arXiv subjects

Christophe Ambroise

Publications and source records attributed to Christophe Ambroise.

At least 19 recordsLinked to original sources

arXiv2026

Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussian

We study the squared $2$-Wasserstein distance to the standard Gaussian as a non-Gaussianity criterion and use it for linear Independent Component Analysis (ICA) and causal discovery in Linear Non-Gaussian Acyclic Models (LiNGAM). Unlike commonly used parametric contrasts and approximations of information-theoretic quantities, this criterion requires no distributional regularity beyond finite second moments, involves neither approximation nor tuning parameters, and can be computed exactly and efficiently from empirical order statistics. Our analysis relies on a strict subadditivity property of the $2$-Wasserstein distance to the Gaussian. At the population level, we prove exact identification of the ICA unmixing matrix, up to signed permutation, and give an analogous characterization of causal orders through sequential least-squares residuals. We then define empirical plug-in estimators and prove distribution-free uniform convergence under finite-moment assumptions, before detailing three practical solvers: a Picard-style orthogonal optimizer for ICA, an exhaustive dynamic program for causal order search, and a greedy order search variant. Empirically, we demonstrate competitive performance for both tasks and provide open-source implementations for source separation and causal discovery.

stat.ML↗

arXiv2026

Inference of Multiscale Gaussian Graphical Model

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering to reduce dimensionality and improve performances. This paper explores a slightly different paradigm where clustering is not knowledge-driven but performed simultaneously with the graph inference task. We introduce a novel Multiscale Graphical Lasso (MGLasso) to improve networks interpretability by proposing graphs at different granularity levels. The method estimates clusters through a convex clustering approach - a relaxation of k-means, and hierarchical clustering. The conditional independence graph is simultaneously inferred through a neighborhood selection scheme for undirected graphical models. MGLasso extends and generalizes the sparse group fused lasso problem to undirected graphical models. We use continuation with Nesterov smoothing in a shrinkage-thresholding algorithm (CONESTA) to propose a regularization path of solutions along the group fused Lasso penalty, while the Lasso penalty is kept constant. Extensive experiments on synthetic data compare the performances of our model to state-of-the-art clustering methods and network inference models. Applications to gut microbiome data and poplar's methylation mixed with transcriptomic data are presented.

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arXiv2025

Causal inference of post-transcriptional regulation timelines from long-read sequencing in Arabidopsis thaliana

We propose a novel framework for reconstructing the chronology of genetic regulation using causal inference based on Pearl's theory. The approach proceeds in three main stages: causal discovery, causal inference, and chronology construction. We apply it to the ndhB and ndhD genes of the chloroplast in Arabidopsis thaliana, generating four alternative maturation timeline models per gene, each derived from a different causal discovery algorithm (HC, PC, LiNGAM, or NOTEARS). Two methodological challenges are addressed: the presence of missing data, handled via an EM algorithm that jointly imputes missing values and estimates the Bayesian network, and the selection of the $\ell_1$-regularization parameter in NOTEARS, for which we introduce a stability selection strategy. The resulting causal models consistently outperform reference chronologies in terms of both reliability and model fit. Moreover, by combining causal reasoning with domain expertise, the framework enables the formulation of testable hypotheses and the design of targeted experimental interventions grounded in theoretical predictions.

stat.ME↗

arXiv2025

A General Framework for Joint Multi-State Models

Conventional joint modeling approaches generally characterize the relationship between longitudinal biomarkers and discrete event occurrences within terminal, recurring or competing risk settings, thereby offering a limited representation of complex, multi-state trajectories. We propose a general multi-state joint modeling framework that unifies longitudinal biomarker dynamics with multi-state time-to-event processes defined on arbitrary directed graphs. The proposed framework also accomodates nonlinear longitudinal submodels and scalable inference via stochastic gradient descent. This formulation encompasses both Markovian and semi-Markovian transition structures, allowing recurrent cycles and terminal absorptions to be naturally represented. The longitudinal and event processes are linked through shared latent structures within nonlinear mixed-effects models, extending classical joint modeling formulations. We derive the complete likelihood, model selection criteria, and develop scalable inference procedures based on stochastic gradient descent to enable high-dimensional and large-scale applications. In addition, we formulate a dynamic prediction framework that provides individualized state-transition probabilities and personalized risk assessments along complex event trajectories. Through simulation and application to the PAQUID cohort, we demonstrate accurate parameter recovery and individualized prediction.

stat.ME↗

arXiv2024

Spectral Bridges

In this paper, Spectral Bridges, a novel clustering algorithm, is introduced. This algorithm builds upon the traditional k-means and spectral clustering frameworks by subdividing data into small Voronoï regions, which are subsequently merged according to a connectivity measure. Drawing inspiration from Support Vector Machine's margin concept, a non-parametric clustering approach is proposed, building an affinity margin between each pair of Voronoï regions. This approach is characterized by minimal hyperparameters and delineation of intricate, non-convex cluster structures. The numerical experiments underscore Spectral Bridges as a fast, robust, and versatile tool for sophisticated clustering tasks spanning diverse domains. Its efficacy extends to large-scale scenarios encompassing both real-world and synthetic datasets. The Spectral Bridge algorithm is implemented both in Python ( ) and R ).

