Gini-regularized Optimal Transport with an Application to Spatio-Temporal Forecasting
This work addresses the need for better evaluation metrics in spatio-temporal forecasting, which is crucial for applications like product and service planning, but it appears incremental as it builds on existing OT frameworks.
The authors tackled the problem of evaluating spatio-temporal forecasts by introducing a new metric based on optimal transport, using Gini impurity as a regularizer. They demonstrated that this Gini-regularized OT converges faster and is more numerically stable than existing entropic-regularized OT methods.
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 λ, 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.