Dimension Reduction via Supervised Clustering of Regression Coefficients: A Review

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.