Thierry Denoeux: Random Fuzzy Sets and Belief Functions – Application to Machine Learning

Orateur: Thierry Denoeux (UTC – IUF)

Résumé: The theory of belief functions is a powerful formalism for uncertain reasoning, with many successful applications to knowledge representation, information fusion, and machine learning. Until now, however, most applications have been limited to problems (such as classification) in which the variables of interest take values in finite domains. Although belief functions can, in theory, be defined in infinite spaces, we lacked practical representations allowing us to manipulate and combine such belief functions. In this talk, I show that the theory of epistemic random fuzzy sets, an extension of Possibility and Dempster-Shafer theories, provides an appropriate framework for evidential reasoning in general spaces. In particular, I introduce Gaussian random fuzzy numbers and vectors, which generalize both Gaussian random variables and Gaussian possibility distributions. I then describe an application of this new formalism to nonlinear regression with uncertainty quantification.