Ordinal quantification through regularization

Quantification,i.e.,thetaskoftrainingpredictorsoftheclass prevalence values in sets of unlabelled data items, has received increased attention in recent years. However, most quantification research has con- centrated on developing algorithms for binary and multiclass problems in which the classes are not ordered. We here study the ordinal case, i.e., the case in which a total order is defined on the set of n > 2 classes. We give three main contributions to this field. First, we create and make available two datasets for ordinal quantification (OQ) research that overcome the inadequacies of the previously available ones. Second, we experimentally compare the most important OQ algorithms proposed in the literature so far. To this end, we bring together algorithms that are proposed by authors from very different research fields, who were unaware of each other's developments. Third, we propose three OQ algorithms, based on the idea of preventing ordinally implausible estimates through regu- larization. Our experiments show that these algorithms outperform the existing ones if the ordinal plausibility assumption holds.