A0915
Title: Non-linear variable selection via kernel regression with high-dimensionality
Authors: Yuta Umezu - Nagasaki University (Japan) [presenting]
Abstract: In a high-dimensional scenario, where the number of covariates is much larger than the sample size, marginal screening is a fundamental technique for model selection. We focus on extracting non-linear relationships between response and covariates based on kernelized marginal regression models with sparsity inducing penalty. From the representer theorem and KKT conditions, our screening method can simply be implemented and enjoys the sure screening property under some mild conditions, that is, all active covariates will be retained with probability converging to one even in a high-dimensional setting. In addition, we consider choosing a thresholding value for screening. Since our screening score can be considered as generalized V-statistics, its asymptotic distribution can be derived, so we can asymptotically control the expected false positive rate at the same time as assuring sure screening property. We will also present several simulation studies and a real data example for checking the performance of our method.
