  We deal with the \textit{selective classification} problem
(supervised-learning problem with a rejection option), where we want to achieve
the best performance at a certain level of coverage of the data. We transform
the original $m$-class classification problem to $(m+1)$-class where the
$(m+1)$-th class represents the model abstaining from making a prediction due
to disconfidence. Inspired by portfolio theory, we propose a loss function for
the selective classification problem based on the doubling rate of gambling.
Minimizing this loss function corresponds naturally to maximizing the return of
a \textit{horse race}, where a player aims to balance between betting on an
outcome (making a prediction) when confident and reserving one's winnings
(abstaining) when not confident. This loss function allows us to train neural
networks and characterize the disconfidence of prediction in an end-to-end
fashion. In comparison with previous methods, our method requires almost no
modification to the model inference algorithm or model architecture.
Experiments show that our method can identify uncertainty in data points, and
achieves strong results on SVHN and CIFAR10 at various coverages of the data.
