Dimension Reduction via Supervised Clustering of Regression Coefficients: A Review

TL;DR

This review discusses dimension reduction methods that cluster predictors based on their effects on the response, highlighting their advantages over traditional methods like OLS and lasso, especially in multicollinear settings.

Contribution

It provides a comprehensive overview of supervised clustering techniques for regression coefficients, emphasizing their applications and performance benefits.

Findings

Supervised clustering improves predictor selection accuracy.

Methods outperform OLS and lasso in multicollinearity scenarios.

Applications span genetics, epidemiology, and neuroimaging.

Abstract

The development and use of dimension reduction methods is prevalent in modern statistical literature. This paper reviews a class of dimension reduction techniques which aim to simultaneously select relevant predictors and find clusters within them which share a common effect on the response. Such methods have been shown to have superior performance relative to OLS estimates and the lasso [Tibshirani, 1996] especially when multicollinearity in the predictors is present. Their applications, which include genetics, epidemiology, and fMRI studies, are also discussed.