arXiv subjects

Pierre Barbillon

Publications and source records attributed to Pierre Barbillon.

At least 19 recordsLinked to original sources

arXiv2025

Common Structure Discovery in Collections of Bipartite Networks: Application to Pollination Systems

Bipartite networks are widely used to encode the ecological interactions. Being able to compare the organization of bipartite networks is a first step toward a better understanding of how environmental factors shape community structure and resilience. Yet current methods for structure detection in bipartite networks overlook shared patterns across collections of networks. We introduce the \emph{colBiSBM}, a family of probabilistic models for collections of bipartite networks that extends the classical Latent Block Model (LBM). The proposed framework assumes that networks are independent realizations of a shared mesoscale structure, encoded through common inter-block connectivity parameters. We establish identifiability conditions for the different variants of \emph{colBiSBM} and develop a variational EM algorithm for parameter estimation, coupled with an adaptation of the Integrated Classification Likelihood (ICL) criterion for model selection. We demonstrate how our approach can be used to classify networks based on their topology or organization. Simulation studies highlight the ability of \emph{colBiSBM} to recover common structures, improve clustering performance, and enhance link prediction by borrowing strength across networks. An application to plant--pollinator networks highlights how the method uncovers shared ecological roles and partitions networks into sub-collections with similar connectivity patterns. These results illustrate the methodological and practical advantages of joint modeling over separate network analyses in the study of bipartite systems.

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arXiv2025

Interpretability of Graph Neural Networks to Assess Effects of Global Change Drivers on Ecological Networks

Pollinators play a crucial role for plant reproduction, either in natural ecosystem or in human-modified landscape. Global change drivers,including climate change or land use modifications, can alter the plant-pollinator interactions. To assess the potential influence of global change drivers on pollination, large-scale interactions, climate and land use data are required. While recent machine learning methods, such as graph neural networks (GNNs), allow the analysis of such datasets, interpreting their results can be challenging. We explore existing methods for interpreting GNNs in order to highlight the effects of various environmental covariates on pollination network connectivity. An extensive simulation study is performed to confirm whether these methods can detect the interactive effect between a covariate and a genus of plant on connectivity, and whether the application of debiasing techniques influences the estimation of these effects. An application on the Spipoll dataset, with and without accounting for sampling effects, highlights the potential impact of land use on network connectivity and shows that accounting for sampling effects partially alters the estimation of these effects.

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arXiv2024

HyperSBINN: A Hypernetwork-Enhanced Systems Biology-Informed Neural Network for Efficient Drug Cardiosafety Assessment

Mathematical modeling in systems toxicology enables a comprehensive understanding of the effects of pharmaceutical substances on cardiac health. However, the complexity of these models limits their widespread application in early drug discovery. In this paper, we introduce a novel approach to solving parameterized models of cardiac action potentials by combining meta-learning techniques with Systems Biology-Informed Neural Networks (SBINNs). The proposed method, hyperSBINN, effectively addresses the challenge of predicting the effects of various compounds at different concentrations on cardiac action potentials, outperforming traditional differential equation solvers in speed. Our model efficiently handles scenarios with limited data and complex parameterized differential equations. The hyperSBINN model demonstrates robust performance in predicting APD90 values, indicating its potential as a reliable tool for modeling cardiac electrophysiology and aiding in preclinical drug development. This framework represents an advancement in computational modeling, offering a scalable and efficient solution for simulating and understanding complex biological systems.

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arXiv2024

Bipartite Graph Variational Auto-Encoder with Fair Latent Representation to Account for Sampling Bias in Ecological Networks

Citizen science monitoring programs can generate large amounts of valuable data, but are often affected by sampling bias. We focus on a citizen science initiative that records plant-pollinator interactions, with the goal of learning embeddings that summarize the observed interactions while accounting for such bias. In our approach, plant and pollinator species are embedded based on their probability of interaction. These embeddings are derived using an adaptation of variational graph autoencoders for bipartite graphs. To mitigate the influence of sampling bias, we incorporate the Hilbert-Schmidt Independence Criterion (HSIC) to ensure independence from continuous variables related to the sampling process. This allows us to integrate a fairness perspective, commonly explored in the social sciences, into the analysis of ecological data. We validate our method through a simulation study replicating key aspects of the sampling process and demonstrate its applicability and effectiveness using the Spipoll dataset.

