论文标题
液体记分卡的粗糙度罚款
Roughness Penalty for liquid Scorecards
论文作者
论文摘要
液体记分卡具有液体特征，在该特征上，特征得分是液态范围内特征的平滑函数。平滑函数基于B-Splines，通常是立方体。相反，传统记分卡的特征得分是特征的步骤函数。以前，有两种方法可以控制液体特征分数的平滑度：（1）较小的类别的粗分类，曲线越平滑； （2）惩罚参数，惩罚得分系数向量的规范。但是，在经典的立方样条拟合理论中，直接衡量曲线粗糙度的度量被用作拟合目标函数中的惩罚项。在本文中，我为我们的特征分数详细介绍了这个概念的详细信息，这是立方b-spline的线性函数。粗糙度惩罚是第二个衍生品平方的组成部分。随着您从零到无穷大的特征平滑度参数，特征得分从粗糙到非常平滑。随着一个人从粗糙移动到光滑，可口的特征得分从页面上跳下来。案例研究说明了这一点。该案例研究还表明，最大化验证差异的平滑度参数并不总是产生最可口的模型。
A liquid scorecard has liquid characteristics, for which the characteristic score is a smooth function of the characteristic over a liquid range. The smooth function is based on B-splines, typically cubic. In contrast, the characteristic scores for traditional scorecards are step functions of the characteristics. Previously, there were two ways to control the smoothness of the liquid characteristic score: (1) coarse classing where the fewer the number of classes, the smoother the curve; (2) the penalty parameter, which penalizes the norm of the score coefficient vector. However, in classical cubic spline fitting theory, a direct measure of curve roughness is used as a penalty term in the fitting objective function. In this paper, I work out the details of this concept for our characteristic scores, which are linear functions of a cubic B-spline basis. The roughness penalty is the integral of the second derivative squared. As you vary the characteristic smoothness parameter from zero to infinity, the characteristic score goes from being rough to being very smooth. As one moves from rough to smooth, the palatable characteristic score jumps off the page. This is illustrated by a case study. This case study also shows that smoothness parameters, which maximize validation divergence, do not always yield the most palatable model.
