The task of quantification consists in providing an aggregate estimation (e.g. the class distribution in a classification problem) for unseen test sets, applying a model that is trained using a training set with a different data distribution. Several real-world applications demand this kind of methods that do not require predictions for individual examples and just focus on obtaining accurate estimates at an aggregate level. During the past few years, several quantification methods have been proposed from different perspectives and with different goals. This paper presents a unified review of the main approaches with the aim of serving as an introductory tutorial for newcomers in the field.

The goal of multilabel (ML) classification is to induce models able to tag objects with the labels that better describe them. The main baseline for ML classification is Binary Relevance (BR), which is commonly criticized in the literature because of its label independence assumption. Despite this fact, this paper discusses some interesting properties of BR, mainly that it produces optimal models for several ML loss functions. Additionally, we present an analytical study about ML benchmarks datasets, pointing out some shortcomings. As a result, this paper proposes the use of synthetic datasets to better analyze the behavior of ML methods in domains with different characteristics. To support this claim, we perform some experiments using synthetic data proving the competitive performance of BR with respect to a more complex method in difficult problems with many labels, a conclusion which was not stated by previous studies.

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Real-world applications demand effective methods to estimate the class distribution of a sample.In many domains, this is more productive than seeking individual predictions. At a first glance, the straightforward conclusion could be that this task, recently identified as quantification, is as simple as counting the predictions of a classifier. However, due to natural distribution changes occurring in real-world problems, this solution is unsatisfactory. Moreover, current quantification models based on classifiers present the drawback of being trained with loss functions aimed at classification rather than quantification. Other recent attempts to address this issue suffer certain limitations regarding reliability, measured in terms of classification abilities. This paper presents a learning method that optimizes an alternative metric that combines simultaneously quantification and classification performance. Our proposal offers a new framework that allows the construction of binary quantifiers that are able to accurately estimate the proportion of positives, based on models with reliable classification abilities.

In this paper we tackle a real world problem, the search of a function to evaluate the merits of beef cattle as meat producers. The independent variables represent a set of live animals' measurements; while the outputs cannot be captured with a single number, since the available experts tend to assess each animal in a relative way, comparing animals with the other partners in the same batch. Therefore, this problem can not be solved by means of regression methods; our approach is to learn the preferences of the experts when they order small groups of animals. Thus, the problem can be reduced to a binary classification, and can be dealt with a Support Vector Machine (SVM) improved with the use of a feature subset selection (FSS) method. We develop a method based on Recursive Feature Elimination (RFE) that employs an adaptation of a metric based method devised for model selection (ADJ). Finally, we discuss the extension of the resulting method to more general settings, and provide a comparison with other possible alternatives.