Matching Distributions Algorithms Based on the Earth Mover's Distance for Ordinal Quantification.

Abstract

The goal of quantification learning is to induce models capable of accurately predicting the class distribution for new bags of unseen examples. These models only return the prevalence of each class in the bag because prediction of individual examples is irrelevant in these tasks. A prototypical application of ordinal quantification is to predict the proportion of opinions that fall into each category from one to five stars. Ordinal quantification has hardly been studied in the literature, and in fact, only one approach has been proposed so far. This article presents a comprehensive study of ordinal quantification, analyzing the applicability of the most important algorithms devised for multiclass quantification and proposing three new methods that are based on matching distributions using Earth mover's distance (EMD). Empirical experiments compare 14 algorithms on synthetic and benchmark data. To statistically analyze the obtained results, we further introduce an EMD-based scoring function. The main conclusion is that methods using a criterion somehow related to EMD, including two of our proposals, obtain significantly better results.