SPOT: Sparse Optimal Transformations for High Dimensional Variable Selection and Exploratory Regression Analysis

We develop a novel method called SParse Optimal Transformations (SPOT) to simultaneously select important variables and explore relationships between the response and predictor variables in high dimensional nonparametric regression analysis. Not only are the optimal transformations identified by SPOT interpretable, they can also be used for response prediction. We further show that SPOT achieves consistency in both variable selection and parameter estimation. Numerical experiments and real data applications demonstrate that SPOT outperforms other existing methods and can serve as an effective tool in practic e.