  Causal mediation analysis can unpack the black box of causality and is
therefore a powerful tool for disentangling causal pathways in biomedical and
social sciences, and also for evaluating machine learning fairness. To reduce
bias for estimating Natural Direct and Indirect Effects in mediation analysis,
we propose a new method called DeepMed that uses deep neural networks (DNNs) to
cross-fit the infinite-dimensional nuisance functions in the efficient
influence functions. We obtain novel theoretical results that our DeepMed
method (1) can achieve semiparametric efficiency bound without imposing
sparsity constraints on the DNN architecture and (2) can adapt to certain low
dimensional structures of the nuisance functions, significantly advancing the
existing literature on DNN-based semiparametric causal inference. Extensive
synthetic experiments are conducted to support our findings and also expose the
gap between theory and practice. As a proof of concept, we apply DeepMed to
analyze two real datasets on machine learning fairness and reach conclusions
consistent with previous findings.