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arXiv2022

Disentangling the structure of ecological bipartite networks from observation processes

The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated on simulation studies. The pratical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.

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arXiv2022

Learning common structures in a collection of networks. An application to food webs

Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.

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arXiv2021

Screening the Discrepancy Function of a Computer Model

Screening traditionally refers to the problem of detecting active inputs in the computer model. In this paper, we develop methodology that applies to screening, but the main focus is on detecting active inputs not in the computer model itself but rather on the discrepancy function that is introduced to account for model inadequacy when linking the computer model with field observations. We contend this is an important problem as it informs the modeler which are the inputs that are potentially being mishandled in the model, but also along which directions it may be less recommendable to use the model for prediction. The methodology is Bayesian and is inspired by the continuous spike and slab prior popularized by the literature on Bayesian variable selection. In our approach, and in contrast with previous proposals, a single MCMC sample from the full model allows us to compute the posterior probabilities of all the competing models, resulting in a methodology that is computationally very fast. The approach hinges on the ability to obtain posterior inclusion probabilities of the inputs, which are very intuitive and easy to interpret quantities, as the basis for selecting active inputs. For that reason, we name the methodology PIPS -- posterior inclusion probability screening.

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arXiv2021

Impact of the mesoscale structure of a bipartite ecological interaction network on its robustness through a probabilistic modeling

The robustness of an ecological network quantifies the resilience of the ecosystem it represents to species loss. It corresponds to the proportion of species that are disconnected from the rest of the network when extinctions occur sequentially. Classically, the robustness is calculated for a given network, from the simulation of a large number of extinction sequences. The link between network structure and robustness remains an open question. Setting a joint probabilistic model on the network and the extinction sequences allows analysis of this relation. Bipartite stochastic block models have proven their ability to model bipartite networks e.g. plant-pollinator networks: species are divided into blocks and interaction probabilities are determined by the blocks of membership. Analytical expressions of the expectation and variance of robustness are obtained under this model, for different distributions of primary extinction sequences. The impact of the network structure on the robustness is analyzed through a set of properties and numerical illustrations. The analysis of a collection of bipartite ecological networks allows us to compare the empirical approach to our probabilistic approach, and illustrates the relevance of the latter when it comes to computing the robustness of a partially observed or incompletely sampled network.

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arXiv2020

Block models for multipartite networks.Applications in ecology and ethnobiology

Modeling relations between individuals is a classical question in social sciences, ecology, etc. In order to uncover a latent structure in the data, a popular approach consists in clustering individuals according to the observed patterns of interactions. To do so, Stochastic block models (SBM) and Latent Block models (LBM) are standard tools for clustering the individuals with respect to their comportment in a unique network. However, when adopting an integrative point of view, individuals are not involved in a unique network but are part of several networks, resulting into a potentially complex multipartite network. In this contribution, we propose a stochastic block model able to handle multipartite networks, thus supplying a clustering of the individuals based on their connection behavior in more than one network. Our model is an extension of the latent block models (LBM) and stochastic block model (SBM). The parameters -- such as the marginal probabilities of assignment to blocks and the matrix of probabilities of connections between blocks -- are estimated through a variational Expectation-Maximization procedure. The numbers of blocks are chosen with the Integrated Completed Likelihood criterion, a penalized likelihood criterion. The pertinence of our methodology is illustrated on two datasets issued from ecology and ethnobiology.

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arXiv2020

Analyzing Stochastic Computer Models: A Review with Opportunities

In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models -- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.

