Roughness Penalty for liquid Scorecards

by   Bruce Hoadley, et al.

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.



There are no comments yet.


page 1

page 2

page 3

page 4


The f-divergence and Loss Functions in ROC Curve

Given two data distributions and a test score function, the Receiver Ope...

Adaptive Smoothing V-Spline for Trajectory Reconstruction

Trajectory reconstruction is the process of inferring the path of a movi...

Monotone cubic spline interpolation for functions with a strong gradient

Spline interpolation has been used in several applications due to its fa...

Efficient Estimation of Pathwise Differentiable Target Parameters with the Undersmoothed Highly Adaptive Lasso

We consider estimation of a functional parameter of a realistically mode...

General P-splines for non-uniform B-splines

P-spline represents an unknown univariate function with uniform B-spline...

A substitute for the classical Neumann–Morgenstern characteristic function in cooperative differential games

In this paper, we present a systematic overview of different endogenous ...

A penalty criterion for score forecasting in soccer

This note proposes a penalty criterion for assessing correct score forec...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.