  Over the last century, risk scores have been the most popular form of
predictive model used in healthcare and criminal justice. Risk scores are
sparse linear models with integer coefficients; often these models can be
memorized or placed on an index card. Typically, risk scores have been created
either without data or by rounding logistic regression coefficients, but these
methods do not reliably produce high-quality risk scores. Recent work used
mathematical programming, which is computationally slow. We introduce an
approach for efficiently producing a collection of high-quality risk scores
learned from data. Specifically, our approach produces a pool of almost-optimal
sparse continuous solutions, each with a different support set, using a
beam-search algorithm. Each of these continuous solutions is transformed into a
separate risk score through a "star ray" search, where a range of multipliers
are considered before rounding the coefficients sequentially to maintain low
logistic loss. Our algorithm returns all of these high-quality risk scores for
the user to consider. This method completes within minutes and can be valuable
in a broad variety of applications.
