Inferring causation from time series data is of scientific interest in different disciplines, particularly in neural connectomics. While different approaches exist in the literature with parametric modeling assumptions, we focus on a non-parametric model for time series satisfying a Markovian structural causal model with stationary distribution and without concurrent effects. We show that the model structure can be used to its advantage to obtain an elegant algorithm for causal inference from time series based on conditional dependence tests, coined Causal Inference in Time Series (CITS) algorithm. We describe Pearson's partial correlation and Hilbert-Schmidt criterion as candidates for such conditional dependence tests that can be used in CITS for the Gaussian and non-Gaussian settings, respectively. We prove the mathematical guarantee of the CITS algorithm in recovering the true causal graph, under standard mixing conditions on the underlying time series. We also conduct a comparative evaluation of performance of CITS with other existing methodologies in simulated datasets. We then describe the utlity of the methodology in neural connectomics -- in inferring causal functional connectivity from time series of neural activity, and demonstrate its application to a real neurobiological dataset of electro-physiological recordings from the mouse visual cortex recorded by Neuropixel probes.

翻译：从时间序列数据中推断因果关系是不同学科领域中的科学问题，尤其在神经连接组学中具有重要意义。现有文献中存在多种基于参数化建模假设的方法，而本文聚焦于满足平稳分布且无并发效应的马尔可夫结构因果模型的非参数化时间序列模型。我们证明该模型结构可被充分利用，从而获得一种基于条件依赖性检验的时间序列因果推断优雅算法，命名为时间序列因果推断（CITS）算法。我们分别描述了皮尔逊偏相关系数和希尔伯特-施密特准则作为高斯与非高斯场景下CITS算法可用的条件依赖性检验候选方案。在时间序列满足标准混合条件的前提下，我们证明了CITS算法恢复真实因果图的数学保证。通过仿真数据集，我们还将CITS算法与现有其他方法进行了性能对比评估。随后，我们阐述了该方法在神经连接组学中的实用性——用于从神经活动时间序列推断因果功能连接，并展示了其对Neuropixel探针记录的小鼠视觉皮层电生理真实神经生物学数据集的应用实例。