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Search Results: 1 - 10 of 2774 matches for " Julien Chiquet "
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Inferring Multiple Graphical Structures
Julien Chiquet,Yves Grandvalet,Christophe Ambroise
Statistics , 2009,
Abstract: Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a single network is inferred from a set of measurements, but, as wetlab data is typically scarce, several assays, where the experimental conditions affect interactions, are usually merged to infer a single network. In this paper, we propose two approaches for estimating multiple related graphs, by rendering the closeness assumption into an empirical prior or group penalties. We provide quantitative results demonstrating the benefits of the proposed approaches. The methods presented in this paper are embeded in the R package 'simone' from version 1.0-0 and later.
Sparsity with sign-coherent groups of variables via the cooperative-Lasso
Julien Chiquet,Yves Grandvalet,Camille Charbonnier
Statistics , 2011, DOI: 10.1214/11-AOAS520
Abstract: We consider the problems of estimation and selection of parameters endowed with a known group structure, when the groups are assumed to be sign-coherent, that is, gathering either nonnegative, nonpositive or null parameters. To tackle this problem, we propose the cooperative-Lasso penalty. We derive the optimality conditions defining the cooperative-Lasso estimate for generalized linear models, and propose an efficient active set algorithm suited to high-dimensional problems. We study the asymptotic consistency of the estimator in the linear regression setup and derive its irrepresentable conditions, which are milder than the ones of the group-Lasso regarding the matching of groups with the sparsity pattern of the true parameters. We also address the problem of model selection in linear regression by deriving an approximation of the degrees of freedom of the cooperative-Lasso estimator. Simulations comparing the proposed estimator to the group and sparse group-Lasso comply with our theoretical results, showing consistent improvements in support recovery for sign-coherent groups. We finally propose two examples illustrating the wide applicability of the cooperative-Lasso: first to the processing of ordinal variables, where the penalty acts as a monotonicity prior; second to the processing of genomic data, where the set of differentially expressed probes is enriched by incorporating all the probes of the microarray that are related to the corresponding genes.
Inferring sparse Gaussian graphical models with latent structure
Christophe Ambroise,Julien Chiquet,Catherine Matias
Statistics , 2008, DOI: 10.1214/08-EJS314
Abstract: Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We describe a novel framework taking into account a latent structure on the concentration matrix. This latent structure is used to drive a penalty matrix and thus to recover a graphical model with a constrained topology. Our method uses an $\ell_1$ penalized likelihood criterion. Inference of the graph of conditional dependencies between the variates and of the hidden variables is performed simultaneously in an iterative \textsc{em}-like algorithm. The performances of our method is illustrated on synthetic as well as real data, the latter concerning breast cancer.
Sparsity by Worst-Case Quadratic Penalties
Yves Grandvalet,Julien Chiquet,Christophe Ambroise
Statistics , 2012,
Abstract: This paper proposes a new robust regression 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 evaluation 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 at machine precision in the time required to get a rough estimate with competing state-of-the-art algorithms.
Weighted-Lasso for Structured Network Inference from Time Course Data
Camille Charbonnier,Julien Chiquet,Christophe Ambroise
Statistics , 2009, DOI: 10.2202/1544-6115.1519
Abstract: We present a weighted-Lasso method to infer the parameters of a first-order vector auto-regressive model that describes time course expression data generated by directed gene-to-gene regulation networks. These networks are assumed to own a prior internal structure of connectivity which drives the inference method. This prior structure can be either derived from prior biological knowledge or inferred by the method itself. We illustrate the performance of this structure-based penalization both on synthetic data and on two canonical regulatory networks, first yeast cell cycle regulation network by analyzing Spellman et al's dataset and second E. coli S.O.S. DNA repair network by analysing U. Alon's lab data.
Fast tree inference with weighted fusion penalties
Julien Chiquet,Pierre Gutierrez,Guillem Rigaill
Statistics , 2014,
Abstract: Given a data set with many features observed in a large number of conditions, it is desirable to fuse and aggregate conditions which are similar to ease the interpretation and extract the main characteristics of the data. This paper presents a multidimensional fusion penalty framework to address this question when the number of conditions is large. If the fusion penalty is encoded by an $\ell_q$-norm, we prove for uniform weights that the path of solutions is a tree which is suitable for interpretability. For the $\ell_1$ and $\ell_\infty$-norms, the path is piecewise linear and we derive a homotopy algorithm to recover exactly the whole tree structure. For weighted $\ell_1$-fusion penalties, we demonstrate that distance-decreasing weights lead to balanced tree structures. For a subclass of these weights that we call "exponentially adaptive", we derive an $\mathcal{O}(n\log(n))$ homotopy algorithm and we prove an asymptotic oracle property. This guarantees that we recover the underlying structure of the data efficiently both from a statistical and a computational point of view. We provide a fast implementation of the homotopy algorithm for the single feature case, as well as an efficient embedded cross-validation procedure that takes advantage of the tree structure of the path of solutions. Our proposal outperforms its competing procedures on simulations both in terms of timings and prediction accuracy. As an example we consider phenotypic data: given one or several traits, we reconstruct a balanced tree structure and assess its agreement with the known taxonomy.
