Golden Ratio-Based Sufficient Dimension Reduction

TL;DR

This paper introduces a neural network-based method for sufficient dimension reduction that effectively identifies the structural dimension and estimates the central space, leveraging neural network approximation capabilities for efficient high-dimensional data analysis.

Contribution

It presents a novel neural network framework for dimension reduction that improves estimation accuracy and computational efficiency over existing methods.

Findings

Effective identification of structural dimension

Accurate estimation of the central space

Reduced computational cost

Abstract

Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the predictors that can retain as much original information as possible in the relationship between the response and the original predictors. We propose a neural network based sufficient dimension reduction method that not only identifies the structural dimension effectively, but also estimates the central space well. It takes advantages of approximation capabilities of neural networks for functions in Barron classes and leads to reduced computation cost compared to other dimension reduction methods in the literature. Additionally, the framework can be extended to fit practical dimension reduction, making the methodology more applicable in practical settings.