arXiv subjects

Gildas Mazo

Publications and source records attributed to Gildas Mazo.

8 recordsLinked to original sources

arXiv2025

Gaussian copula correlation network analysis with application to multi-omics data

Reconstructing gene regulatory networks from large-scale heterogeneous data is a key challenge in biology. In multi-omics data analysis, networks based on pairwise statistical association measures remain popular, as they are easy to build and understand. In the presence of mixed-type (discrete and continuous) data, however, the choice of good association measures remains an important issue. We propose here a novel approach based on the Gaussian copula, the parameters of which represent the links of the network. Novel properties of the model are obtained to guide the interpretation of the network. To estimate the copula parameters, we calculated a semiparametric pairwise likelihood for mixed data. In an extensive simulation study, we showed that the proposed estimation procedure was able to accurately estimate the copula correlation matrix. The proposed methodology was also applied to a real ICGC dataset on breast cancer, and is implemented in a freely available R package heterocop.

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arXiv2024

A new paradigm for global sensitivity analysis

It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we show that Sobol indices are a particular instance of a more general concept which we call sensitivity measures. A sensitivity measure of a system taking inputs and returning outputs is a set function that is null at a subset of inputs if and only if, with probability one, the output actually does not depend on those inputs. A sensitivity measure evaluated at the whole set of inputs represents the uncertainty about the output. We show that measuring sensitivity to a particular subset is akin to measuring the expected output's uncertainty conditionally on the fact that the inputs belonging to that subset have been fixed to random values. By considering all of the possible combinations of inputs, sensitivity measures induce an implicit symmetric factorial experiment with two levels, the factorial effects of which can be calculated. This new paradigm generalizes many known sensitivity indices, can create new ones, and defines interaction effects independently of the choice of the sensitivity measure. No assumption about the distribution of the inputs is required.

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arXiv2022

A smoothed semiparametric likelihood for estimation of nonparametric finite mixture models with a copula-based dependence structure

In this manuscript, we consider a finite multivariate nonparametric mixture model where the dependence between the marginal densities is modeled using the copula device. Pseudo EM stochastic algorithms were recently proposed to estimate all of the components of this model under a location-scale constraint on the marginals. Here, we introduce a deterministic algorithm that seeks to maximize a smoothed semiparametric likelihood. No location-scale assumption is made about the marginals. The algorithm is monotonic in one special case, and, in another, leads to ``approximate monotonicity'' -- whereby the difference between successive values of the objective function becomes non-negative up to an additive term that becomes negligible after a sufficiently large number of iterations. The behavior of this algorithm is illustrated on several simulated datasets. The results suggest that, under suitable conditions, the proposed algorithm may indeed be monotonic in general. A discussion of the results and some possible future research directions round out our presentation.

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arXiv2022

Regularizing nested Monte Carlo Sobol' index estimators to balance the trade-off between explorations and repetitions in global sensitivity analysis of stochastic models

Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the explorations, the inner loop repeats model runs to estimate conditional expectations. Although the optimal allocation between explorations and repetitions of one's computational budget is well-known for nested Monte Carlo estimators, it is less clear how to deal with functions of nested Monte Carlo estimators, especially when those functions have unbounded Hessian matrices, as it is the case for Sobol' index estimators. To address this problem, a regularization method is introduced to bound the mean squared error of functions of nested Monte Carlo estimators. Based on a heuristic, an allocation strategy that seeks to minimize a bias-variance trade-off is proposed. The method is applied to Sobol' index estimators for stochastic models. A practical algorithm that adapts to the level of intrinsic randomness in the models is given and illustrated on numerical experiments.

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arXiv2022

Performing global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology

In this paper we apply a methodology introduced in Navarro Jimenez et al (2016) in the framework of chemical reaction networks to perform a global sensitivity analysis on simulations of a continuous-time Markov chain model motivated by epidemiology. Our goal is to quantify not only the effects of uncertain parameters such as epidemic parameters (transmission rate, mean sojourn duration in compartments), but also those of intrinsic randomness and interactions between epidemic parameters and intrinsic randomness. For that purpose, following what was proposed in Navarro Jimenez et al, we leverage three exact simulation algorithms for continuous-time Markov chains from the state of the art which we combine with common tools from variance-based sensitivity analysis as introduced in Sobol (1993). Also, we discuss the impact of the choice of the simulation algorithm used for the simulations on the results of sensitivity analysis. Such a discussion is new, at least to our knowledge. In a numerical section, we implement and compare three sensitivity analyses based on simulations obtained from different exact simulation algorithms of a SARS-CoV-2 epidemic model.

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arXiv2021

Inference on extremal dependence in the domain of attraction of a structured Hüsler-Reiss distribution motivated by a Markov tree with latent variables

A Markov tree is a probabilistic graphical model for a random vector indexed by the nodes of an undirected tree encoding conditional independence relations between variables. One possible limit distribution of partial maxima of samples from such a Markov tree is a max-stable Hüsler-Reiss distribution whose parameter matrix inherits its structure from the tree, each edge contributing one free dependence parameter. Our central assumption is that, upon marginal standardization, the data-generating distribution is in the max-domain of attraction of the said Hüsler-Reiss distribution, an assumption much weaker than the one that data are generated according to a graphical model. Even if some of the variables are unobservable (latent), we show that the underlying model parameters are still identifiable if and only if every node corresponding to a latent variable has degree at least three. Three estimation procedures, based on the method of moments, maximum composite likelihood, and pairwise extremal coefficients, are proposed for usage on multivariate peaks over thresholds data when some variables are latent. A typical application is a river network in the form of a tree where, on some locations, no data are available. We illustrate the model and the identifiability criterion on a data set of high water levels on the Seine, France, with two latent variables. The structured Hüsler-Reiss distribution is found to fit the observed extremal dependence patterns well. The parameters being identifiable we are able to quantify tail dependence between locations for which there are no data.

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arXiv2018

Parametric versus nonparametric: the fitness coefficient

The fitness coefficient, introduced in this paper, results from a competition between parametric and nonparametric density estimators within the likelihood of the data. As illustrated on several real datasets, the fitness coefficient generally agrees with p-values but is easier to compute and interpret. Namely, the fitness coefficient can be interpreted as the proportion of data coming from the parametric model. Moreover, the fitness coefficient can be used to build a semiparamteric compromise which improves inference over the parametric and nonparametric approaches. From a theoretical perspective, the fitness coefficient is shown to converge in probability to one if the model is true and to zero if the model is false. From a practical perspective, the utility of the fitness coefficient is illustrated on real and simulated datasets.

math.ST↗

arXiv2016

Extending one-factor copulas

So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new parametric factor copulas with a varying conditional dependence structure. We discuss estimation and properties of these representations. In order to distinguish between conditionally independent and conditionally dependent factor copulas, we provide a novel statistical test which does not assume any parametric form for the conditional dependence structure. Illustrations of our framework are provided through examples, numerical experiments, as well as a real data analysis.

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