In this work, we propose an original method for aggregating multiple clustering coming from different sources of information.Each partition is encoded by a co-membership matrix between observations.Our approach uses a mixture of Stochastic Block Models (SBM) to group co-membership matrices with similar information into components and to partition observations into different clusters, taking into account their specificities within the components.The parameters are estimated using a Variational Bayesian EM algorithm.The Bayesian framework allows for selecting an optimal numbers of clusters and components.

BACKGROUND: Genome-Wide Association Studies (GWAS) seek to identify causal genomic variants associated with rare human diseases. The classical statistical approach for detecting these variants is based on univariate hypothesis testing, with healthy individuals being tested against affected individuals at each locus. Given that an individual's genotype is characterized by up to one million SNPs, this approach lacks precision, since it may yield a large number of false positives that can lead to erroneous conclusions about genetic associations with the disease. One way to improve the detection of true genetic associations is to reduce the number of hypotheses to be tested by grouping SNPs. RESULTS: We propose a dimension-reduction approach which can be applied in the context of GWAS by making use of the haplotype structure of the human genome. We compare our method with standard univariate and group-based approaches on both synthetic and real GWAS data. CONCLUSION: We show that reducing the dimension of the predictor matrix by aggregating SNPs gives a greater precision in the detection of associations between the phenotype and genomic regions.

In this paper, we introduce a novel approach, called Input Output Kernel Regression (IOKR), for learning mappings between structured inputs and structured outputs. The approach belongs to the family of Output Kernel Regression methods devoted to regression in feature space endowed with some output kernel. In order to take into account structure in input data and benefit from kernels in the input space as well, we use the Reproducing Kernel Hilbert Space theory for vector-valued functions. We first recall the ridge solution for supervised learning and then study the regularized hinge loss-based solution used in Maximum Margin Regression. Both models are also developed in the context of semi-supervised setting. In addition we derive an extension of Generalized Cross Validation for model selection in the case of the least-square model. Finally we show the versatility of the IOKR framework on two different problems: link prediction seen as a structured output problem and multi-task regression seen as a multiple and interdependent output problem. Eventually, we present a set of detailed numerical results that shows the relevance of the method on these two tasks.

Data representation is a crucial issue in signal processing and machine learning. In this work, we propose to guide the learning process with a prior knowledge describing how similarities between examples are organized. This knowledge is encoded in a tree structure that represents nested groups of similarities that are the pyramids of kernels. We propose a framework that learns a Support Vector Machine (SVM) on pyramids of arbitrary heights and identifies the relevant groups of similarities groups are relevant for classifying the examples. A weighted combination of (groups of) similarities is learned jointly with the SVM parameters, by optimizing a criterion that is shown to be an equivalent formulation regularized with a mixed norm of the original fitting problem. Our approach is illustrated on a Brain Computer Interfaces classification problem.

We address the problem of learning classifiers using several kernel functions. On the contrary to many contributions in the field of learning from different sources of information using kernels, we here do not assume that the kernels used are positive definite. The learning problem that we are interested in involves a misclassification loss term and a regularization term that is expressed by means of a mixed norm. The use of a mixed norm allows us to enforce some sparsity structure, a particular case of which is, for instance, the Group Lasso. We solve the convex problem by employing proximal minimization algorithms, which can be viewed as refined versions of gradient descent procedures capable of naturally dealing with nondifferentiability. A numerical simulation on a Uci dataset shows the modularity of our approach.

The Support Vector Machine (SVM) is an acknowledged powerful tool for building classifiers, but it lacks flexibility, in the sense that the kernel is chosen prior to learning. Multiple Kernel Learning (MKL) enables to learn the kernel, from an ensemble of basis kernels, whose combination is optimized in the learning process. Here, we propose Composite Kernel Learning to address the situation where distinct components give rise to a group structure among kernels. Our formulation of the learning problem encompasses several setups, putting more or less emphasis on the group structure. We characterize the convexity of the learning problem, and provide a general wrapper algorithm for computing solutions. Finally, we illustrate the behavior of our method on multi-channel data where groups correpond to channels.

Hierarchical penalization is a generic framework for incorporating prior informa- tion in the fitting of statistical models, when the explicative variables are organized in a hierarchical structure. The penalizer is a convex functional that performs soft selection at the group level, and shrinks variables within each group. This favors solutions with few leading terms in the final combination. The framework, orig- inally derived for taking prior knowledge into account, is shown to be useful in linear regression, when several parameters are used to model the influence of one feature, or in kernel regression, for learning multiple kernels. Keywords – Optimization: constrained and convex optimization. Supervised learning: regression, kernel methods, sparsity and feature selection.