arXiv subjects

Bruce Hoadley

Publications and source records attributed to Bruce Hoadley.

5 recordsLinked to original sources

arXiv2020

Score Engineered Logistic Regression

In several FICO studies logistic regression has been shown to be a very competitive technology for developing unrestricted scoring models, especially for performance metrics like ROC area. Application of logistic regression has been hampered by the lack of software to handle complex score engineering such as shape and pattern constraints. The purpose of this paper is to develop a sequential quadratic programming algorithm for score engineered logistic regression. This approach is based on a simple Taylor series expansion of minus log likelihood, which is locally quadratic. and fits in with the method that applies quadratic programming to B-Splines.

stat.ME↗

arXiv2020

Score Engineered Robust Least Squares Regression

In other FICO Technical Papers, I have shown how to fit Generalized Additive Models (GAM) with shape constraints using quadratic programming applied to B-Spline component functions. In this paper, I extend the method to Robust Least Squares Regression.

stat.ME↗

arXiv2020

Roughness Penalty for liquid Scorecards

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.

stat.ME↗

arXiv2020

A Quadratic Programming Solution to the FICO Credit Scoring Problem

After decades of experience in developing credit scores, the FICO corporation has formulated the FICO Credit Scoring Problem as follows: Find the Generalized Additive Model (GAM), with component step functions, that maximizes divergence subject to the PILE (Palatability, Interpretability, Legal, Explain-ability) constraints. The PILE constraints are also called shape constraints, and satisfying them is called score engineering. Before 2003, FICO used an algorithm, based on Linear Programing, to approximately solve the FICO Credit Scoring Problem. In this paper, I develop an exact solution to the FICO Credit Scoring Problem. Finding the exact solution has eluded FICO for years. Divergence is a ratio of quadratic functions of the score weights. I show that the max divergence problem can be transformed into a quadratic program. The quadratic programming formulation allows one to handle the PILE constraints very easily. FICO currently uses aspects of this technology to develop the famous FICO Credit Score.

stat.ME↗

arXiv2020

Liquid Scorecards

Traditional credit scorecards are generalized additive models (GAMs) with step functions as the component functions. The shapes of the step functions may be constrained in order to satisfy the PILE (Palatability, Interpretability, Legal, Explain-ability) constraints. Before 2003, FICO used Linear Programming to find the traditional scorecard that approximately maximizes divergence subject to the PILE constraints. In this paper, I introduce the Liquid Scorecard, that allows the component functions to be, at least partially, smooth curves. I use Quadratic Programming and B-Spline theory to find the Liquid Scorecard that exactly maximizes divergence subject to the PILE constraints. FICO uses aspects of this technology to develop the famous FICO Credit Score.

stat.OT↗