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.

翻译：从观测数据中学习因果结构是许多科学和政策领域的核心问题，但常见于多学科的时间序列设置因存在时间依赖性而带来若干挑战。本文聚焦于多元时间序列的基于分数的因果发现，并介绍了TS-BOSS——这是对近期提出的最优序分数搜索方法的时间序列扩展。TS-BOSS在动态贝叶斯网络结构上执行基于置换的搜索，同时利用增长-收缩树缓存中间分数计算，从而在静态场景中保持了BOSS的可扩展性和强大的实证性能。我们在适当假设下建立了TS-BOSS可靠性的理论保证，并提出了一个将经典基于置换方法的子图最小性结果扩展到动态（时间序列）场景的中间结果。在合成数据上的实验表明，TS-BOSS在高自相关区域特别有效，在精度相当的情况下持续获得比标准基于约束方法更高的邻接召回率。总体而言，TS-BOSS为时间序列因果发现提供了一种高性能、可扩展的方法，我们的结果为将基于稀疏性、置换驱动的因果学习理论扩展到动态场景建立了原则性桥梁。