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.

Abstract 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 for tasks of quantification in scenarios where it is possible to apply a symmetric supervised approach that eliminates the need for classification as an intermediate step, thus directly addressing the quantification problem. Additionally, it discusses existing permutation-invariant layers designed for set processing and assesses their suitability for quantification. Based on our analysis, we propose HistNetQ, a novel neural architecture that relies on a permutation-invariant representation based on histograms that is especially suited for quantification problems. Our experiments carried out in two standard competitions, which have become a reference in the quantification field, show that HistNetQ outperforms other deep neural network architectures designed for set processing, as well as the current 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.

Abstract Quantification is the supervised learning task that consists of training predictors of the class prevalence values of sets of unlabelled data, and is of special interest when the labelled data on which the predictor has been trained and the unlabelled data are not IID, i.e., suffer from dataset shift . To date, quantification methods have mostly been tested only on a special case of dataset shift, i.e., prior probability shift ; the relationship between quantification and other types of dataset shift remains, by and large, unexplored. In this work we carry out an experimental analysis of how current quantification algorithms behave under different types of dataset shift, in order to identify limitations of current approaches and hopefully pave the way for the development of more broadly applicable methods. We do this by proposing a fine-grained taxonomy of types of dataset shift, by establishing protocols for the generation of datasets affected by these types of shift, and by testing existing quantification methods on the datasets thus generated. One finding that results from this investigation is that many existing quantification methods that had been found robust to prior probability shift are not necessarily robust to other types of dataset shift. A second finding is that no existing quantification method seems to be robust enough to dealing with all the types of dataset shift we simulate in our experiments. The code needed to reproduce all our experiments is publicly available at https://github.com/pglez82/quant_datasetshift .

The goal of quantification learning is to induce models capable of accurately predicting the class distribution for new bags of unseen examples. These models only return the prevalence of each class in the bag because prediction of individual examples is irrelevant in these tasks. A prototypical application of ordinal quantification is to predict the proportion of opinions that fall into each category from one to five stars. Ordinal quantification has hardly been studied in the literature, and in fact, only one approach has been proposed so far. This article presents a comprehensive study of ordinal quantification, analyzing the applicability of the most important algorithms devised for multiclass quantification and proposing three new methods that are based on matching distributions using Earth mover's distance (EMD). Empirical experiments compare 14 algorithms on synthetic and benchmark data. To statistically analyze the obtained results, we further introduce an EMD-based scoring function. The main conclusion is that methods using a criterion somehow related to EMD, including two of our proposals, obtain significantly better results.

Quantification (or prevalence estimation) algorithms aim at predicting the class distribution of unseen sets (or bags) of examples. These methods are useful for two main tasks: 1) quantification applications, for instance when we need to track the proportions of several groups of interest over time, and 2) domain adaptation problems, in which we usually need to adapt a previously trained classifier to a different --albeit related-- target distribution according to the estimated prevalences. This paper analyzes several binary quantification algorithms showing that not only do they share a common framework but are, in fact, equivalent. Inspired by this study, we propose a new method that extends one of the approaches analyzed. After an empirical evaluation of all these methods using synthetic and benchmark datasets, the paper concludes recommending three of them due to their precision, efficiency, and diversity.

Learning to Quantify (LQ) is the task of training class prevalence estimators via supervised learning. The task of these estimators is to estimate, given an unlabelled set of data items D and a set of classes C ={c1,...., c|C|}, the prevalence (i.e., relative frequency) of each class c_i in D. LQ is interesting in all applications of classification in which the final goal is not determining which class (or classes) individual unlabelled data items belong to, but estimating the distribution of the unlabelled data items across the classes of interest. Example disciplines whose interest in labelling data items is at the aggregate level (rather than at the individual level) are the social sciences, political science, market research, ecological modelling, and epidemiology. While LQ may in principle be solved by classifying each data item in D and counting how many such items have been labelled with c_i, it has been shown that this "classify and count'' (CC) method yields suboptimal quantification accuracy. As a result, quantification is now no longer considered a mere byproduct of classification and has evolved as a task of its own. The goal of this workshop is bringing together all researchers interested in methods, algorithms, and evaluation measures and methodologies for LQ, as well as practitioners interested in their practical application to managing large quantities of data.

In many applications, the mistakes made by an automatic classifier are not equal, they have different costs. These problems may be solved using a cost-sensitive learning approach. The main idea is not to minimize the number of errors, but the total cost produced by such mistakes. This brief presents a new multiclass cost-sensitive algorithm, in which each example has attached its corresponding misclassification cost. Our proposal is theoretically well-founded and is designed to optimize cost-sensitive loss functions. This research was motivated by a real-world problem, the biomass estimation of several plankton taxonomic groups. In this particular application, our method improves the performance of traditional multiclass classification approaches that optimize the accuracy.