Overview of sufficient dimension reduction

Abstract

Dimension reduction plays an essential role when working with large datasets, especially when the number of predictors is much larger than the number of observations. In the context of regression, sufficient dimension reduction (SDR) refers to a class of methodologies that both perform dimension reduction on covariates and no information to predict the outcome from the original covariates is lost after the reduction. Combining dimension reduction with the sufficiency principle of statistical inference, SDR has increasingly gained popularity and showed strong performance in large and big datasets. The talk will provide an overview of some popular SDR methods and their recent developments on some complex settings, such as high-dimensional and longitudinal datasets.