Measuring Multivariate Divergences to Improve Neural Network Performances

Measuring distances in multidimensional settings poses a significant challenge encountered across various scientific and engineering disciplines. In this paper, we introduce a novel measure of divergence to quantify the discrepancy between two multidimensional distributions - one predicted by a machine learning model and the other expected. Our approach builds upon the class of Energy Distances and incorporates a whitening pre-processing step, resulting in a divergence that is strictly connected to the new multivariate Gini index. To validate the proposed divergence, we demonstrate its effectiveness as a loss function for training a neural network designed to predict the financial performance of small and medium enterprises.