This paper investigates the efficient solution of penalized quadratic regressions in high-dimensional settings. We propose a novel and efficient algorithm for ridge-penalized quadratic regression that leverages the matrix structures of the regression with interactions. Building on this formulation, we develop an alternating direction method of multipliers (ADMM) framework for penalized quadratic regression with general penalties, including both single and hybrid penalty functions. Our approach greatly simplifies the calculations to basic matrix-based operations, making it appealing in terms of both memory storage and computational complexity.

翻译：本文研究了高维背景下带惩罚二次回归的高效求解方法。我们提出了一种新颖且高效的岭回归惩罚二次回归算法，该算法充分利用了含交互项回归中的矩阵结构。基于这一公式，我们开发了一个交替方向乘子法（ADMM）框架，适用于具有一般惩罚（包括单一和混合惩罚函数）的带惩罚二次回归。该方法将计算大幅简化为基本的矩阵运算，在内存存储和计算复杂度方面均具有显著优势。