Multi-label quantification

Quantification, variously called supervised prevalence estimation or learning to quantify, is the supervised learning task of generating predictors of the relative frequencies (a.k.a. prevalence values) of the classes of interest in unlabelled data samples. While many quantification methods have been proposed in the past for bi- nary problems and, to a lesser extent, single-label multiclass problems, the multi-label setting (i.e., the scenario in which the classes of interest are not mutually exclusive) remains by and large unexplored. A straightfor- ward solution to the multi-label quantification problem could simply consist of recasting the problem as a set of independent binary quantification problems. Such a solution is simple but naïve, since the independence assumption upon which it rests is, in most cases, not satisfied. In these cases, knowing the relative frequency of one class could be of help in determining the prevalence of other related classes. We propose the first truly multi-label quantification methods, i.e., methods for inferring estimators of class prevalence values that strive to leverage the stochastic dependencies among the classes of interest in order to predict their relative frequencies more accurately. We show empirical evidence that natively multi-label solutions outperform the naïve approaches by a large margin. The code to reproduce all our experiments is available online.