Model-free Variable Selection via Learning Gradients

Description

Variable selection has attracted tremendous interests in the past two decades. It has awide spectrum of applications, including computational biology, information compression,text mining, and social network modeling. Given the large number of variables in thesescenarios, variable selection becomes increasingly important, since it is generally believedthat only a small number of variables are truly informative while others are noises for theobjective of analysis.This proposed research project aims to develop novel statistical theories, methods,and computing algorithms for model-free variable selection. The key idea is to formu-late the proposed variable selection method in a gradient learning framework equippedwith a flexible reproducing kernel Hilbert space. It assumes no distributional model,admits general predictor effects, allows for efficient computation, and attains desirabletheoretical properties. This is in sharp contrast to most existing variable selection meth-ods whose success largely relies on restrictive model assumptions. Theoretical propertiesof the proposed method will be investigated, and asymptotic and finite-sample upperbounds will be established. Besides methodological and theoretical developments, thePI will also develop efficient computing algorithms and platforms to facilitate large-scaleoptimization, involving high-dimensional parameter estimation and requiring real-timeand on-line processing for a vast amount of data.