Model-based SIR for dimension reduction

TL;DR

This paper introduces a model-based sliced inverse regression (MSIR) method that overcomes the symmetric relationship limitation of traditional SIR, offering improved flexibility and performance in dimension reduction tasks across various datasets.

Contribution

The paper proposes a novel MSIR approach based on Gaussian mixtures, extending SIR to handle symmetric relationships without additional assumptions.

Findings

MSIR outperforms traditional SIR and other methods as sample size increases.

MSIR is flexible and effective across different regression functions.

Real data applications demonstrate MSIR's practical utility.

Abstract

A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further assumptions. Extensive numerical studies are presented to compare the new method with some of most popular dimension reduction methods, such as SIR, sliced average variance estimation, principal Hessian direction, and directional regression. MSIR appears sufficiently flexible to accommodate various regression functions, and its performance is comparable with or better, particularly as sample size grows, than other available methods. Lastly, MSIR is illustrated with two real data examples about ozone concentration regression, and hand-written digit classification.