  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 binary 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 straightforward 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
na\"ive, 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 na\"ive approaches by a large margin. The
code to reproduce all our experiments is available online.
