Quantification using Permutation-Invariant Networks based on Histograms
Olaya Pérez-Mon Alejandro Moreo Juan José del Coz Pablo González
Quantification, also known as class prevalence estimation, is the supervised
learning task in which a model is trained to predict the prevalence of each
class in a given bag of examples. This paper investigates the application of
deep neural networks to tasks of quantification in scenarios where it is
possible to apply a symmetric supervised approach that eliminates the need for
classification as an intermediary step, directly addressing the quantification
problem. Additionally, it discusses existing permutation-invariant layers
designed for set processing and assesses their suitability for quantification.
In light of our analysis, we propose HistNetQ, a novel neural architecture that
relies on a permutation-invariant representation based on histograms that is
specially suited for quantification problems. Our experiments carried out in
the only quantification competition held to date, show that HistNetQ
outperforms other deep neural architectures devised for set processing, as well
as the state-of-the-art quantification methods. Furthermore, HistNetQ offers
two significant advantages over traditional quantification methods: i) it does
not require the labels of the training examples but only the prevalence values
of a collection of training bags, making it applicable to new scenarios; and
ii) it is able to optimize any custom quantification-oriented loss function.