A Regularized Method for Selecting Nested Groups of Relevant Genes from Microarray Data

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. Small changes in the expression values often produce different gene lists, and solutions which are both sparse and stable are difficult to obtain. We propose a two-stage regularization method able to learn linear models characterized by a high prediction performance. By varying a suitable parameter these linear models allow to trade sparsity for the inclusion of correlated genes and to produce gene lists which are almost perfectly nested. Experimental results on synthetic and microarray data confirm the interesting properties of the proposed method and its potential as a starting point for further biological investigationsComment: 17 pages, 8 Post-script figure

Nonparametric Sparsity and Regularization

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 model by making use of partial derivatives. Based on this intuition we propose and study a new regularizer and a corresponding least squares regularization scheme. Using concepts and results from the theory of reproducing kernel Hilbert spaces and proximal methods, we show that the proposed learning algorithm corresponds to a minimization problem which can be provably solved by an iterative procedure. The consistency properties of the obtained estimator are studied both in terms of prediction and selection performance. An extensive empirical analysis shows that the proposed method performs favorably with respect to the state-of-the-art

Iterative Projection Methods for Structured Sparsity Regularization

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 become popular in machine learning since they allow to enforce various kinds of sparsity properties in the solution. Leveraging on the theory of Fenchel duality and subdifferential calculus, we derive explicit optimality conditions for the regularized solution and propose a general iterative projection algorithm whose convergence to the optimal solution can be proved. The generality of the framework is illustrated, considering several examples of regularization schemes, including l1 regularization (and several variants), multiple kernel learning and multi-task learning. Finally, some features of the proposed framework are empirically studied

A biology-driven approach identifies the hypoxia gene signature as a predictor of the outcome of neuroblastoma patients

Background 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. Results We obtained the gene expression profile of 11 hypoxic neuroblastoma cell lines and we derived a robust 62 probesets signature (NB-hypo) taking advantage of the strong discriminating power of the l1-l2 feature selection technique combined with the analysis of differential gene expression. We profiled gene expression of the tumors of 88 neuroblastoma patients and divided them according to the NB-hypo expression values by K-means clustering. The NB-hypo successfully stratifies the neuroblastoma patients into good and poor prognosis groups. Multivariate Cox analysis revealed that the NB-hypo is a significant independent predictor after controlling for commonly used risk factors including the amplification of MYCN oncogene. NB-hypo increases the resolution of the MYCN stratification by dividing patients with MYCN not amplified tumors in good and poor outcome suggesting that hypoxia is associated with the aggressiveness of neuroblastoma tumor independently from MYCN amplification. Conclusions Our results demonstrate that the NB-hypo is a novel and independent prognostic factor for neuroblastoma and support the view that hypoxia is negatively correlated with tumors' outcome. We show the power of the biology-driven approach in defining hypoxia as a critical molecular program in neuroblastoma and the potential for improvement in the current criteria for risk stratification.Foundation KiKaChildren's Neuroblastoma Cancer FoundationSKK FoundationDutch Cancer Societ

Dimensionality Reduction and Generalization

In this paper we investigate the regularization property of Kernel Principal Component Analysis (KPCA), by studying its application as a preprocessing step to supervised learning problems. We show that performing KPCA and then ordinary least squares on the projected data, a procedure known as kernel principal component regression (KPCR), is equivalent to spectral cut-off regularization, the regularization parameter being exactly the number of principal components to keep. Using probabilistic estimates for integral operators we can prove error estimates for KPCR and propose a parameter choice procedure allowing to prove consistency of the algorithm. 1