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.

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