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B0785
Title: Functional Fisher rules and reproducing kernel Hilbert spaces Authors:  Antonio Cuevas - Autonomous University of Madrid (Spain)
Jose Luis Torrecilla - Universidad Autonoma de Madrid (Spain)
Jose Berrendero - Universidad Autonoma de Madrid (Spain) [presenting]
Abstract: The Hajek-Feldman dichotomy establishes that two Gaussian measures are either equivalent (and hence there is a Radon-Nikodym (RN) density for each measure with respect to the other one) or mutually singular. Unlike the case of finite dimensional Gaussian measures, there are non-trivial examples of both situations when dealing with Gaussian stochastic processes. It is often possible to derive the optimal (Bayes) rule and the minimal classification error probability in several relevant problems of supervised binary functional classification defined by two equivalent measures. On the other hand, near perfect classification phenomena arise when the measures are mutually singular. We establish some results to formalize these ideas, which rely on the theory of Reproducing Kernel Hilbert Spaces (RKHS). We also propose a new method for variable selection in binary classification problems, which arises in a very natural way from the explicit knowledge of the RN-derivatives and the underlying RKHS structure. As a consequence, the optimal classifier in a wide class of functional classification problems can be expressed in terms of a classical, linear finite-dimensional Fisher's rule.