Model selection for high-dimensional linear regression with dependent observations
This addresses model selection challenges for researchers in statistics and machine learning dealing with high-dimensional data, though it is incremental as it builds on existing greedy algorithms and information criteria.
The paper tackles the problem of model selection in high-dimensional linear regression with dependent observations by proposing the orthogonal greedy algorithm (OGA) combined with a high-dimensional Akaike's information criterion (HDAIC) to determine iterations, achieving optimal convergence rates without prior knowledge of sparsity.
We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike's information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achieve the optimal convergence rate without knowledge of how sparse the underlying high-dimensional model is.