Fusing sufficient dimension reduction with neural networks

Neural networks are combined with sufficient dimension reduction methodology in order to remove the limitation of small p and n of the latter. NN-SDR applies when the dependence of the response Y on a set of predictors X is fully captured by the regression function g(B′X), for an unknown function g and low rank parameter B matrix. It is shown that the proposed estimator is on par with competing sufficient dimension reduction methods, such as minimum average variance estimation and conditional variance estimation, in small p and n settings in simulations. Its main advantage is its scalability in regressions with large data, for which the other methods are infeasible.