Inverse Modeling: A Strategy To Cope With Non-Linearity

In the big data era, discovering and modeling potentially non-linear relationships between predictors and responses might be one of the toughest challenges in modern data analysis. Most forward regression modeling procedures are seriously compromised due to the curse of dimension. In this chapter, we show that the inverse modeling idea, originated from the Sliced Inverse Regression (SIR), can help us detect nonlinear relations effectively, and survey a few recent advances, both algorithmically and theoretically, in which the inverse modeling idea leads to unforeseeable benefits in nonlinear variable selection and nonparametric screening.