In this paper, we propose a non-negative feature selection/feature grouping (nnFSG) method for general sign-constrained high-dimensional regression problems that allows regression coefficients to be disjointly homogeneous, with sparsity as a special case. To solve the resulting non-convex optimization problem, we provide an algorithm that incorporates the difference of convex programming, augmented Lagrange and coordinate descent methods. Furthermore, we show that the aforementioned nnFSG method recovers the oracle estimate consistently, and that the mean-squared errors are bounded. Additionally, we examine the performance of our method using finite sample simulations and applying it to a real protein mass spectrum dataset.

中文翻译：

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高维符号约束特征选择和分组

在本文中，我们为一般符号约束的高维回归问题提出了一种非负特征选择/特征分组 (nnFSG) 方法，该方法允许回归系数不相交地齐次，稀疏性作为特例。为了解决由此产生的非凸优化问题，我们提供了一种算法，该算法结合了凸规划、增广拉格朗日和坐标下降方法的差异。此外，我们表明上述 nnFSG 方法一致地恢复了预言机估计，并且均方误差是有界的。此外，我们使用有限样本模拟检查我们的方法的性能，并将其应用于真实的蛋白质质谱数据集。