Traditional methods for matching in causal
inference are impractical for high-dimensional
datasets. They suffer from the curse of dimensionality: exact matching and coarsened exact
matching find exponentially fewer matches
as the input dimension grows, and propensity score matching may match highly unrelated units together. To overcome this problem, we develop theoretical results which motivate the use of neural networks to obtain
non-trivial, multivariate balancing scores of a
chosen level of coarseness, in contrast to the
classical, scalar propensity score. We leverage
these balancing scores to perform matching
for high-dimensional causal inference and call
this procedure neural score matching. We
show that our method is competitive against
other matching approaches on semi-synthetic
high-dimensional datasets, both in terms of
treatment effect estimation and reducing imbalanc