arXiv subjects

Mahendra Mariadassou

Publications and source records attributed to Mahendra Mariadassou.

14 recordsLinked to original sources

arXiv2026

Leveraging hologenomic data for phenotypic prediction: potential and pitfalls

The microbiota is increasingly recognized as an active component of host biology, influencing various host phenotypes. Advances in high-throughput sequencing and the emergence of the holobiont perspective have raised expectations regarding hologenomic-informed prediction. Yet, whether and under which conditions integrating microbiota and genomic data meaningfully improves phenotypic prediction remains unclear. The biological characteristics of the microbiota, including but not limited to transmission mechanisms, environmental effects and interactions with host genetics, complicate their integration into classical evaluation frameworks. In addition, microbiota datasets are high-dimensional, highly dispersed, sparse and compositional. Finally, analytical choices such as the taxonomic granularity considered for aggregation or the similarity matrix used in prediction models may impact downstream inference and prediction accuracy. Here we explore these challenges using a comprehensive set of transgenerational hologenomic simulations. By generating controlled and contrasted biological scenarios across a broad parameter space, we examine how microbiota granularity, variance structure and host modulation influence (i) the estimation of variance components and (ii) the accuracy of phenotypic prediction. We show that the added value of hologenomic, compared to genomic prediction, is highly context dependent. Our results provide a structured framework to interrogate when and how integrating microbiota may enhance phenotypic prediction in breeding applications.

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arXiv2026

Simulating transgenerational hologenomes under selection with RITHMS

A holobiont is made up of a host organism together with its microbiota. In the context of animal breeding, the holobiont can be viewed as the single unit upon which selection operates. Therefore, integrating microbiota data into genomic prediction models may be a promising approach to improve predictions of phenotypic and genetic values. Nevertheless, there is a paucity of hologenomic transgenerational data to address this hypothesis, and thus to fill this gap, we propose a new simulation framework. Our approach, an R Implementation of a Transgenerational Hologenomic Model-based Simulator (RITHMS) is an open-source package. It builds upon simulated transgenerational genotypes from the Modular Breeding Program Simulator (MoBPS) package and incorporates distinctive characteristics of the microbiota, notably vertical and horizontal transmission as well as modulation due to the environment and host genetics. In addition, RITHMS can account for a variety of selection strategies and is adaptable to different genetic architectures. We simulated transgenerational hologenomic data using RITHMS under a wide variety of scenarios, varying heritability, microbiability, and microbiota transmissibility. We found that simulated data accurately preserved key characteristics across generations, notably microbial diversity metrics, exhibited the expected behavior in terms of correlation between taxa and of modulation of vertical and horizontal transmission, response to environmental effects and the evolution of phenotypic values depending on selection strategy. Our results support the relevance of our simulation framework and illustrate its possible use for building a selection index balancing genetic gain and microbial diversity and for evaluating the impact of partially observed microbiota data. RITHMS is an advanced, flexible tool for generating transgenerational hologenomes under selection that incorporate the complex interplay between genetics, microbiota and environment.

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arXiv2025

Zero-inflation in the Multivariate Poisson Lognormal Family

Analyzing high-dimensional count data is a challenge and statistical model-based approaches provide an adequate and efficient framework that preserves explainability. The (multivariate) Poisson-Log-Normal (PLN) model is one such model: it assumes count data are driven by an underlying structured latent Gaussian variable, so that the dependencies between counts solely stems from the latent dependencies. However PLN doesn't account for zero-inflation, a feature frequently observed in real-world datasets. Here we introduce the Zero-Inflated PLN (ZIPLN) model, adding a multivariate zero-inflated component to the model, as an additional Bernoulli latent variable. The Zero-Inflation can be fixed, site-specific, feature-specific or depends on covariates. We estimate model parameters using variational inference that scales up to datasets with a few thousands variables and compare two approximations: (i) independent Gaussian and Bernoulli variational distributions or (ii) Gaussian variational distribution conditioned on the Bernoulli one. The method is assessed on synthetic data and the efficiency of ZIPLN is established even when zero-inflation concerns up to 90% of the observed counts. We then apply both ZIPLN and PLN to a cow microbiome dataset, containing 90.6% of zeroes. Accounting for zero-inflation significantly increases log-likelihood and reduces dispersion in the latent space, thus leading to improved group discrimination.

