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In this paper we propose a general framework to characterize and solve the optimization problems underlying a large class of sparsity based regularization algorithms. More precisely, we study the minimization of learning functionals that are sums of a differentiable data term and a convex non differentiable penalty. These latter penalties have recently(More)
Gene expression analysis aims at identifying the genes able to accurately predict biological parameters like, for example, disease subtyping or progression. While accurate prediction can be achieved by means of many different techniques, gene identification, due to gene correlation and the limited number of available samples, is a much more elusive problem.(More)
Proximal methods have recently been shown to provide effective optimization procedures to solve the variational problems defining the !1 regularization algorithms. The goal of the paper is twofold. First we discuss how proximal methods can be applied to solve a large class of machine learning algorithms which can be seen as extensions of !1 regularization,(More)
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric model, hence avoiding linear or additive models. The key idea is to measure the importance of each variable in the(More)
Hypoxia is a condition of low oxygen tension occurring in the tumor microenvironment and it is related to poor prognosis in human cancer. To examine the relationship between hypoxia and neuroblastoma, we generated and tested an in vitro derived hypoxia gene signature for its ability to predict patients' outcome. We obtained the gene expression profile of 11(More)
Our goal is proposing an unbiased framework for gene expression analysis based on variable selection combined with a significance assessment step. We start by discussing the need of such a framework by illustrating the dramatic effect of a biased approach especially when the sample size is small. Then we describe our analysis protocol, based on two main(More)
PURPOSE To evaluate survival and clinical outcome for patients with a large uveal melanoma treated by either enucleation or proton beam radiotherapy (PBRT). PROCEDURES This retrospective non-randomized study evaluated 132 consecutive patients with T3 and T4 choroidal melanoma classified according to TNM stage grouping. RESULTS Cumulative all-cause(More)
We deal with the problem of variable selection when variables must be selected group-wise, with possibly overlapping groups defined a priori. In particular we propose a new optimization procedure for solving the regularized algorithm presented in [12], where the group lasso penalty is generalized to overlapping groups of variables. While in [12] the(More)
In this paper we consider a regularization approach to variable selection when the regression function depends nonlinearly on a few input variables. The proposed method is based on a regularized least square estimator penalizing large values of the partial derivatives. An efficient iterative procedure is proposed to solve the underlying variational problem,(More)