论文标题
平稳适应性的中心山脊估计器
Smoothly Adaptively Centered Ridge Estimator
论文作者
论文摘要
侧重于具有平滑功能协变量的线性模型，我们提出了一个基于非零的山脊的惩罚框架（CARCH），在该山脊中，惩罚的中心以监督的方式最佳地重新恢复，从普通的山脊解决方案开始作为初始中心功能。特别是，我们引入了一个凸公式，该公式共同估计模型的系数和重量函数，对中心功能的粗糙度惩罚和重量的约束，以恢复可能平滑和/或稀疏的解决方案。这允许使用非著作和连续的可变选择机制，因为重量函数可以膨胀或使初始中心膨胀，以将惩罚靶向适当的中心，目的是减少非零系数上不需要的收缩，而不是均匀地缩小整个系数函数。作为我们方法的可解释性和预测能力的经验证据，我们提供了一项模拟研究和两种现实世界光谱应用，并具有分类和回归。
With a focus on linear models with smooth functional covariates, we propose a penalization framework (SACR) based on the nonzero centered ridge, where the center of the penalty is optimally reweighted in a supervised way, starting from the ordinary ridge solution as the initial centerfunction. In particular, we introduce a convex formulation that jointly estimates the model's coefficients and the weight function, with a roughness penalty on the centerfunction and constraints on the weights in order to recover a possibly smooth and/or sparse solution. This allows for a non-iterative and continuous variable selection mechanism, as the weight function can either inflate or deflate the initial center, in order to target the penalty towards a suitable center, with the objective to reduce the unwanted shrinkage on the nonzero coefficients, instead of uniformly shrinking the whole coefficient function. As empirical evidence of the interpretability and predictive power of our method, we provide a simulation study and two real world spectroscopy applications with both classification and regression.
