6.1.1 Global implicit function theorems and the online EM algorithm

Participants: Florence Forbes.

Joint work with: Hien Nguyen, La Trobe University Melbourne Australia.

The expectation–maximisation (EM) algorithm is an important tool for statistical computation. Due to the changing nature of data, online and mini-batch variants of EM and EM-like algorithms have become increasingly popular. The consistency of the estimator sequences that are produced by these EM variants often rely on an assumption regarding the continuous differentiability of a parameter update function. In many cases, the parameter update function is often not in closed form and may only be defined implicitly, which makes the verification of the continuous differentiability property difficult. We demonstrate how a global implicit function theorem can be used to verify such properties in the cases of finite mixtures of distributions in the exponential family and more generally when the component specific distribution admits a data augmentation scheme in the exponential family. We demonstrate the use of such a theorem in the case of mixtures of beta distributions, gamma distributions, fully-visible Boltzmann machines and Student distributions. Via numerical simulations, we provide empirical evidence towards the consistency of the online EM algorithm parameter estimates in such cases. Details can be found in 62.

6.1.2 Fast Bayesian Inversion for high dimensional inverse problems

Participants: Florence Forbes, Benoit Kugler.

Joint work with: Sylvain Douté from Institut de Planétologie et d’Astrophysique de Grenoble (IPAG).

We investigated the use of learning approaches to handle Bayesian inverse problems in a computationally efficient way when the signals to be inverted present a moderately high number of dimensions and are in large number. We proposed a tractable inverse regression approach which has the advantage to produce full probability distributions as approximations of the target posterior distributions. In addition to provide confidence indices on the predictions, these distributions allow a better exploration of inverse problems when multiple equivalent solutions exist. We then showed how these distributions could be used for further refined predictions using importance sampling, while also providing a way to carry out uncertainty level estimation if necessary. The relevance of the proposed approach was illustrated both on simulated and real data in the context of a physical model inversion in planetary remote sensing. The approach showed interesting capabilities both in terms of computational efficiency and multimodal inference. Details can be found in 60.

6.1.3 Bayesian inverse regression for vascular magnetic resonance fingerprinting

Participants: Florence Forbes, Fabien Boux, Julyan Arbel.

Joint work with: Emmanuel Barbier from Grenoble Institute of Neuroscience.

Standard parameter estimation from vascular magnetic resonance fingerprinting (MRF) data is based on matching the MRF signals to their best counterparts in a grid of coupled simulated signals and parameters, referred to as a dictionary. To reach a good accuracy, the matching requires an informative dictionary whose cost, in terms of design, storage and exploration, is rapidly prohibitive for even moderate numbers of parameters. In this work, we propose an alternative dictionary-based statistical learning (DB-SL) approach made of three steps: 1) a quasi-random sampling strategy to produce efficiently an informative dictionary, 2) an inverse statistical regression model to learn from the dictionary a correspondence between fingerprints and parameters, and 3) the use of this mapping to provide both parameter estimates and their confidence indices. The proposed DB-SL approach is compared to both the standard dictionary-based matching (DBM) method and to a dictionary-based deep learning (DB-DL) method. Performance is illustrated first on synthetic signals including scalable and standard MRF signals with spatial undersampling noise. Then, vascular MRF signals are considered both through simulations and real data acquired in tumor bearing rats. Overall, the two learning methods yield more accurate parameter estimates than matching and to a range not limited to the dictionary boundaries. DB-SL in particular resists to higher noise levels and provides in addition confidence indices on the estimates at no additional cost. DB-SL appears as a promising method to reduce simulation needs and computational requirements, while modeling sources of uncertainty and providing both accurate and interpretable results. More details can be found in 18.

6.1.4 Unannounced Meal Detection for Artificial Pancreas Systems Using Extended Isolation Forest.

Participants: Florence Forbes, Fei Zheng.

Joint work with: Stéphane Bonnet from CEA Leti.

This study aims at developing an unannounced meal detection method for artificial pancreas, based on a recent extension of Isolation Forest. The proposed method makes use of features accounting for individual Continuous Glucose Monitoring (CGM) profiles and benefits from a two-threshold decision rule detection. The advantage of using Extended Isolation Forest (EIF) instead of the standard one is supported by experiments on data from virtual diabetic patients, showing good detection accuracy with acceptable detection delays.

6.1.5 Dirichlet process mixtures under affine transformations of the data

Participants: Julyan Arbel.