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arXiv2019

A Stochastic Block Model Approach for the Analysis of Multilevel Networks: an Application to the Sociology of Organizations

A multilevel network is defined as the junction of two interaction networks, one level representing the interactions between individuals and the other the interactions between organizations. The levels are linked by an affiliation relationship, each individual belonging to a unique organization. A new Stochastic Block Model is proposed as a unified probalistic framework tailored for multilevel networks. This model contains latent blocks accounting for heterogeneity in the patterns of connection within each level and introducing dependencies between the levels. The sought connection patterns are not specified a priori which makes this approach flexible. Variational methods are used for the model inference and an Integrated Classified Likelihood criterion is developed for choosing the number of blocks and also for deciding whether the two levels are dependent or not. A comprehensive simulation study exhibits the benefit of considering this approach, illustrates the robustness of the clustering and highlights the reliability of the criterion used for model selection. This approach is applied on a sociological dataset collected during a television program trade fair, the inter-organizational level being the economic network between companies and the inter-individual level being the informal network between their representatives. It brings a synthetic representation of the two networks unraveling their intertwined structure and confirms the coopetition at stake.

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arXiv2019

missSBM: An R Package for Handling Missing Values in the Stochastic Block Model

The Stochastic Block Model (SBM) is a popular probabilistic model for random graphs. It is commonly used for clustering network data by aggregating nodes that share similar connectivity patterns into blocks. When fitting an SBM to a network which is partially observed, it is important to take into account the underlying process that generates the missing values, otherwise the inference may be biased. This paper introduces missSBM, an R-package fitting the SBM when the network is partially observed, i.e., the adjacency matrix contains not only 1's or 0's encoding presence or absence of edges but also NA's encoding missing information between pairs of nodes. This package implements a set of algorithms for fitting the binary SBM, possibly in the presence of external covariates, by performing variational inference adapted to several observation processes. Our implementation automatically explores different block numbers to select the most relevant model according to the Integrated Classification Likelihood (ICL) criterion. The ICL criterion can also help determine which observation process better corresponds to a given dataset. Finally, missSBM can be used to perform imputation of missing entries in the adjacency matrix. We illustrate the package on a network data set consisting of interactions between political blogs sampled during the French presidential election in 2007.

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arXiv2019

Bayesian calibration of a numerical code for prediction

Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of problems. The code intends to be as close as possible to the physical system. It turns out that, despite continuous code development, the difference between the code outputs and experiments can remain significant. Two kinds of uncertainties are observed. The first one comes from the difference between the physical phenomenon and the values recorded experimentally. The second concerns the gap between the code and the physical system. To reduce this difference, often named model bias, discrepancy, or model error, computer codes are generally complexified in order to make them more realistic. These improvements lead to time consuming codes. Moreover, a code often depends on parameters to be set by the user to make the code as close as possible to field data. This estimation task is called calibration. This paper proposes a review of Bayesian calibration methods and is based on an application case which makes it possible to discuss the various methodological choices and to illustrate their divergences. This example is based on a code used to predict the power of a photovoltaic plant.

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arXiv2019

Computer code validation via mixture model estimation

When computer codes are used for modeling complex physical systems, their unknown parameters are tuned by calibration techniques. A discrepancy function may be added to the computer code in order to capture its discrepancy with the real physical process. By considering the validation question of a computer code as a Bayesian selection model problem, Damblin et al. (2016) have highlighted a possible confounding effect in certain configurations between the code discrepancy and a linear computer code by using a Bayesian testing procedure based on the intrinsic Bayes factor. In this paper, we investigate the issue of code error identifiability by applying another Bayesian model selection technique which has been recently developed by Kamary et al. (2014). By embedding the competing models within an encompassing mixture model, Kamary et al. (2014)'s method allows each observation to belong to a different mixing component, providing a more flexible inference, while remaining competitive in terms of computational cost with the intrinsic Bayesian approach. By using the technique of sharing parameters mentioned in Kamary et al. (2014), an improper non-informative prior can be used for some computer code parameters and we demonstrate that the resulting posterior distribution is proper. We then check the sensitivity of our posterior estimates to the choice of the parameter prior distributions. We illustrate that the value of the correlation length of the discrepancy Gaussian process prior impacts the Bayesian inference of the mixture model parameters and that the model discrepancy can be identified by applying the Kamary et al. (2014) method when the correlation length is not too small. Eventually, the proposed method is applied on a hydraulic code in an industrial context.

