  Existing causal discovery methods based on combinatorial optimization or
search are slow, prohibiting their application on large-scale datasets. In
response, more recent methods attempt to address this limitation by formulating
causal discovery as structure learning with continuous optimization but such
approaches thus far provide no statistical guarantees. In this paper, we show
that by efficiently parallelizing existing causal discovery methods, we can in
fact scale them to thousands of dimensions, making them practical for
substantially larger-scale problems. In particular, we parallelize the LiNGAM
method, which is quadratic in the number of variables, obtaining up to a
32-fold speed-up on benchmark datasets when compared with existing sequential
implementations. Specifically, we focus on the causal ordering subprocedure in
DirectLiNGAM and implement GPU kernels to accelerate it. This allows us to
apply DirectLiNGAM to causal inference on large-scale gene expression data with
genetic interventions yielding competitive results compared with specialized
continuous optimization methods, and Var-LiNGAM for causal discovery on U.S.
stock data.
