Enhancing Sufficient Dimension Reduction via Hellinger Correlation

TL;DR

This paper introduces a new method for sufficient dimension reduction in single-index models using Hellinger correlation, offering improved detection of the reduction subspace with strong theoretical support and superior empirical performance.

Contribution

The paper develops a novel SDR method based on Hellinger correlation, providing theoretical justification and demonstrating significant performance improvements over existing techniques.

Findings

Enhanced detection of dimension reduction subspace

Outperforms existing SDR methods in experiments

Provides theoretical guarantees for the proposed approach

Abstract

In this work, we develop a new theory and method for sufficient dimension reduction (SDR) in single-index models, where SDR is a sub-field of supervised dimension reduction based on conditional independence. Our work is primarily motivated by the recent introduction of the Hellinger correlation as a dependency measure. Utilizing this measure, we develop a method capable of effectively detecting the dimension reduction subspace, complete with theoretical justification. Through extensive numerical experiments, we demonstrate that our proposed method significantly enhances and outperforms existing SDR methods. This improvement is largely attributed to our proposed method's deeper understanding of data dependencies and the refinement of existing SDR techniques.