Model selection for high-dimensional linear regression with dependent\n observations

2019/06/18 by Ching‐Kang Ing, Ing, Ching-Kang · 2 citations
Computer Science · Engineering · Mathematics · #62F07 #62F12 #63M30 #Bayesian Methods and Mixture Models #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1906.07395

openalex publication_date 2019/06/18 · openalex created_date 2022/07/12 · openalex updated_date 2026/07/28

Abstract

We investigate the prediction capability of the orthogonal greedy algorithm\n(OGA) in high-dimensional regression models with dependent observations. The\nrates of convergence of the prediction error of OGA are obtained under a\nvariety of sparsity conditions. To prevent OGA from overfitting, we introduce a\nhigh-dimensional Akaike's information criterion (HDAIC) to determine the number\nof OGA iterations. A key contribution of this work is to show that OGA, used in\nconjunction with HDAIC, can achieve the optimal convergence rate without\nknowledge of how sparse the underlying high-dimensional model is.\n

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• Forward Variable Selection in Ultra-High Dimensional Linear Regression Using Gram-Schmidt Orthogonalization
• High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality

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