Title: Model selection for high-dimensional sparse nonlinear models using Chebyshev greedy algorithms
Authors: Ching-Kang Ing - National Tsing Hua University (Taiwan) [presenting]
Abstract: Model selection problems in high-dimensional sparse nonlinear models are considered. We first use the Chebyshev greedy algorithm (CGA) to perform variable screening and derive, under a fairly general sparsity condition, its rate of convergence in terms of the number of iterations and the approximation error. We then introduce a high-dimensional information criterion (HDIC) to determine the number of CGA iterations and show that CGA used in conjunction with HDIC achieves the optimal rate of convergence. Finally, the proposed method is applied to the analysis of high-dimensional logistic and Cox regressions.