A1647
Title: Adaptive variable selection on high-dimensional non-parametric regression models
Authors: ChienTong Lin - National Sun Yat-sen University (Taiwan) [presenting]
Suneel Babu Chatla - University of Texas at El Paso (United States)
Ching-Kang Ing - National Tsing Hua University (Taiwan)
Abstract: Sparse linear models that incorporate non-parametric elements have gained significant prominence because of their flexibility in high-dimensional applications. While standard estimation frameworks often rely on finite basis expansions and assume an underlying sparse structure to achieve parsimony, the practical implementation of these models is hindered by the fact that both the degree of sparsity and the functional smoothness are generally unknown. Conventional approaches often circumvent this by pre-specifying the number of basis functions, focusing solely on variable selection. The convergence properties of the Orthogonal Greedy Algorithm (OGA) across diverse regimes of sparsity and smoothness are investigated. A unified framework is proposed that utilizes a high-dimensional information criterion (HDIC) to jointly determine the optimal number of OGA iterations and the basis dimension. The resulting procedure, OGA combined with HDIC (OGA+HDIC), 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. Furthermore, OGA+HDIC attains the optimal convergence rate in two fundamental high-dimensional contexts: the linear additive model and the varying coefficient model.
