  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.
