Support vector machine (SVM) is one of the
most popular classification algorithms in the machine learning
literature. We demonstrate that SVM can be used to balance
covariates and estimate average causal effects under the
unconfoundedness assumption. Specifically, we adapt the SVM
classifier as a kernel-based weighting procedure that minimizes the
maximum mean discrepancy between the treatment and control groups
while simultaneously maximizing effective sample size. We also show
that SVM is a continuous relaxation of the quadratic integer program
for computing the largest balanced subset, establishing its direct
relation to the cardinality matching method. Another important
feature of SVM is that the regularization parameter controls the
trade-off between covariate balance and effective sample size. As a
result, the existing SVM path algorithm can be used to compute the
balance-sample size frontier. We characterize the bias of causal
effect estimation arising from this trade-off, connecting the
proposed SVM procedure to the existing kernel balancing methods.
Finally, we conduct simulation and empirical studies to evaluate the
performance of the proposed methodology and find that SVM is
competitive with the state-of-the-art covariate balancing methods.
(Last updated in February 2021) |