  This paper focuses on causal structure estimation from time series data in
which measurements are obtained at a coarser timescale than the causal
timescale of the underlying system. Previous work has shown that such
subsampling can lead to significant errors about the system's causal structure
if not properly taken into account. In this paper, we first consider the search
for the system timescale causal structures that correspond to a given
measurement timescale structure. We provide a constraint satisfaction procedure
whose computational performance is several orders of magnitude better than
previous approaches. We then consider finite-sample data as input, and propose
the first constraint optimization approach for recovering the system timescale
causal structure. This algorithm optimally recovers from possible conflicts due
to statistical errors. More generally, these advances allow for a robust and
non-parametric estimation of system timescale causal structures from subsampled
time series data.
