Thanks to the development technological action MPAGenomics, the team has created one of the first french instances of Galaxy publicly available on the French Bioinformatics cloud. This instance is original as it offers complex statistical tools for genomic data analysis in a user-friendly interface (see ).

The team obtained bilateral contracts with companies as Auchan or RougeGorge thanks to its just emerging, but promising, clustering software MixtComp (see ), dedicated to full mixed and missing data.

An extension of the latent class model is proposed for clustering categorical data by relaxing the classical class conditional independence assumption of variables. In this model (called CCM for Conditional Correlated Model), variables are grouped into inter-independent and intra-dependent blocks in order to consider the main intra-class correlations. The dependence between variables grouped into the same block is taken into account by mixing two extreme distributions, which are respectively the independence and the maximum dependence ones. In the conditionally correlated data case, this approach is expected to reduce biases involved by the latent class model and to produce a meaningful model with few additional parameters. The parameters estimation by maximum likelihood is performed by an EM algorithm while a MCMC algorithm avoiding combinatorial problems involved by the block structure search is used for model selection. Applications on sociological and biological data sets bring out the proposed model interest. These results strengthen the idea that the proposed model is meaningful and that biases induced by the conditional independence assumption of the latent class model are reduced. This work has been now accepted in an international journal . Furthermore, an R package (Clustericat) is available on CRAN (see ).

It is a model-based clustering proposal (called CMM for Conditional Modes Model) where categorical data are grouped into conditionally independent blocks. The corresponding block distribution is a parsimonious multinomial distribution where the few free parameters correspond to the most likely modality crossings, while the remaining probability mass is uniformly spread over the other modality crossings. The exact computation of the integrated complete-data likelihood allows to perform the model selection, by a Gibbs sampler, reducing the computing time consuming by parameter estimation and avoiding BIC criterion biases pointed out by our experiments. An article has been now submitted to an international journal . Furthermore, an R package (CoModes) is available on Rforge (see ).

A mixture model of Gaussian copula allows to cluster mixed kind of data. Each component is composed by classical margins while the conditional dependencies between the variables is modeled by a Gaussian copula. The parameter estimation is performed by a Gibbs sampler. An article has been presented to an international conference and has been also submitted to an international journal . Furthermore, an R package (MixCluster) is available on Rforge (see ).

The generative models allow to handle missing data. This can be easily performed by using the EM algorithm, which has a closed form M-step in the Gaussian setting. This can for instance be useful for distance estimation with missing data. It has been proposed to improve the distance estimation by fitting a mixture of Gaussian distributions instead of a considering only one Gaussian component . This is a joint work with Emil Eirola and Amaury Lendrasse .

A new framework is proposed to address the issue of simultaneous linear regression and clustering of predictors where regression coefficients are assumed to be drawn from a Gaussian mixture distribution. Prediction is thus performed using the conditional distribution of the regression coefficients given the data, while clusters are easily derived from posterior distribution in groups given the data. This work is now published in . Furthermore, an R package (clere) is available on Rforge (see ) and an improved version of the initial model has been submitted to an international journal .

The first model-based clustering algorithm dedicated to multivariate partial ranking data is now published in an internation journal . This is an extension of the (ISR) model for ranking data published in 2013. The proposed algorithm has allowed to exhibit regional alliances between European countries in the Eurovision contest, which are often suspected but never proved.

Linear regression outcomes (estimates, prevision) are known to be damaged by highly correlated covariates. However most modern datasets are expected to mechanically convey more and more highly correlated covariates due to the global increase of the amount of variables they contain. We propose to explicitly model such correlations by a family of linear regressions between the covariates. It leads to a particular generative model through the distribution explicitly introduced between correlated covariates. It has been presented to a conference and is currently written as a research paper . Furthermore, an R package (CorReg) is available on CRAN (see ). Extension is now available for missing covariables also. It is a joint work with Gaétan Loridant.

