DE VITO , Ernesto

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Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie [H. Zou, T. Hastie, Regularization and variable selection via the elastic net, J. R. Stat. Soc. Ser. B, 67(2) (2005) 301–320] for the selection of groups of correlated variables. To investigate the...

We give a definition of square-integrability for imprimitivity systems and we provethat the square-integrable ones share most of the properties of square-integrablerepresentations of groups

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In this paper we consider the problem of learning from data the support of a probability distribution when the distribution does not have a density (with respect to some reference measure). We propose a new class of regularized spectral estimators based on a new notion of reproducing kernel Hilbert space, which we call "completely regular"....

Given an irreducible representation of a group G , we show that all the covariant positive operator valued measures based on G / Z , where Z is a central subgroup, are described by trace class, trace one positive operators.

We describe the quantum states of an elementary particle invariant with respect to asymmetry group as solutions of an invariant wave equation. From the mathematical point ofview the wave equation is a set of differential operators on the space of vector-valued dis-tributions over the space-time. As an application, we consider the Galilei...

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We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space X into Cn. Given a finite measure μ on X, we represent the reproducing kernel K as a convergent series in terms of the eigenfunctions of a suitable compact operator depending on K and μ. Our result holds under the...

Given a unitary representation U of an Abelian group G and a subgroup H , we characterize the positive operator valued measures based on the quotient group G / H and covariant with respect to U. Some physical examples are considered. Among them, phase and phase-difference observables are particularly important

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The regularization parameter choice is a fundamental problem in Learn- ing Theory since the performance of most supervised algorithms crucially depends on the choice of one or more of such parameters. In particular a main theoretical issue regards the amount of prior knowledge needed to choose the regularization pa- rameter in order to obtain...

In the framework of supervised learning we prove that the iterative algorithm introduced in Umanità and Villa (2010) allows to estimate in a consistent way the relevant features of the regression function under the a priori assumption that it admits a sparse representation.

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