Regularization-Based Methods for Ordinal Quantification
Mirko Bunse Alejandro Moreo Fabrizio Sebastiani Martin Senz
Quantification, i.e., the task of training predictors of the class prevalence
values in sets of unlabeled data items, has received increased attention in
recent years. However, most quantification research has concentrated on
developing algorithms for binary and multiclass problems in which the classes
are not ordered. Here, we 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 proposed by authors from very different research fields, such as
data mining and astrophysics, who were unaware of each others' developments.
Third, we propose a novel class of regularized OQ algorithms, which outperforms
existing algorithms in our experiments. The key to this gain in performance is
that our regularization prevents ordinally implausible estimates, assuming that
ordinal distributions tend to be smooth in practice. We informally verify this
assumption for several real-world applications.