  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 measurement is much lower than that of
causal influence. To overcome this problem, numerous methods have been
proposed, yet either was limited to the linear case or failed to achieve
identifiability. In this paper, we propose a constraint-based algorithm that
can identify the entire causal structure from subsampled time series, without
any parametric constraint. Our observation is that the challenge of subsampling
arises mainly from hidden variables at the unobserved time steps. Meanwhile,
every hidden variable has an observed proxy, which is essentially itself at
some observable time in the future, benefiting from the temporal structure.
Based on these, we can leverage the proxies to remove the bias induced by the
hidden variables and hence achieve identifiability. Following this intuition,
we propose a proxy-based causal discovery algorithm. Our algorithm is
nonparametric and can achieve full causal identification. Theoretical
advantages are reflected in synthetic and real-world experiments.
