Learning Causal Structure of Time Series using Best Order Score Search

TL;DR

This paper introduces TS-BOSS, a scalable score-based method for causal discovery in multivariate time series, demonstrating superior performance in high auto-correlation scenarios and extending static causal learning theories to dynamic data.

Contribution

TS-BOSS extends the BOSS algorithm to time series, providing theoretical guarantees and efficient permutation-based search for dynamic causal structure learning.

Findings

TS-BOSS outperforms standard methods in high auto-correlation regimes.

It achieves higher adjacency recall at similar precision levels.

The method is scalable and maintains strong empirical performance.

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.