Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurements is much lower than that of causal influence. To overcome this problem, numerous model-based and model-free methods have been proposed, yet either limited to the linear case or failed to establish identifiability. In this work, we propose a model-free algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint. The idea is that the challenge of subsampling arises mainly from \emph{unobserved} time steps and therefore should be handled with tools designed for unobserved variables. Among these tools, we find the proxy variable approach particularly fits, in the sense that the proxy of an unobserved variable is naturally itself at the observed time step. Following this intuition, we establish comprehensive structural identifiability results. Our method is constraint-based and requires no more regularities than common continuity and differentiability. Theoretical advantages are reflected in experimental results.

翻译：从时间序列数据中推断因果结构是许多科学研究的核心目标。此类推断的主要障碍之一是子采样问题，即测量频率远低于因果影响频率。为克服这一问题，已有多种基于模型和无模型的方法被提出，但要么局限于线性情形，要么未能建立可辨识性。本文提出一种无模型算法，可在无任何参数约束的情况下，从子采样时间序列中识别完整因果结构。其核心思想是：子采样的挑战主要源于未观测的时间步，因此应使用针对未观测变量设计的工具来处理。在这些工具中，我们发现代理变量方法尤为契合，因为未观测变量的代理自然就是其在观测时间步上的自身。遵循这一直觉，我们建立了全面的结构可辨识性结果。本方法基于约束，且所需正则性条件不高于常见的连续性与可微性。理论优势在实验结果中得以体现。