Joint work with: Riccardo Corradin and Bernardo Nipoti from Milano Bicocca, Italy.

Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation. In 14, we first devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformation of the data. Second, we formalize the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. As a by-product, we derive weaker assumptions than those provided in the literature for ensuring posterior consistency of Dirichlet process mixtures, which could reveal of independent interest. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419.

6.1.6 Approximate Bayesian computation with surrogate posteriors

Participants: Julyan Arbel, Florence Forbes.

Joint work with: Hien Nguyen, La Trobe University Melbourne Australia and Trung Tin Nguyen from University Caen Normandy.

A key ingredient in approximate Bayesian computation (ABC) procedures is the choice of a discrepancy that describes how different the simulated and observed data are, often based on a set of summary statistics when the data cannot be compared directly. Unless discrepancies and summaries are available from experts or prior knowledge, which seldom occurs, they have to be chosen and this can affect the approximations. Their choice is an active research topic, which has mainly considered data discrepancies requiring samples of observations or distances between summary statistics, to date. In this work, we introduce a preliminary learning step in which surrogate posteriors are built from finite Gaussian mixtures using an inverse regression approach. These surrogate posteriors are then used in place of summary statistics and compared using metrics between distributions in place of data discrepancies. Two such metrics are investigated, a standard L${}_2$ distance and an optimal transport-based distance. The whole procedure can be seen as an extension of the semi-automatic ABC framework to functional summary statistics. The resulting ABC quasi-posterior distribution is shown to converge to the true one, under standard conditions. Performance is illustrated on both synthetic and real data sets, where it is shown that our approach is particularly useful when the posterior is multimodal. Details can be found in 55.

6.1.7 Joint supervised classification and reconstruction of irregularly sampled satellite image times series

Participants: Alexandre Constantin, Stephane Girard.

Joint work with: Mathieu Fauvel, INRAE

Recent satellite missions have led to a huge amount of earth observation data, most of them being freely available. In such a context, satellite image time series have been used to study land use and land cover information. However, optical time series, like Sentinel-2 or Landsat ones, are provided with an irregular time sampling for different spatial locations, and images may contain clouds and shadows. Thus, pre-processing techniques are usually required to properly classify such data. The proposed approach is able to deal with irregular temporal sampling and missing data directly in the classification process. It is based on Gaussian processes and allows to perform jointly the classification of the pixel labels as well as the reconstruction of the pixel time series. The method complexity scales linearly with the number of pixels, making it amenable in large scale scenarios. Experimental classification and reconstruction results show that the method does not compete yet with state of the art classifiers but yields reconstructions that are robust with respect to the presence of undetected clouds or shadows and does not require any temporal preprocessing 52.

6.2.1 Subtle anomaly detection in MRI brain scans: Application to biomarkers extraction in patients with de novo Parkinson's disease

Participants: Florence Forbes, Veronica Munoz Ramirez, Virgilio Kmetzsch Rosa E Silva.

Joint work with: Michel Dojat from Grenoble Institute of Neuroscience and Elena Mora from CHUGA.

With the advent of recent deep learning techniques, computerized methods for automatic lesion segmentation have reached performances comparable to those of medical practitioners. However, little attention has been paid to the detection of subtle physiological changes caused by evolutive pathologies such as neurodegenerative diseases. In this work, we investigated the ability of deep learning models to detect anomalies in magnetic resonance imaging (MRI) brain scans of recently diagnosed and untreated (de novo) patients with Parkinson's disease (PD). We evaluated two families of auto-encoders, fully convolutional and variational auto-encoders. The models were trained with diffusion tensor imaging (DTI) parameter maps of healthy controls. Then, reconstruction errors computed by the models in different brain regions allowed to classify controls and patients with ROC AUC up to 0.81. Moreover, the white matter and the subcortical structures, particularly the substantia nigra, were identified as the regions the most impacted by the disease, in accordance with the physio-pathology of PD. Our results suggest that deep learning-based anomaly detection models, even trained on a moderate number of images, are promising tools for extracting robust neuroimaging biomarkers of PD. Interestingly, such models can be seamlessly extended with additional quantitative MRI parameters and could provide new knowledge about the physio-pathology of neuro-degenerative diseases.

6.2.2 Estimation of extreme risk measures

Participants: Stephane Girard, Antoine Usseglio Carleve.

