Identifying causal interactions in complex dynamical systems is a fundamental challenge across the computational sciences. Existing functional connectivity methods capture correlations but not causation. While addressing directionality, popular causal inference tools such as Granger causality and the Peter-Clark algorithm rely on restrictive assumptions that limit their applicability to high-resolution time-series data, such as the large-scale recordings now standard in neuroscience. Here, we introduce CITS (Causal Inference in Time Series), a nonparametric framework for inferring statistically causal structure from multivariate time series. CITS models dynamics using a structural causal model of arbitrary Markov order and statistical tests for lagged conditional independence. We prove consistency under mild assumptions and demonstrate superior accuracy over state-of-the-art baselines across simulated linear, nonlinear, and recurrent neural network benchmarks. Applying CITS to large-scale neuronal recordings from the mouse visual cortex, thalamus, and hippocampus, we uncover stimulus-specific causal pathways and inter-regional hierarchies that align with known anatomy while revealing new functional insights. We further highlight CITS ability in accurately identifying conditional dependencies within small inferred neuronal motifs. These results establish CITS as a theoretically grounded and empirically validated method for discovering interpretable statistically causal networks in neural time series. Beyond neuroscience, the framework is broadly applicable to causal discovery in complex temporal systems across domains.

翻译：识别复杂动力系统中的因果相互作用是计算科学领域的一个基本挑战。现有的功能连接性方法仅能捕捉相关性而非因果关系。尽管诸如格兰杰因果和Peter-Clark算法等流行的因果推断工具能够处理方向性问题，但它们依赖于限制性假设，这限制了其在高分辨率时间序列数据（如当前神经科学标准的大规模记录数据）中的适用性。本文提出CITS（时间序列因果推断），一种从多元时间序列推断统计因果结构的非参数框架。CITS使用任意马尔可夫阶数的结构因果模型对动态进行建模，并通过滞后条件独立性统计检验进行推断。我们在温和假设下证明了其一致性，并在模拟的线性、非线性和循环神经网络基准测试中展示了其优于现有先进基线的准确性。将CITS应用于小鼠视觉皮层、丘脑和海马的大规模神经元记录数据，我们发现了与已知解剖结构一致且能揭示新功能见解的刺激特异性因果通路和区域间层级结构。我们进一步展示了CITS在准确识别小型推断神经元基序内条件依赖关系方面的能力。这些结果确立了CITS作为一种理论基础坚实且经验证有效的方法，可用于发现神经时间序列中可解释的统计因果网络。除神经科学外，该框架广泛适用于跨领域复杂时间系统中的因果发现。