stat.AP↗

arXiv2024

Mixture of multilayer stochastic block models for multiview clustering

In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of multilayer Stochastic Block Models (SBM) to group co-membership matrices with similar information into components and to partition observations into different clusters, taking into account their specificities within the components. The identifiability of the model parameters is established and a variational Bayesian EM algorithm is proposed for the estimation of these parameters. The Bayesian framework allows for selecting an optimal number of clusters and components. The proposed approach is compared using synthetic data with consensus clustering and tensor-based algorithms for community detection in large-scale complex networks. Finally, the method is utilized to analyze global food trading networks, leading to structures of interest.

cs.LG↗

arXiv2021

Hierarchical correction of p-values via an ultrametric tree running Ornstein-Uhlenbeck process

Statistical testing is classically used as an exploratory tool to search for association between a phenotype and many possible explanatory variables. This approach often leads to multiple testing under dependence. We assume a hierarchical structure between tests via an Ornstein-Uhlenbeck process on a tree. The process correlation structure is used for smoothing the p-values. We design a penalized estimation of the mean of the Ornstein-Uhlenbeck process for p-value computation. The performances of the algorithm are assessed via simulations. Its ability to discover new associations is demonstrated on a metagenomic dataset. The corresponding R package is available from https://github.com/abichat/zazou.

stat.AP↗

arXiv2020

Accounting for missing actors in interaction network inference from abundance data

Network inference aims at unraveling the dependency structure relating jointly observed variables. Graphical models provide a general framework to distinguish between marginal and conditional dependency. Unobserved variables (missing actors) may induce apparent conditional dependencies.In the context of count data, we introduce a mixture of Poisson log-normal distributions with tree-shaped graphical models, to recover the dependency structure, including missing actors. We design a variational EM algorithm and assess its performance on synthetic data. We demonstrate the ability of our approach to recover environmental drivers on two ecological datasets. The corresponding R package is available from github.com/Rmomal/nestor.

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arXiv2020

High heritability does not imply accurate prediction under the small additive effects hypothesis

Genome-Wide Association Studies (GWAS) explain only a small fraction of heritability for most complex human phenotypes. Genomic heritability estimates the variance explained by the SNPs on the whole genome using mixed models and accounts for the many small contributions of SNPs in the explanation of a phenotype. This paper approaches heritability from a machine learning perspective, and examines the close link between mixed models and ridge regression. Our contribution is twofold. First, we propose estimating genomic heritability using a predictive approach via ridge regression and Generalized Cross Validation (GCV). We show that this is consistent with classical mixed model based estimation. Second, we derive simple formulae that express prediction accuracy as a function of the ratio n/p, where n is the population size and p the total number of SNPs. These formulae clearly show that a high heritability does not imply an accurate prediction when p>n. Both the estimation of heritability via GCV and the prediction accuracy formulae are validated using simulated data and real data from UK Biobank.

stat.ME↗

arXiv2020

Fast Computation of Genome-Metagenome Interaction Effects

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.

stat.AP↗

arXiv2019

Tree-based Inference of Species Interaction Network from Abundance Data

The behavior of ecological systems mainly relies on the interactions between the species it involves. We consider the problem of inferring the species interaction network from abundance data. To be relevant, any network inference methodology needs to handle count data and to account for possible environmental effects. It also needs to distinguish between direct interactions and indirect associations and graphical models provide a convenient framework for this purpose. We introduce a generic statistical model for network inference based on abundance data. The model includes fixed effects to account for environmental covariates and sampling efforts, and correlated random effects to encode species interactions. The inferred network is obtained by averaging over all possible tree-shaped (and therefore sparse) networks, in a computationally efficient manner. An output of the procedure is the probability for each edge to be part of the underlying network. A simulation study shows that the proposed methodology compares well with state-of-the-art approaches, even when the underlying graph strongly differs from a tree. The analysis of two datasets highlights the influence of covariates on the inferred network. Accounting for covariates is critical to avoid spurious edges. The proposed approach could be extended to perform network comparison or to look for missing species.

stat.AP↗

arXiv2019

Adjacency-constrained hierarchical clustering of a band similarity matrix with application to Genomics

Motivation: Genomic data analyses such as Genome-Wide Association Studies (GWAS) or Hi-C studies are often faced with the problem of partitioning chromosomes into successive regions based on a similarity matrix of high-resolution, locus-level measurements. An intuitive way of doing this is to perform a modified Hierarchical Agglomerative Clustering (HAC), where only adjacent clusters (according to the ordering of positions within a chromosome) are allowed to be merged. A major practical drawback of this method is its quadratic time and space complexity in the number of loci, which is typically of the order of 10^4 to 10^5 for each chromosome. Results: By assuming that the similarity between physically distant objects is negligible, we propose an implementation of this adjacency-constrained HAC with quasi-linear complexity. Our illustrations on GWAS and Hi-C datasets demonstrate the relevance of this assumption, and show that this method highlights biologically meaningful signals. Thanks to its small time and memory footprint, the method can be run on a standard laptop in minutes or even seconds. Availability and Implementation: Software and sample data are available as an R package, adjclust, that can be downloaded from the Comprehensive R Archive Network (CRAN).

