AI 中文总结
该研究提出结合协方差估计的多元回归的凸重参数化方法，证明其缩放高斯损失为标准自协调，推导两种算法，模拟及蛋白质表达应用显示其预测误差相近且稠密精度矩阵时速度显著提升。
AI 中文摘要
我们基于多元线性回归的一种重参数化方法，该方法可在重参数化后的回归系数矩阵与精度矩阵上产生联合凸的惩罚似然函数，证明由此得到的缩放高斯损失是标准自协调的。这将联合估计问题纳入复合自协调优化框架，并得到两种算法：近端梯度法与阻尼近端牛顿法。在模拟中，我们评估了算法鲁棒性、收敛迭代次数与运行时间。在蛋白质表达应用中，与经典参数化公式相比，所提出的凸公式取得了相近的均方预测误差，且当拟合的精度矩阵为稠密时，速度可显著提升。
英文摘要
Building on a reparameterization for multivariate linear regression that yields a jointly convex penalized likelihood in the reparameterized regression coefficient matrix and the precision matrix, we show that the resulting scaled Gaussian loss is standard self-concordant. This places the joint estimation problem within composite self-concordant optimization and leads to two algorithms: a proximal gradient method and a damped proximal Newton method. In simulations, we evaluate algorithmic robustness, iterations to convergence, and elapsed time. In a protein expression application, compared with the classical-parameterization formulation, the proposed convex formulation attains similar mean squared prediction error and can be substantially faster when the fitted precision matrix is dense.
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