论文标题
带有自适应添加剂矩形和其他分段功能模板的脊回归
Ridge regression with adaptive additive rectangles and other piecewise functional templates
论文作者
论文摘要
我们为功能性线性回归模型提出了$ L_ {2} $ - 基于罚款算法，其中系数函数通过数据驱动的形状模板$γ$缩小，该模型被限制通过限制其基础扩展来属于一类零件函数。特别是，我们专注于可以将$γ$表示为$ q $矩形的总和，这些矩形与回归误差相对于$ q $矩形的总和。由于找到分段函数的最佳结位置的问题是非convex，因此所提出的参数化允许减少全局优化方案中的变量数量，从而导致拟合算法在近似合适的模板和求解convex Ridge样问题之间交替。我们方法的预测能力和解释性在多个模拟和两个现实世界案例研究上显示。
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $γ$, which is constrained to belong to a class of piecewise functions by restricting its basis expansion. In particular, we focus on the case where $γ$ can be expressed as a sum of $q$ rectangles that are adaptively positioned with respect to the regression error. As the problem of finding the optimal knot placement of a piecewise function is nonconvex, the proposed parametrization allows to reduce the number of variables in the global optimization scheme, resulting in a fitting algorithm that alternates between approximating a suitable template and solving a convex ridge-like problem. The predictive power and interpretability of our method is shown on multiple simulations and two real world case studies.