Structured Regularization for conditional Gaussian Graphical Models
Julien Chiquet,Tristan Mary-Huard,Stéphane Robin
Statistics , 2014,
Abstract: Conditional Gaussian graphical models (cGGM) are a recent reparametrization of the multivariate linear regression model which explicitly exhibits $i)$ the partial covariances between the predictors and the responses, and $ii)$ the partial covariances between the responses themselves. Such models are particularly suitable for interpretability since partial covariances describe strong relationships between variables. In this framework, we propose a regularization scheme to enhance the learning strategy of the model by driving the selection of the relevant input features by prior structural information. It comes with an efficient alternating optimization procedure which is guaranteed to converge to the global minimum. On top of showing competitive performance on artificial and real datasets, our method demonstrates capabilities for fine interpretation of its parameters, as illustrated on three high-dimensional datasets from spectroscopy, genetics, and genomics.
A model for gene deregulation detection using expression data
Thomas Picchetti,Julien Chiquet,Mohamed Elati,Pierre Neuvial,Rémy Nicolle,Etienne Birmelé
Quantitative Biology , 2015,
Abstract: In tumoral cells, gene regulation mechanisms are severely altered, and these modifications in the regulations may be characteristic of different subtypes of cancer. However, these alterations do not necessarily induce differential expressions between the subtypes. To answer this question, we propose a statistical methodology to identify the misregulated genes given a reference network and gene expression data. Our model is based on a regulatory process in which all genes are allowed to be deregulated. We derive an EM algorithm where the hidden variables correspond to the status (under/over/normally expressed) of the genes and where the E-step is solved thanks to a message passing algorithm. Our procedure provides posterior probabilities of deregulation in a given sample for each gene. We assess the performance of our method by numerical experiments on simulations and on a bladder cancer data set.
Site-Specific Expression of Gelatinolytic Activity during Morphogenesis of the Secondary Palate in the Mouse Embryo
Nikolaos Gkantidis, Susan Blumer, Christos Katsaros, Daniel Graf, Matthias Chiquet
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0047762
Abstract: Morphogenesis of the secondary palate in mammalian embryos involves two major events: first, reorientation of the two vertically oriented palatal shelves into a horizontal position above the tongue, and second, fusion of the two shelves at the midline. Genetic evidence in humans and mice indicates the involvement of matrix metalloproteinases (MMPs). As MMP expression patterns might differ from sites of activity, we used a recently developed highly sensitive in situ zymography technique to map gelatinolytic MMP activity in the developing mouse palate. At embryonic day 14.5 (E14.5), we detected strong gelatinolytic activity around the lateral epithelial folds of the nasopharyngeal cavity, which is generated as a consequence of palatal shelf elevation. Activity was concentrated in the basement membrane of the epithelial fold but extended into the adjacent mesenchyme, and increased in intensity with lateral outgrowth of the cavity at E15.5. Gelatinolytic activity at this site was not the consequence of epithelial fold formation, as it was also observed in Bmp7-deficient embryos where shelf elevation is delayed. In this case, gelatinolytic activity appeared in vertical shelves at the exact position where the epithelial fold will form during elevation. Mmp2 and Mmp14 (MT1-MMP), but not Mmp9 and Mmp13, mRNAs were expressed in the mesenchyme around the epithelial folds of the elevated palatal shelves; this was confirmed by immunostaining for MMP-2 and MT1-MMP. Weak gelatinolytic activity was also found at the midline of E14.5 palatal shelves, which increased during fusion at E15.5. Whereas MMPs have been implicated in palatal fusion before, this is the first report showing that gelatinases might contribute to tissue remodeling during early stages of palatal shelf elevation and formation of the nasopharynx.
Stackelberg-Walras and Cournot-Walras Equilibria in Mixed Markets: A Comparison  [PDF]
Ludovic A. Julien
Theoretical Economics Letters (TEL) , 2012, DOI: 10.4236/tel.2012.21013
Abstract: In this note, we compare two strategic general equilibrium concepts: the Stackelberg-Walras equilibrium and the Cournot-Walras equilibrium. We thus consider a market exchange economy embodying atoms and a continuum of traders. It is shown that, when the preferences of the small traders are represented by Cobb-Douglas utility functions, the Stackel-berg-Walras and the Cournot-Walras equilibria can coincide only if 1) the endowments and preferences of atoms are identical and 2) the elasticity of the followers’ best response functions are equal to zero in equilibrium.
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