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.

中文翻译：

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具有相关观测值的高维线性回归模型选择

我们研究了正交贪婪算法 (OGA) 在具有相关观测值的高维回归模型中的预测能力。OGA 预测误差的收敛速度是在各种稀疏条件下获得的。为了防止 OGA 过拟合，我们引入了高维 Akaike 信息准则 (HDAIC) 来确定 OGA 迭代次数。这项工作的一个关键贡献是表明 OGA 与 HDAIC 结合使用，可以在不了解底层高维模型的稀疏程度的情况下实现最佳收敛速度。