynamic settings.

Problem

• causal structure learning
• time series
• temporal dependence
• multivariate time series
• observational data

Innovation

• causal discovery
• time series
• dynamic Bayesian networks
• score-based learning
• permutation search