Designing multi-label classifiers that maximize F measures: state of the art

Multi-label classification problems usually occur in tasks related to information retrieval, like text and image annotation, and are receiving increasing attention from the machine learning and pattern recognition fields. One of the main issues under investigation is the development of classification algorithms capable of maximizing specific accuracy measures based on precision and recall. We focus on the widely used F measure, defined for binary, single-label problems as the weighted harmonic mean of precision and recall, and later extended to multi-label problems in three ways: macro-averaged, micro-averaged and instance-wise. In this paper we give a comprehensive survey of theoretical results and algorithms aimed at maximizing F measures. We subdivide it according to the two main existing approaches: empirical utility maximization, and decision-theoretic. Under the former approach, we also derive the optimal (Bayes) classifier at the population level for the instance-wise and micro-averaged F, extending recent results about the single-label F. In a companion paper we shall focus on the micro-averaged F measure, for which relatively fewer solutions exist, and shall develop novel maximization algorithms under both approaches

On the Bayes-optimality of F-measure maximizers

The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems

Multi-label Rule Learning

Research on multi-label classification is concerned with developing and evaluating algorithms that learn a predictive model for the automatic assignment of data points to a subset of predefined class labels. This is in contrast to traditional classification settings, where individual data points cannot be assigned to more than a single class. As many practical use cases demand a flexible categorization of data, where classes must not necessarily be mutually exclusive, multi-label classification has become an established topic of machine learning research. Nowadays, it is used for the assignment of keywords to text documents, the annotation of multimedia files, such as images, videos, or audio recordings, as well as for diverse applications in biology, chemistry, social network analysis, or marketing. During the past decade, increasing interest in the topic has resulted in a wide variety of different multi-label classification methods. Following the principles of supervised learning, they derive a model from labeled training data, which can afterward be used to obtain predictions for yet unseen data. Besides complex statistical methods, such as artificial neural networks, symbolic learning approaches have not only been shown to provide state-of-the-art performance in many applications but are also a common choice in safety-critical domains that demand human-interpretable and verifiable machine learning models. In particular, rule learning algorithms have a long history of active research in the scientific community. They are often argued to meet the requirements of interpretable machine learning due to the human-legible representation of learned knowledge in terms of logical statements. This work presents a modular framework for implementing multi-label rule learning methods. It does not only provide a unified view of existing rule-based approaches to multi-label classification, but also facilitates the development of new learning algorithms. Two novel instantiations of the framework are investigated to demonstrate its flexibility. Whereas the first one relies on traditional rule learning techniques and focuses on interpretability, the second one is based on a generalization of the gradient boosting framework and focuses on predictive performance rather than the simplicity of models. Motivated by the increasing demand for highly scalable learning algorithms that are capable of processing large amounts of training data, this work also includes an extensive discussion of algorithmic optimizations and approximation techniques for the efficient induction of rules. As the novel multi-label classification methods that are presented in this work can be viewed as instantiations of the same framework, they can both benefit from most of these principles. Their effectiveness and efficiency are compared to existing baselines experimentally