  Quantification learning deals with the task of estimating the target label
distribution under label shift. In this paper, we first present a unifying
framework, distribution feature matching (DFM), that recovers as particular
instances various estimators introduced in previous literature. We derive a
general performance bound for DFM procedures, improving in several key aspects
upon previous bounds derived in particular cases. We then extend this analysis
to study robustness of DFM procedures in the misspecified setting under
departure from the exact label shift hypothesis, in particular in the case of
contamination of the target by an unknown distribution. These theoretical
findings are confirmed by a detailed numerical study on simulated and
real-world datasets. We also introduce an efficient, scalable and robust
version of kernel-based DFM using the Random Fourier Feature principle.
