  As standardly implemented in R or the Tetrad program, causal search
algorithms used most widely or effectively by scientists have severe
dimensionality constraints that make them inappropriate for big data problems
without sacrificing accuracy. However, implementation improvements are
possible. We explore optimizations for the Greedy Equivalence Search that allow
search on 50,000-variable problems in 13 minutes for sparse models with 1000
samples on a four-processor, 16G laptop computer. We finish a problem with 1000
samples on 1,000,000 variables in 18 hours for sparse models on a supercomputer
node at the Pittsburgh Supercomputing Center with 40 processors and 384 G RAM.
The same algorithm can be applied to discrete data, with a slower discrete
score, though the discrete implementation currently does not scale as well in
our experiments; we have managed to scale up to about 10,000 variables in
sparse models with 1000 samples.
