Section: New Results

Statistical analysis of genomic data

Participants : Gilles Celeux, Mélina Gallopin, Christine Keribin, Yann Vasseur.

Mélina Gallopin defended her thesis supervised by Gilles Celeux, Florence Jaffrezic and Andrea Rau (INRA, animal genetics department), This thesis was concerned with modeling and model selection in the analysis of RNA-seq data. Its highlights are the following:

• Presentation of a model selection criterion for model-based clustering of annotated gene expression data. This criterion is an ICL-like criterion taking into account annotation.

• An objective comparison of discrete and continuous modeling after transformations for RNA-seq data based on a comparison of likelihoods (possibly penalized) of the possible models.

• A block diagonal covariance selection method for high dimensional Gaussian graphical models. This non-asymptotic model selection procedure is supported by strong theoretical guarantees, based on an oracle inequality and a minimax lower bound. This work was in collaboration with Emilie Devijver.

The subject of Yann Vasseur's PhD Thesis, supervised by Gilles Celeux and Marie-Laure Martin-Magniette (INRA URGV), is the inference of a regulatory network on Transcriptions Factors (TFs), which are specific genes, of Arabidopsis thaliana. To that purpose, a transciptome dataset with a similar number of TFs and statistical units is available. The first aim consists of reducing the dimension of the network to avoid high-dimensional difficulties. Representing this network with a Gaussian graphical model, the following procedure has been defined:

1. Selection step: choose the set of TF regulators (supports) of each TF.

2. Classification step: deduce co-factors groups (TFs with similar expression levels) from these supports.

Thus, the reduced network would be built on the co-factors groups. Currently, several selection methods based on Gauss-LASSO and resampling procedures have been applied to the dataset. The study of stability and parameter calibration of these methods is in progress. The TFs are clustered with the Latent Block Model in a number of co-factor groups, selected with BIC or the exact ICL criterion.

In a collaboration with Marie-Laure Martin-Magniette, Cathy Maugis and Andrea Rau, Gilles Celeux has studied gene expression obtained from high-throughput sequencing technology. The focus is on the question of clustering gene expression profiles as a means to discover groups of co-expressed genes. A Poisson mixture model is proposed, using a rigorous framework for parameter estimation as well as for the choice of the appropriate number of clusters. They illustrate co-expression analyses using this approach on two real RNA-seq datasets. A set of simulation studies also compares the performance of the proposed model with that of several related approaches developed to cluster RNA-seq and serial analysis of gene expression data. The proposed method is implemented in the open-source R package HTSCluster , available on CRAN. It can now be compared with Gaussian mixtures obtained after relevant data transformations.