Christophe Ambroise

Kylliann De Santiago, Marie Szafranski, Christophe Ambroise

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 multilayer 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 identifiability of the model parameters is established and a variational Bayesian EM algorithm is proposed for the estimation of these parameters. The Bayesian framework allows for selecting an optimal number of clusters and components. The proposed approach is compared using synthetic data with consensus clustering and tensor-based algorithms for community detection in large-scale complex networks. Finally, the method is utilized to analyze global food trading networks, leading to structures of interest.

Do Edmond Sanou, Christophe Ambroise, Geneviève Robin

Gaussian Graphical Models (GGMs) are widely used for exploratory data analysis in various fields such as genomics, ecology, psychometry. In a high-dimensional setting, when the number of variables exceeds the number of observations by several orders of magnitude, the estimation of GGM is a difficult and unstable optimization problem. Clustering of variables or variable selection is often performed prior to GGM estimation. We propose a new method allowing to simultaneously infer a hierarchical clustering structure and the graphs describing the structure of independence at each level of the hierarchy. This method is based on solving a convex optimization problem combining a graphical lasso penalty with a fused type lasso penalty. Results on real and synthetic data are presented.

Florent Guinot, Marie Szafranski, Julien Chiquet et al.

Motivation. Association studies have been widely used to search for associations between common genetic variants observations and a given phenotype. However, it is now generally accepted that genes and environment must be examined jointly when estimating phenotypic variance. In this work we consider two types of biological markers: genotypic markers, which characterize an observation in terms of inherited genetic information, and metagenomic marker which are related to the environment. Both types of markers are available in their millions and can be used to characterize any observation uniquely. Objective. Our focus is on detecting interactions between groups of genetic and metagenomic markers in order to gain a better understanding of the complex relationship between environment and genome in the expression of a given phenotype. Contributions. We propose a novel approach for efficiently detecting interactions between complementary datasets in a high-dimensional setting with a reduced computational cost. The method, named SICOMORE, reduces the dimension of the search space by selecting a subset of supervariables in the two complementary datasets. These supervariables are given by a weighted group structure defined on sets of variables at different scales. A Lasso selection is then applied on each type of supervariable to obtain a subset of potential interactions that will be explored via linear model testing. Results. We compare SICOMORE with other approaches in simulations, with varying sample sizes, noise, and numbers of true interactions. SICOMORE exhibits convincing results in terms of recall, as well as competitive performances with respect to running time. The method is also used to detect interaction between genomic markers in Medicago truncatula and metagenomic markers in its rhizosphere bacterial community. Software availability. A R package is available, along with its documentation and associated scripts, allowing the reader to reproduce the results presented in the paper.

Yves Grandvalet, Julien Chiquet, Christophe Ambroise

This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our experiments demonstrate that this strategy, implemented on the elastic-net, is computationally extremely efficient for small to medium size problems. Our accompanying software solves problems very accurately, at machine precision, in the time required to get a rough estimate with competing state-of-the-art algorithms. We illustrate on real and artificial datasets that this accuracy is required to for the correctness of the support of the solution, which is an important element for the interpretability of sparsity-inducing penalties.