Matching distributions algorithms based on the Earth Mover's distance for Ordinal Quantification

Alberto Castaño, Pablo González, Jaime Alonso, Juan Jose del Coz

Abstract:

The goal of quantization 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 1 to 5 stars. Ordinal quantification has hardly been studied in the literature, in fact only one approach has been proposed
so far. This paper 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 Movement
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.