Fusing Sufficient Dimension Reduction with Neural Networks

TL;DR

This paper introduces a neural network-based method that combines with sufficient dimension reduction to efficiently handle high-dimensional regression problems where the response depends on predictors through a low-dimensional projection.

Contribution

It proposes a novel neural network approach that extends sufficient dimension reduction techniques to large p and n settings, overcoming previous computational limitations.

Findings

Performs comparably to existing methods in small p and n scenarios

Is computationally feasible for large p and n datasets

Maintains accuracy while scaling to high-dimensional data

Abstract

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.