Julien Chiquet

Daniel Agyapong, Julien Chiquet, Jane Marks et al.

Multivariate count models are often justified by their ability to capture latent dependence, but researchers receive little guidance on when this added structure improves on simpler penalized marginal Poisson regression. We study this question using real microbiome data under a unified held-out evaluation framework. For count prediction, we compare PLN and GLMNet(Poisson) on 20 datasets spanning 32 to 18,270 samples and 24 to 257 taxa, using held-out Poisson deviance under leave-one-taxon-out prediction with 3-fold sample cross-validation rather than synthetic or in-sample criteria. For network inference, we compare PLNNetwork and GLMNet(Poisson) neighborhood selection on five publicly available datasets with experimentally validated microbial interaction truth. PLN outperforms GLMNet(Poisson) on most count-prediction datasets, with gains up to 38 percent. The primary predictor of the winner is the sample-to-taxon ratio, with mean absolute correlation as the strongest secondary signal and overdispersion as an additional predictor. PLNNetwork performs best on broad undirected interaction benchmarks, whereas GLMNet(Poisson) is better aligned with local or directional effects. Taken together, these results provide guidance for choosing between latent multivariate count models and penalized Poisson regression in biological count prediction and interaction recovery.

Hugues Van Assel, Thibault Espinasse, Julien Chiquet et al.

Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full understanding of their properties and limitations. To that extent, we introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. These graphs induce a Markov random field dependency structure among the observations in both input and latent spaces. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Moreover this reveals that these methods suffer from a statistical deficiency that explains poor performances in conserving coarse-grain dependencies. Our model is leveraged and extended to address this issue while new links are drawn with Laplacian eigenmaps and PCA.

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.