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arXiv2019

Post-processing multi-ensemble temperature and precipitation forecasts through an Exchangeable Gamma Normal model and its Tobit extension

Meteorological ensembles are a collection of scenarios for future weather delivered by a meteorological center. Such ensembles form the main source of valuable information for probabilistic forecasting which aims at producing a predictive probability distribution of the quantity of interest instead of a single best guess estimate. Unfortunately, ensembles cannot generally be considered as a sample from such a predictive probability distribution without a preliminary post-processing treatment to calibrate the ensemble. Two main families of post-processing methods, either competing such as BMA or collaborative such as EMOS, can be found in the literature. This paper proposes a mixed effect model belonging to the collaborative family. The structure of the model is based on the hypothesis of invariance under the relabelling of the ensemble members. Its interesting specificities are as follows: 1) exchangeability, which contributes to parsimony, with a latent pivot variable synthesizing the essential meteorological features of the ensembles, 2) a multi-ensemble implementation, allowing to take advantage of various information so as to increase the sharpness of the forecasting procedure. Focus is cast onto Normal statistical structures, first with a direct application for temperatures, then with its Tobit extension for precipitation. Inference is performed by EM algorithms with recourse made to stochastic conditional simulations in the precipitation case. After checking its good behavior on artificial data, the proposed post-processing technique is applied to temperature and precipitation ensemble forecasts produced over five river basins managed by Hydro-Qu$é$bec. These ensemble forecasts were extracted from the THORPEX Interactive Grand Global Ensemble (TIGGE) database. The results indicate that post-processed ensemble are calibrated and generally sharper than the raw ensembles.

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arXiv2019

Variational Inference for Stochastic Block Models from Sampled Data

This paper deals with non-observed dyads during the sampling of a network and consecutive issues in the inference of the Stochastic Block Model (SBM). We review sampling designs and recover Missing At Random (MAR) and Not Missing At Random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM under various sampling designs (MAR and NMAR) all available as an R package. Model selection criteria based on Integrated Classification Likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore two real-world networks from ethnology (seed circulation network) and biology (protein-protein interaction network), where the interpretations considerably depends on the sampling designs considered.

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arXiv2018

Sensitivity analysis of spatio-temporal models describing nitrogen transfers, transformations and losses at the landscape scale

Modelling complex systems such as agroecosystems often requires the quantification of a large number of input factors. Sensitivity analyses are useful to determine the appropriate spatial and temporal resolution of models and to reduce the number of factors to be measured or estimated accurately. Comprehensive spatial and temporal sensitivity analyses were applied to the NitroScape model, a deterministic spatially distributed model describing nitrogen transfers and transformations in rural landscapes. Simulations were led on a theoretical landscape that represented five years of intensive farm management and covering an area of $3\, km^2$. Cluster analyses were applied to summarize the results of the sensitivity analysis on the ensemble of model outputs. The methodology we applied is useful to synthesize sensitivity analyses of models with multiple space-time input and output variables and could be ported to other models than NitroScape.

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arXiv2018

CaliCo: a R package for Bayesian calibration

In this article, we present a recently released R package for Bayesian calibration. Many industrial fields are facing unfeasible or costly field experiments. These experiments are replaced with numerical/computer experiments which are realized by running a numerical code. Bayesian calibration intends to estimate, through a posterior distribution, input parameters of the code in order to make the code outputs close to the available experimental data. The code can be time consuming while the Bayesian calibration implies a lot of code calls which makes studies too burdensome. A discrepancy might also appear between the numerical code and the physical system when facing incompatibility between experimental data and numerical code outputs. The package CaliCo deals with these issues through four statistical models which deal with a time consuming code or not and with discrepancy or not. A guideline for users is provided in order to illustrate the main functions and their arguments. Eventually, a toy example is detailed using CaliCo. This example (based on a real physical system) is in five dimensions and uses simulated data.

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