國立政治大學統計學系 學術演講

主講人：林建同 助理教授
國立中山大學應用數學系

題 目：Adaptive Variable Selection on High-Dimensional Non-Parametric Regression Models

時 間：民國115年11月9日 (星期一) 下午1：30

地 點：國立政治大學逸仙樓050101教室

摘 要：
Sparse linear models that incorporate non-parametric elements have gained significant prominence due to their flexibility in high-dimensional applications. We examine the classical basis-expansion framework, which typically requires preselecting the number of basis functions to be specified in advance despite the unknown target smoothness and often focuses on variable selection even when the sparsity structure is also unknown. We addresses this gap by investigating the convergence properties of the Orthogonal Greedy Algorithm (OGA) across diverse regimes of sparsity and smoothness. We propose a unified framework that utilizes a high-dimensional Akaike's information criterion (HDAIC) to jointly determine the optimal number of OGA iterations and the basis dimension. We show that the resulting procedure, OGA combined with HDAIC (OGA+HDAIC), is adaptive in the sense that it automatically achieves the optimal trade-off between variance and squared bias without prior knowledge of the sparsity or the smoothness levels.

Keywords: Variable selection, Weak sparsity, Orthogonal Greedy Algorithm, High-dimensional Akaike’s Information Criterion, Non-parametric regression.