Joint work with: A. Daouia (Univ. Toulouse), L. Gardes (Univ. Strasbourg) and G. Stupfler (Ensai).

One of the most popular risk measures is the Value-at-Risk (VaR) introduced in the 1990's. In statistical terms, the VaR at level $\alpha \in (0,1)$ corresponds to the upper $\alpha$-quantile of the loss distribution. The Value-at-Risk however suffers from several weaknesses. First, it provides us only with a pointwise information: VaR($\alpha$) does not take into consideration what the loss will be beyond this quantile. Second, random loss variables with light-tailed distributions or heavy-tailed distributions may have the same Value-at-Risk. Finally, Value-at-Risk is not a coherent risk measure since it is not subadditive in general. A first coherent alternative risk measure is the Conditional Tail Expectation (CTE), also known as Tail-Value-at-Risk, Tail Conditional Expectation or Expected Shortfall in case of a continuous loss distribution. The CTE is defined as the expected loss given that the loss lies above the upper $\alpha$-quantile of the loss distribution. This risk measure thus takes into account the whole information contained in the upper tail of the distribution.

However, the asymptotic normality of the empirical CTE estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in heavy-tailed models which constitute the favoured class of models in actuarial and financial applications. One possible solution in very heavy-tailed models where this assumption fails could be to use the more robust Median Shortfall, but this quantity is actually just a quantile, which therefore only gives information about the frequency of a tail event and not about its typical magnitude. In 25, we construct a synthetic class of tail $L_p$-medians, which encompasses the Median Shortfall (for $p=1$) and Conditional Tail Expectation (for $p=2$). We show that, for $1<p<2$, a tail $L_p$-median always takes into account both the frequency and magnitude of tail events, and its empirical estimator is, within the range of the data, asymptotically normal under a condition weaker than a finite variance. We extrapolate this estimator, along with another technique, to proper extreme levels using the heavy-tailed framework. The estimators are showcased on a simulation study and on a set of real fire insurance data showing evidence of a very heavy right tail.

Risk measures of a financial position are, from an empirical point of view, mainly based on quantiles. Replacing quantiles with their least squares analogues, called expectiles, has recently received increasing attention. The novel expectile-based risk measures satisfy all coherence requirements. We revisit their extreme value estimation for heavy-tailed distributions. First, we estimate the underlying tail index via weighted combinations of top order statistics and asymmetric least squares estimates. The resulting expectHill estimators are then used as the basis for estimating tail expectiles and Expected Shortfall. The asymptotic theory of the proposed estimators is provided, along with numerical simulations and applications to actuarial and financial data 22.

The estimation of expectiles typically requires to consider non-explicit asymmetric least squares estimates rather than the traditional order statistics used for quantile estimation. This makes the study of the tail expectile process a lot harder than that of the standard tail quantile process. Under the challenging model of heavy-tailed distributions, we derive joint weighted Gaussian approximations of the tail empirical expectile and quantile processes. We then use this powerful result to introduce and study new estimators of extreme expectiles and the standard quantile-based expected shortfall, as well as a novel expectile-based form of expected shortfall. Our estimators are built on general weighted combinations of both top order statistics and asymmetric least squares estimates. Some numerical simulations and applications to actuarial and financial data are provided 23.

Currently available estimators of extreme expectiles are typically biased and hence may show poor finite-sample performance even in fairly large samples. In 59, we focus on the construction of bias-reduced extreme expectile estimators for heavy-tailed distributions. The rationale for our construction hinges on a careful investigation of the asymptotic proportionality relationship between extreme expectiles and their quantile counterparts, as well as of the extrapolation formula motivated by the heavy-tailed context. We accurately quantify and estimate the bias incurred by the use of these relationships when constructing extreme expectile estimators. This motivates the introduction of a class of bias-reduced estimators whose asymptotic properties are rigorously shown, and whose finite-sample properties are assessed on a simulation study and three samples of real data from economics, insurance and finance. The results are submitted for publication.

6.2.3 Conditional extremal events

Participants: Stephane Girard, Antoine Usseglio Carleve.