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arXiv2024

Evaluating Parameter Uncertainty in the Poisson Lognormal Model with Corrected Variational Estimators

Count data analysis is essential across diverse fields, from ecology and accident analysis to single-cell RNA sequencing (scRNA-seq) and metagenomics. While log transformations are computationally efficient, model-based approaches such as the Poisson-Log-Normal (PLN) model provide robust statistical foundations and are more amenable to extensions. The PLN model, with its latent Gaussian structure, not only captures overdispersion but also enables correlation between variables and inclusion of covariates, making it suitable for multivariate count data analysis. Variational approximations are a golden standard to estimate parameters of complex latent variable models such as PLN, maximizing a surrogate likelihood. However, variational estimators lack theoretical statistical properties such as consistency and asymptotic normality. In this paper, we investigate the consistency and variance estimation of PLN parameters using M-estimation theory. We derive the Sandwich estimator, previously studied in Westling and McCormick (2019), specifically for the PLN model. We compare this approach to the variational Fisher Information method, demonstrating the Sandwich estimator's effectiveness in terms of coverage through simulation studies. Finally, we validate our method on a scRNA-seq dataset.

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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.

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arXiv2020

Consistency and Asymptotic Normality of Stochastic Block Models Estimators from Sampled Data

Statistical analysis of network is an active research area and the literature counts a lot of papers concerned with network models and statistical analysis of networks. However, very few papers deal with missing data in network analysis and we reckon that, in practice, networks are often observed with missing values. In this paper we focus on the Stochastic Block Model with valued edges and consider a MCAR setting by assuming that every dyad (pair of nodes) is sampled identically and independently of the others with probability $ρ> 0$. We prove that maximum likelihood estimators and its variational approximations are consistent and asymptotically normal in the presence of missing data as soon as the sampling probability $ρ$ satisfies $ρ\gg\log(n)/n$.

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arXiv2020

Consistency and Asymptotic Normality of Latent Block Model Estimators

The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have been proposed and are now well understood empirically, theoretical guarantees about their asymptotic behavior is rather sparse and most results are limited to the binary setting. We prove here theoretical guarantees in the valued settings. We show that under some mild conditions on the parameter space, and in an asymptotic regime where $\log(d)/n$ and $\log(n)/d$ tend to $0$ when $n$ and $d$ tend to infinity, (1) the maximum-likelihood estimate of the complete model (with known labels) is consistent and (2) the log-likelihood ratios are equivalent under the complete and observed (with unknown labels) models. This equivalence allows us to transfer the asymptotic consistency, and under mild conditions, asymptotic normality, to the maximum likelihood estimate under the observed model. Moreover, the variational estimator is also consistent and, under the same conditions, asymptotically normal.

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arXiv2018

Variational inference for sparse network reconstruction from count data

In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework. Unfortunately, the Gaussian assumption does not apply to count data which are encountered in domains such as genomics, social sciences or ecology. To circumvent this limitation, state-of-the-art approaches use two-step strategies that first transform counts to pseudo Gaussian observations and then apply a (partial) correlation-based approach from the abundant literature of GGM inference. We adopt a different stance by relying on a latent model where we directly model counts by means of Poisson distributions that are conditional to latent (hidden) Gaussian correlated variables. In this multivariate Poisson lognormal-model, the dependency structure is completely captured by the latent layer. This parametric model enables to account for the effects of covariates on the counts. To perform network inference, we add a sparsity inducing constraint on the inverse covariance matrix of the latent Gaussian vector. Unlike the usual Gaussian setting, the penalized likelihood is generally not tractable, and we resort instead to a variational approach for approximate likelihood maximization. The corresponding optimization problem is solved by alternating a gradient ascent on the variational parameters and a graphical-Lasso step on the covariance matrix. We show that our approach is highly competitive with the existing methods on simulation inspired from microbiological data. We then illustrate on three various data sets how accounting for sampling efforts via offsets and integrating external covariates (which is mostly never done in the existing literature) drastically changes the topology of the inferred network.

