arXiv subjects

Julien Chiquet

Publications and source records attributed to Julien Chiquet.

28 records · Page 2Linked to original sources

arXiv2017

Sparsity by Worst-Case Penalties

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.

stat.ML↗

arXiv2017

Variable selection in multivariate linear models with high-dimensional covariance matrix estimation

In this paper, we propose a novel variable selection approach in the framework of multivariate linear models taking into account the dependence that may exist between the responses. It consists in estimating beforehand the covariance matrix of the responses and to plug this estimator in a Lasso criterion, in order to obtain a sparse estimator of the coefficient matrix. The properties of our approach are investigated both from a theoretical and a numerical point of view. More precisely, we give general conditions that the estimators of the covariance matrix and its inverse have to satisfy in order to recover the positions of the null and non null entries of the coefficient matrix when the size of the covariance matrix is not fixed and can tend to infinity. We prove that these conditions are satisfied in the particular case of some Toeplitz matrices. Our approach is implemented in the R package MultiVarSel available from the Comprehensive R Archive Network (CRAN) and is very attractive since it benefits from a low computational load. We also assess the performance of our methodology using synthetic data and compare it with alternative approaches. Our numerical experiments show that including the estimation of the covariance matrix in the Lasso criterion dramatically improves the variable selection performance in many cases.

math.ST↗

arXiv2016

Fast Detection of Block Boundaries in Block Wise Constant Matrices: An Application to HiC data

We propose a novel approach for estimating the location of block boundaries (change-points) in a random matrix consisting of a block wise constant matrix observed in white noise. Our method consists in rephrasing this task as a variable selection issue. We use a penalized least-squares criterion with an $\ell_1$-type penalty for dealing with this issue. We first provide some theoretical results ensuring the consistency of our change-point estimators. Then, we explain how to implement our method in a very efficient way. Finally, we provide some empirical evidence to support our claims and apply our approach to HiC data which are used in molecular biology for better understanding the influence of the chromosomal conformation on the cells functioning.

stat.AP↗

arXiv2016

A model for gene deregulation detection using expression data

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.

stat.AP↗

arXiv2015

Fast tree inference with weighted fusion penalties

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.

stat.CO↗

arXiv2014

Structured Regularization for conditional Gaussian Graphical Models

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.

stat.ME↗

arXiv2012

Sparsity with sign-coherent groups of variables via the cooperative-Lasso

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.

stat.ME↗

arXiv2010

Inferring Multiple Graphical Structures

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.

stat.ME↗

arXiv2009

Weighted-Lasso for Structured Network Inference from Time Course Data

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.

stat.AP↗

arXiv2008

Inferring sparse Gaussian graphical models with latent structure

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.

stat.ME↗