We design the first univariate probability distribution for ordinal data which strictly respects the ordinal nature of data. More precisely, it relies only on order comparisons between modalities, the proposed distribution being obtained by modeling the data generating process which is assumed, from optimality arguments, to be a stochastic binary search algorithm in a sorted table. The resulting distribution is natively governed by two meaningful parameters (position and precision) and has very appealing properties: decrease around the mode, shape tuning from uniformity to a Dirac, identifiability. Moreover, it is easily estimated by an EM algorithm since the path in the stochastic binary search algorithm is missing. Using then the classical latent class assumption, the previous univariate ordinal model is straightforwardly extended to model-based clustering for multivariate ordinal data. Again, parameters of this mixture model are estimated by an EM algorithm. Both simulated and real data sets illustrate the great potential of this model by its ability to parsimoniously identify particularly relevant clusters which were unsuspected by some traditional competitors. This work is currently in revision in an international journal .

This is a joint work with Charles Bouveyron (Paris 5) and Etienne Côme (Inrets).

A model-based clustering method for time series has been developed, based on a discriminative functional mixture model which allows the clustering of the data in a functional subspace. This model presents the advantage to be parsimonious and can therefore handle long time series. This model has been used for analyzing different bike sharing systems In Europe.

In the case of Gaussian mixtures, unbounded likelihood is an important theoretical and practical problem. Using the weak information that the latent sample size of each component has to be greater than the space dimension, we derive a simple non-asymptotic stochastic lower bound on variances. We prove also that maximizing the likelihood under this data-driven constraint leads to consistent estimates. This work has been presented to a conference . This is a joint work with Gwënaelle Castellan.

Auto-Associative models cover a large class of methods used in data analysis, among them are for example the famous PCA and the auto-associative neural networks. We describe the general properties of these models when the projection component is linear and we propose and test an easy to implement Probabilistic Semi-Linear Auto-Associative model in a Gaussian setting. This work is now published in .

We characterized the behavior of cross-validation (Lpo) in density estimation with the $L^2$-loss. We considered two aspects: risk estimation and model selection. For the first one, we settled leave-one-out is optimal. On the contrary for the second one, we provided the first guidelines toward an optimal choice of the parameter $p$. In particular, this choice depends on the convergence rate of the best estimator in the family we consider.

This is a joint work with Tristan Mary-Huard (INRA).

We extended known results about leave-one-out to the case of leave-p-out for the $k$-nearest neighbor estimator in classification with the 0-1 loss. In particular, our strategy relies on the relationship between leave-p-out and U-statistics. We derive upper bounds on the moments on the leave-p-out estimator as well as an exponential concentration inequality.

This is a joint work with Guillem Rigaill and Morgane Pierre-Jean (Univ. Evry).

Based on a previous work, we successfully applied kernel methods to change-point detection in the context of next generation sequencing with multivariate complex data. We also provided greatly improved algorithm in terms of computational complexity (both in time and space). With very huge amounts of data, we also suggest a new strategy based on the idea of approximating the Gram matrix by a low-rank matrix, which leads to a linear time complexity algorithm.

In the kernel method framework, we use the MMD (maximum mean discrepancy) to derive a new goodness-of-fit test that can be used in the RKHS. When applied to the usual $R^d$ setting, our test does not seem too sensitive to any increase on the dimension $d$ unlike other ongoing approaches. With an infinite dimension RKHS, it exhibits a good power for a prescribed level of type-I error control.

This is a joint work with Andrea Rau and Florence Jaffrézic (INRA, Jouy-en-Josas).

An adaptation of meta-analysis methods initially proposed for microarray studies has been proposed for RNA-seq data. The research paper has been published in and the associated R package metaRNASeq is now available on CRAN (see ).

Tests performed during Development Technological Action MPAgenomics have shown on real data that it was also important to suggest automatic and appropriate calibrations for parameters in segmentation methods than to look for common markers able to predict patient's response. In the R package MPAgenomics (see ), we have thus proposed two independent pipelines described in . The choice of a given pipeline depends on the heterogeneity degree of studied genomic profiles.

Dependent models of type block factors are introduced for scan statistics as an extension of the models based on the independent and identically distributed assumption. Approximations and errors are derived for one and two dimensions. Matlab software has been developed for this purpose.