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arXiv2018

Variational inference for probabilistic Poisson PCA

Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to understand the co-variations between these species. The Gaussian setting provides a canonical way to model such dependencies, but does not apply in general. We consider here the multivariate exponential family framework for which we introduce a generic model with multivariate Gaussian latent variables. We show that approximate maximum likelihood inference can be achieved via a variational algorithm for which gradient descent easily applies. We show that this setting enables us to account for covariates and offsets. We then focus on the case of the Poisson-lognormal model in the context of community ecology. We demonstrate the efficiency of our algorithm on microbial ecology datasets. We illustrate the importance of accounting for the effects of covariates to better understand interactions between species.

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arXiv2016

Multiple Comparative Metagenomics using Multiset k-mer Counting

Background. Large scale metagenomic projects aim to extract biodiversity knowledge between different environmental conditions. Current methods for comparing microbial communities face important limitations. Those based on taxonomical or functional assignation rely on a small subset of the sequences that can be associated to known organisms. On the other hand, de novo methods, that compare the whole sets of sequences, either do not scale up on ambitious metagenomic projects or do not provide precise and exhaustive results. Methods. These limitations motivated the development of a new de novo metagenomic comparative method, called Simka. This method computes a large collection of standard ecological distances by replacing species counts by k-mer counts. Simka scales-up today's metagenomic projects thanks to a new parallel k-mer counting strategy on multiple datasets. Results. Experiments on public Human Microbiome Project datasets demonstrate that Simka captures the essential underlying biological structure. Simka was able to compute in a few hours both qualitative and quantitative ecological distances on hundreds of metagenomic samples (690 samples, 32 billions of reads). We also demonstrate that analyzing metagenomes at the k-mer level is highly correlated with extremely precise de novo comparison techniques which rely on all-versus-all sequences alignment strategy or which are based on taxonomic profiling.

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arXiv2016

Detection of adaptive shifts on phylogenies using shifted stochastic processes on a tree

Comparative and evolutive ecologists are interested in the distribution of quantitative traits among related species. The classical framework for these distributions consists of a random process running along the branches of a phylogenetic tree relating the species. We consider shifts in the process parameters, which reveal fast adaptation to changes of ecological niches. We show that models with shifts are not identifiable in general. Constraining the models to be parsimonious in the number of shifts partially alleviates the problem but several evolutionary scenarios can still provide the same joint distribution for the extant species. We provide a recursive algorithm to enumerate all the equivalent scenarios and to count the effectively different scenarios. We introduce an incomplete-data framework and develop a maximum likelihood estimation procedure based on the EM algorithm. Finally, we propose a model selection procedure, based on the cardinal of effective scenarios, to estimate the number of shifts and prove an oracle inequality.

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arXiv2015

Convergence of the groups posterior distribution in latent or stochastic block models

We propose a unified framework for studying both latent and stochastic block models, which are used to cluster simultaneously rows and columns of a data matrix. In this new framework, we study the behaviour of the groups posterior distribution, given the data. We characterize whether it is possible to asymptotically recover the actual groups on the rows and columns of the matrix, relying on a consistent estimate of the parameter. In other words, we establish sufficient conditions for the groups posterior distribution to converge (as the size of the data increases) to a Dirac mass located at the actual (random) groups configuration. In particular, we highlight some cases where the model assumes symmetries in the matrix of connection probabilities that prevents recovering the original groups. We also discuss the validity of these results when the proportion of non-null entries in the data matrix converges to zero.

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arXiv2010

Uncovering latent structure in valued graphs: A variational approach

As more and more network-structured data sets are available, the statistical analysis of valued graphs has become common place. Looking for a latent structure is one of the many strategies used to better understand the behavior of a network. Several methods already exist for the binary case. We present a model-based strategy to uncover groups of nodes in valued graphs. This framework can be used for a wide span of parametric random graphs models and allows to include covariates. Variational tools allow us to achieve approximate maximum likelihood estimation of the parameters of these models. We provide a simulation study showing that our estimation method performs well over a broad range of situations. We apply this method to analyze host--parasite interaction networks in forest ecosystems.

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arXiv2009

Assessing the Distribution Consistency of Sequential Data

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The keypoint is to approximate the distribution of the n+k observations by the distribution of n-k among the n observations. Edgeworth expansion gives the correcting term and the rate of convergence. We also study the discrete distribution case, for which Cramèr's condition of smoothness is not satisfied. The rate of convergence for the various cases are compared.

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