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

Extensions of qualitative approach to case-based decision making: Uncertainty and fuzzy quantification in act evaluation

Verlag Mainz , 1999 - Proceedings of EUFIT'99: Final programme; abstracts of the papers & proceedings on CD-ROM ; abstracts pp. 251-252 + CDRom (12)International audienc

Instance-based prediction in the framework of possibility theory

International audienceA possibilistic framework for instance-based prediction is presented which formalizes the generalization beyond experience by means of fuzzy rules. In comparison with related instance-based approaches such as the well-known Nearest Neighbor classifier, this method distinguishes itself by the following: First, by suggesting (guaranteed) degrees of possibility for competing outcomes rather than making precise predictions, it takes the uncertain character of similarity-based inference into account. Second, the possibilistic framework can easily be extended so as to cope with incompletely specified cases. Thirdly, the close connection between possibility theory and fuzzy sets suggests the extension of the basic model by means of fuzzy set-based (linguistic) modeling techniques. This paper especially highlights two of these aspects, namely the modeling of uncertainty and the handling of incomplete information

Fuzzy Rules in Case-Based Reasoning

Dates de conférence : juin 1999 1999.International audienceSimilarity-based fuzzy rules are proposed as a basic tool for modelling and formalizing parts of the case-based reasoning methodology within the framework of approximate reasoning. The use of different types of rules for encoding the heuristic reasoning principle underlying casebased problem solving is discussed, which leads to different approaches to case-based inference. A model which combines a constraint-based and an example-oriented approach is advocated more particularly. Besides, the use of modifiers in fuzzy rules is proposed for adapting the proposed formal model to the respective applications, and the problem of determining appropriate modifiers is considered in the context of case-based learning

Fuzzy Sets and Systems : Special Issue Celebrating the 50th Anniversary of Fuzzy Sets (2015)

International audienceThis special issue celebrates the publication of the first paper on fuzzy sets by its founder Lotfi Zadeh in 1965.1 Without any doubt, this paper is the most important landmark for the research field in general and for Fuzzy Sets and Systems in particular. In fact, the mere existence of the oldest scientific journal on the topic is only due to Zadeh's publication. On this occasion, we invited a number of esteemed colleagues, many of whom are serving the journal as members of the editorial board, to deliver their thoughts on their topic of predilection and competence. We thus managed to collect twenty position papers that altogether provide a relatively exhaustive overview of the current activity on fuzzy sets and their applications, and of questions regarding the role and appropriateness of fuzzy sets in various topics. Thus, going beyond a pure celebration of the past, this issue is also meant to indicate promising directions of future research on fuzzy sets. A tout seigneur tout honneur,2 we are extremely lucky to publish one more paper by the author of the publication we celebrate. Lotfi Zadeh himself provides his own testimony about the genesis of his first paper on fuzzy sets, and he also expresses his opinions concerning new directions to be explored in the future. In a second contribution, Dubois and Prade provide a glimpse at the various areas of research that were influenced by fuzzy sets, pointing out mature fields, barren directions, and promising areas of research. One of their main points is the necessity of interpreting membership functions in applied research. It is important to articulate the contribution of fuzzy sets in the various problems they are applied to. This question is crucial to explain where degrees of membership come from and how they can be measured. The answer will be different if membership functions encode ideas of similarity, of uncertainty or yet of preference. The rest of the issue is clustered into various themes: logic, mathematics, systems engineering, decision and optimization, data analysis and management

Representing, Processing, and Learning Preferences : Theoretical and Practical Challenges

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Proceedings of the DA2PL'2016 EURO Mini Conference

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