We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

翻译：我们提出了一种基于约束的算法，用于在存在潜在混杂因素的情况下，从观测时间序列数据中学习因果结构。我们假设一个离散时间、平稳的结构向量自回归过程，其中包含时间因果关系和同期因果关系。我们可能会问，时间因果关系和同期因果关系是否应该区别对待。所提出的算法通过先学习长期时间因果关系，再学习短期时间因果关系，最后学习同期因果关系，逐步精炼因果图。这种因果关系的学习顺序减少了所需的统计检验次数。我们在实验中验证了这一减少，并证明与现有最优算法相比，该算法在合成数据上具有更高的准确性，在实际数据上能生成更合理的因果图。