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- Andrea Caponnetto, Ernesto De Vito
- Foundations of Computational Mathematics
- 2007

- Lorenzo Rosasco, Ernesto De Vito, Andrea Caponnetto, Michele Piana, Alessandro Verri
- Neural Computation
- 2004

In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also derive a general result on the minimizer of… (More)

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel.

- Lorenzo Rosasco, Mikhail Belkin, Ernesto De Vito
- Journal of Machine Learning Research
- 2010

A large number of learning algorithms, for example, spectral clustering, kernel Principal Components Analysis and many manifold methods are based on estimating eigenvalues and eigenfunctions of operators defined by a similarity function or a kernel, given empirical data. Thus for the analysis of algorithms, it is an important problem to be able to assess… (More)

- Ernesto De Vito, Lorenzo Rosasco, Andrea Caponnetto, Umberto De Giovannini, Francesca Odone
- Journal of Machine Learning Research
- 2005

Many works related learning from examples to regularization techniques for inverse problems, emphasizing the strong algorithmic and conceptual analogy of certain learning algorithms with regularization algorithms. In particular it is well known that regularization schemes such as Tikhonov regularization can be effectively used in the context of learning and… (More)

- L. Lo Gerfo, Lorenzo Rosasco, Francesca Odone, Ernesto De Vito, Alessandro Verri
- Neural Computation
- 2008

We discuss how a large class of regularization methods, collectively known as spectral regularization and originally designed for solving ill-posed inverse problems, gives rise to regularized learning algorithms. All of these algorithms are consistent kernel methods that can be easily implemented. The intuition behind their derivation is that the same… (More)

- Ernesto De Vito, Andrea Caponnetto, Lorenzo Rosasco
- Foundations of Computational Mathematics
- 2005

We investigate the problem of model selection for learning algorithms depending on a continuous parameter. We propose a model selection procedure based on a worst case analysis and data-independent choice of the parameter. For regularized least-squares algorithm we bound the generalization error of the solution by a quantity depending on few known constants… (More)

- Christine De Mol, Ernesto De Vito, Lorenzo Rosasco
- J. Complexity
- 2009

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 statistical… (More)

- Ernesto De Vito, Lorenzo Rosasco, Andrea Caponnetto, Michele Piana, Alessandro Verri
- Journal of Machine Learning Research
- 2004

In regularized kernel methods, the solution of a learning problem is found by minimizing functionals consisting of the sum of a data and a complexity term. In this paper we investigate some properties of a more general form of the above functionals in which the data term corresponds to the expected risk. First, we prove a quantitative version of the… (More)

- Ernesto De Vito, Sergei V. Pereverzyev, Lorenzo Rosasco
- Foundations of Computational Mathematics
- 2010

The regularization parameter choice is a fundamental problem in Learning 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 parameter in order to obtain good learning… (More)