  Quantification represents the problem of predicting class distributions in a
given target set. It also represents a growing research field in supervised
machine learning, for which a large variety of different algorithms has been
proposed in recent years. However, a comprehensive empirical comparison of
quantification methods that supports algorithm selection is not available yet.
In this work, we close this research gap by conducting a thorough empirical
performance comparison of 24 different quantification methods. To consider a
broad range of different scenarios for binary as well as multiclass
quantification settings, we carried out almost 3 million experimental runs on
40 data sets. We observe that no single algorithm generally outperforms all
competitors, but identify a group of methods including the Median Sweep and the
DyS framework that perform significantly better in binary settings. For the
multiclass setting, we observe that a different, broad group of algorithms
yields good performance, including the Generalized Probabilistic Adjusted
Count, the readme method, the energy distance minimization method, the EM
algorithm for quantification, and Friedman's method. More generally, we find
that the performance on multiclass quantification is inferior to the results
obtained in the binary setting. Our results can guide practitioners who intend
to apply quantification algorithms and help researchers to identify
opportunities for future research.
