Toward a General Framework for Information Fusion

National audienceDepending on the representation setting, different combination rules have been proposed for fusing information from distinct sources. Moreover in each setting, different sets of axioms that combination rules should satisfy have been advocated, thus justifying the existence of alternative rules (usually motivated by situations where the behavior of other rules was found unsatisfactory). These sets of axioms are usually purely considered in their own settings, without in-depth analysis of common properties essential for all the settings. This paper introduces core properties that, once properly instantiated, are meaningful in different representation settings ranging from logic to imprecise probabilities. The following representation settings are especially considered: classical set representation, possibility theory, and evidence theory, the latter encompassing the two other ones as special cases. This unified discussion of combination rules across different settings is expected to provide a fresh look on some old but basic issues in information fusion

Density Estimation with Imprecise Kernels: Application to Classification

International audienceIn this paper, we explore the problem of estimating lower and upper densities from imprecisely defined families of parametric kernels. Such estimations allow to rely on a single bandwidth value, and we show that it provides good results on classification tasks when extending the naive Bayesian classifie

Relevance of Evidence in Bayesian Networks

For many inference tasks in Bayesian networks, computational efforts can be restricted to a relevant part of the network. Researchers have studied the relevance of a network’s variables and parameter probabilities for such tasks as sensitivity analysis and probabilistic inference in general, and identified relevant sets of variables by graphical considerations. In this paper we study relevance of the evidence variables of a network for such tasks as evidence sensitivity analysis and diagnostic test selection, and identify sets of variables on which computational efforts can focus. We relate the newly identified sets of relevant variables to previously established relevance sets and address their computation compared to these sets. We thereby paint an overall picture of the relevance of various variable sets for answering questions concerning inference and analysis in Bayesian network applications

Inferring from an imprecise Plackett–Luce model : application to label ranking

Learning ranking models is a difficult task, in which data may be scarce and cautious predictions desirable. To address such issues, we explore the extension of the popular parametric probabilistic Plackett–Luce model, often used to model rankings, to the imprecise setting where estimated parameters are set-valued. In particular, we study how to achieve cautious or conservative inference with it, and illustrate their application on label ranking problems, a specific supervised learning task

UNIFYING PRACTICAL UNCERTAINTY REPRESENTATIONS: I. GENERALIZED P-BOXES

Pre-print of final version.International audienceThere exist several simple representations of uncertainty that are easier to handle than more general ones. Among them are random sets, possibility distributions, probability intervals, and more recently Ferson's p-boxes and Neumaier's clouds. Both for theoretical and practical considerations, it is very useful to know whether one representation is equivalent to or can be approximated by other ones. In this paper, we define a generalized form of usual p-boxes. These generalized p-boxes have interesting connections with other previously known representations. In particular, we show that they are equivalent to pairs of possibility distributions, and that they are special kinds of random sets. They are also the missing link between p-boxes and clouds, which are the topic of the second part of this study

Comments on “Learning from imprecise and fuzzy observations: Data disambiguation through generalized loss minimization” by Eyke Hüllermeier

International audienceEyke Hüllermeier provides a very convincing approach to learn from fuzzy data, both about the model and about the data themselves. In the process, he links the shape of fuzzy sets with classical loss functions, therefore providing strong theoretical links between fuzzy modeling and more classical machine learning approaches. This short note discusses various aspects of his proposal as well as possible extensions. I will first discuss the opportunity to consider more general uncertainty representations, before considering various alternatives to the proposed learning procedure. Finally, I will briefly discuss the differences I perceive about a loss-based and a likelihood-based approach

Comments on “A distance-based statistical analysis of fuzzy number-valued data” by the SMIRE research group

International audienceThis paper is a fine review of various aspects related to the statistical handling of "on-tic" random fuzzy sets by the means of appropriate distances. It is quite comprehensive and helpful, as it clarifies the status of fuzzy sets in such methods, explains the advan-tages of using a distance-based approach, specifies the pitfalls in which one should not fall when dealing with "ontic" random fuzzy sets and provides some illustration of practical computations. Not being a statistician but an occasional user of statistics, my discussion will mainly focus on this more practical aspect

Methods for the evaluation and synthesis of multiple sources of information applied to nuclear computer codes

This work is devoted to methods used to evaluate and synthesize information given by multiple sources about a variable which true value is not precisely known. We first recall probabilistic and possibilistic approaches to solve the problem. Each approach offers a formal setting to evaluate, synthesize and analyze information coming from multiple sources. They are then applied to the results of uncertainty studies performed in the framework of BEMUSE project. © 2008 Elsevier B.V. All rights reserved