Quantification via Gaussian Latent Space Representations

Quantification, or prevalence estimation, is the task of predicting the prevalence of each class within an unknown bag of examples. Most existing quantification methods in the literature rely on prior probability shift assumptions to create a quantification model that uses the predictions of an underlying classifier to make optimal prevalence estimates. In this work, we present an end-to-end neural network that uses Gaussian distributions in latent spaces to obtain invariant representations of bags of examples. This approach addresses the quantification problem using deep learning, enabling the optimization of specific loss functions relevant to the problem and avoiding the need for an intermediate classifier, tackling the quantification problem as a direct optimization problem. Our method achieves state-of-the-art results, both against traditional quantification methods and other deep learning approaches for quantification. The code needed to reproduce all our experiments is publicly available at https://github.com/AICGijon/gmnet.

Quantification using Permutation-Invariant Networks based on Histograms

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.