Fusing Sufficient Dimension Reduction with Neural Networks

We consider the regression problem where the dependence of the response Y on a set of predictors X is fully captured by the regression function E(Y | X)=g(B'X), for an unknown function g and low rank parameter B matrix. We combine neural networks with sufficient dimension reduction in order to remove the limitation of small p and n of the latter. We show in simulations that the proposed estimator is on par with competing sufficient dimension reduction methods in small p and n settings, such as minimum average variance estimation and conditional variance estimation. Among those, it is the only computationally applicable in large p and n problems.