math.ST↗

arXiv2018

Learning the optimal scale for GWAS through hierarchical SNP aggregation

Motivation: Genome-Wide Association Studies (GWAS) seek to identify causal genomic variants associated with rare human diseases. The classical statistical approach for detecting these variants is based on univariate hypothesis testing, with healthy individuals being tested against affected individuals at each locus. Given that an individual's genotype is characterized by up to one million SNPs, this approach lacks precision, since it may yield a large number of false positives that can lead to erroneous conclusions about genetic associations with the disease. One way to improve the detection of true genetic associations is to reduce the number of hypotheses to be tested by grouping SNPs. Results: We propose a dimension-reduction approach which can be applied in the context of GWAS by making use of the haplotype structure of the human genome. We compare our method with standard univariate and multivariate approaches on both synthetic and real GWAS data, and we show that reducing the dimension of the predictor matrix by aggregating SNPs gives a greater precision in the detection of associations between the phenotype and genomic regions.

stat.ME↗

arXiv2018

Incomplete graphical model inference via latent tree aggregation

Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical cases, not all variables involved in the network have been observed, and the samples are actually drawn from a distribution where some variables have been marginalized out. This challenges the sparsity assumption commonly made in graphical model inference, since marginalization yields locally dense structures, even when the original network is sparse. We present a procedure for inferring Gaussian graphical models when some variables are unobserved, that accounts both for the influence of missing variables and the low density of the original network. Our model is based on the aggregation of spanning trees, and the estimation procedure on the Expectation-Maximization algorithm. We treat the graph structure and the unobserved nodes as missing variables and compute posterior probabilities of edge appearance. To provide a complete methodology, we also propose several model selection criteria to estimate the number of missing nodes. A simulation study and an illustration flow cytometry data reveal that our method has favorable edge detection properties compared to existing graph inference techniques. The methods are implemented in an R package.

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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

Eigen-Epistasis for detecting Gene-Gene interactions

A large amount of research has been devoted to the detection and investigation of epistatic interactions in genome-wide association studies (GWASs). Most of the literature focuses on low-order interactions between single-nucleotide polymorphisms (SNPs) with significant main effects.In this paper we propose an original approach for detecting epistasis at the gene level, without systematically filtering on significant genes. We first compute interaction variables for each gene pair by finding its Eigen-Epistasis component, defined as the linear combination of Gene SNPs having the highest correlation with the phenotype. The selection of significant effects is done using a penalized regression method based on Group Lasso controlling the False Discovery Rate.The method is tested against two recent alternative proposals from the literature using synthetic data, and shows good performances in different settings. We demonstrate the power of our approach by detecting new gene-gene interactions on three genome-wide association studies.

stat.AP↗

arXiv2015

Beyond Support in Two-Stage Variable Selection

Numerous variable selection methods rely on a two-stage procedure, where a sparsity-inducing penalty is used in the first stage to predict the support, which is then conveyed to the second stage for estimation or inference purposes. In this framework, the first stage screens variables to find a set of possibly relevant variables and the second stage operates on this set of candidate variables, to improve estimation accuracy or to assess the uncertainty associated to the selection of variables. We advocate that more information can be conveyed from the first stage to the second one: we use the magnitude of the coefficients estimated in the first stage to define an adaptive penalty that is applied at the second stage. We give two examples of procedures that can benefit from the proposed transfer of information, in estimation and inference problems respectively. Extensive simulations demonstrate that this transfer is particularly efficient when each stage operates on distinct subsamples. This separation plays a crucial role for the computation of calibrated p-values, allowing to control the False Discovery Rate. In this setup, the proposed transfer results in sensitivity gains ranging from 50% to 100% compared to state-of-the-art.

stat.AP↗

arXiv2011

Defining a robust biological prior from Pathway Analysis to drive Network Inference

Inferring genetic networks from gene expression data is one of the most challenging work in the post-genomic era, partly due to the vast space of possible networks and the relatively small amount of data available. In this field, Gaussian Graphical Model (GGM) provides a convenient framework for the discovery of biological networks. In this paper, we propose an original approach for inferring gene regulation networks using a robust biological prior on their structure in order to limit the set of candidate networks. Pathways, that represent biological knowledge on the regulatory networks, will be used as an informative prior knowledge to drive Network Inference. This approach is based on the selection of a relevant set of genes, called the "molecular signature", associated with a condition of interest (for instance, the genes involved in disease development). In this context, differential expression analysis is a well established strategy. However outcome signatures are often not consistent and show little overlap between studies. Thus, we will dedicate the first part of our work to the improvement of the standard process of biomarker identification to guarantee the robustness and reproducibility of the molecular signature. Our approach enables to compare the networks inferred between two conditions of interest (for instance case and control networks) and help along the biological interpretation of results. Thus it allows to identify differential regulations that occur in these conditions. We illustrate the proposed approach by applying our method to a study of breast cancer's response to treatment.

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