Title: Gini-regularized Optimal Transport with an Application to Spatio-Temporal Forecasting,
Abstract: Rapidly growing product lines and services require a finer-granularity
forecast that considers geographic locales. However the open question remains,
how to assess the quality of a spatio-temporal forecast? In this manuscript we
introduce a metric to evaluate spatio-temporal forecasts. This metric is based
on an Opti- mal Transport (OT) problem. The metric we propose is a constrained
OT objec- tive function using the Gini impurity function as a regularizer. We
demonstrate through computer experiments both the qualitative and the
quantitative charac- teristics of the Gini regularized OT problem. Moreover, we
show that the Gini regularized OT problem converges to the classical OT
problem, when the Gini regularized problem is considered as a function of
{\lambda}, the regularization parame-ter. The convergence to the classical OT
solution is faster than the state-of-the-art Entropic-regularized OT[Cuturi,
2013] and results in a numerically more stable algorithm.