液体记分卡的粗糙度惩罚

摘要：

流动记分卡具有流动特性，对于该流动特性，特性分数是流动范围内的特性的平滑函数。平滑函数基于B样条，通常是三次。相比之下，传统记分卡的特征分数是特征的阶跃函数。以前，有两种方法来控制液体特征分数的平滑度：（1）粗分类，其中类的数量越少，曲线越平滑;（2）惩罚参数，惩罚分数系数向量的范数。然而，在经典的三次样条拟合理论中，曲线粗糙度的直接测量被用作拟合目标函数中的惩罚项。在本文中，我工作的细节，这一概念为我们的特征分数，这是一个三次B样条基的线性函数。粗糙度惩罚是二阶导数平方的积分。当您将特征平滑度参数从零变化到无穷大时，特征得分将从粗糙变为非常平滑。当一个人从粗糙到光滑的移动，可口的特征得分跳离页面。一个案例研究说明了这一点。这个案例研究还表明，平滑参数，最大限度地提高验证分歧，并不总是产生最可口的模型。

英文摘要：

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.

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