# Gini-regularized Optimal Transport with an Application to Spatio-Temporal Forecasting

arXiv: https://arxiv.org/abs/1712.02512 · HTML: https://mlsanity.com/paper/1712.02512/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2017.

## Built on by (most cited first, 4 of 4)

- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Optimal transport with f-divergence regularization and generalized Sinkhorn algorithm](https://mlsanity.com/paper/2105.14337/) (2021)
- [Bringing regularized optimal transport to lightspeed: a splitting method adapted for GPUs](https://mlsanity.com/paper/2305.18483/) (2023)
- [GeOT: A spatially explicit framework for evaluating spatio-temporal predictions](https://mlsanity.com/paper/2410.11709/) (2024)

## Abstract (arXiv)

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.