The goal of the PhD thesis of Aboubacrene Ag Ahmad is to contribute to the development of theoretical and algorithmic models to tackle conditional extreme value analysis, ie the situation where some covariate information $X$ is recorded simultaneously with a quantity of interest $Y$. In such a case, extreme quantiles and expectiles are functions of the covariate. In 11, we consider a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

As explained in Paragraph 6.2.2, expectiles have recently started to be considered as serious candidates to become standard tools in actuarial and financial risk management. However, expectiles and their sample versions do not benefit from a simple explicit form, making their analysis significantly harder than that of quantiles and order statistics. This difficulty is compounded when one wishes to integrate auxiliary information about the phenomenon of interest through a finite-dimensional covariate, in which case the problem becomes the estimation of conditional expectiles. In 26, we exploit the fact that the expectiles of a distribution $F$ are in fact the quantiles of another distribution $E$ explicitly linked to $F$, in order to construct nonparametric kernel estimators of extreme conditional expectiles. We analyze the asymptotic properties of our estimators in the context of conditional heavy-tailed distributions. Applications to simulated data and real insurance data are provided. The extension to functional covariates is investigated in 58 and submitted for publication.

In 57, we build a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise. Our approach is supported by general results of independent interest on residual-based extreme value estimators in heavy-tailed regression models, and is intended to cope with covariates having a large but fixed dimension. We demonstrate how our results can be applied to a wide class of important examples, among which linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data. The results are submitted for publication.

6.2.4 Dimension reduction for extremes

Participants: Meryem Bousebata, Stephane Girard.

Joint work with: G. Enjolras (CERAG).

In the context of the PhD thesis of Meryem Bousebata, we propose a new approach, called Extreme-PLS, for dimension reduction in regression and adapted to distribution tails. The objective is to find linear combinations of predictors that best explain the extreme values of the response variable in a non-linear inverse regression model. The asymptotic normality of the Extreme-PLS estimator is established in the single-index framework and under mild assumptions. The performance of the method is assessed on simulated data. A statistical analysis of French farm income data, considering extreme cereal yields, is provided as an illustration. The results are submitted for publication 49.

6.2.5 Estimation of the variability in the distribution tail

Participants: Stephane Girard.

Joint work with: L. Gardes (Univ. Strasbourg).

We propose a new measure of variability in the tail of a distribution by applying a Box-Cox transformation of parameter $p\ge 0$ to the tail-Gini functional. It is shown that the so-called Box-Cox Tail Gini Variability measure is a valid variability measure whose condition of existence may be as weak as necessary thanks to the tuning parameter $p$. The tail behaviour of the measure is investigated under a general extreme-value condition on the distribution tail. We then show how to estimate the Box-Cox Tail Gini Variability measure within the range of the data. These methods provide us with basic estimators that are then extrapolated using the extreme-value assumption to estimate the variability in the very far tails. The finite sample behavior of the estimators is illustrated both on simulated and real data. This work is published in 24.

6.2.6 Extrapolation limits associated with extreme-value methods

Participants: Stephane Girard.

Joint work with: L. Gardes (Univ. Strasbourg) and A. Dutfoy (EDF R&D).

In 13, we investigate the asymptotic behavior of the (relative) extrapolation error associated with some estimators of extreme quantiles based on extreme-value theory. It is shown that the extrapolation error can be interpreted as the remainder of a first order Taylor expansion. Necessary and sufficient conditions are then provided such that this error tends to zero as the sample size increases. Interestingly, in case of the so-called Exponential Tail estimator, these conditions lead to a subdivision of Gumbel maximum domain of attraction into three subsets. In contrast, the extrapolation error associated with Weissman estimator has a common behavior over the whole Fréchet maximum domain of attraction. First order equivalents of the extrapolation error are then derived and their accuracy is illustrated numerically.

In 12, we propose a new estimator for extreme quantiles under the log-generalized Weibull-tail model, introduced by Cees de Valk. This model relies on a new regular variation condition which, in some situations, permits to extrapolate further into the tails than the classical assumption in extreme-value theory. The asymptotic normality of the estimator is established and its finite sample properties are illustrated both on simulated and real datasets.

6.2.7 Approximations of Bayesian nonparametric models

Participant: Julyan Arbel, Daria Bystrova.

Joint work with: Stefano Favaro from Collegio Carlo Alberto, Turin, Italy, Guillaume Kon Kam King and François Deslandes from MaIAGE - Mathématiques et Informatique Appliquées du Génome à l'Environnement (INRAE Jouy-En-Josas)

In this work, we approximate predictive probabilities of Gibbs-type random probability measures, or Gibbs-type priors, which are arguably the most “natural” generalization of the celebrated Dirichlet prior. Among them the Pitman–Yor process certainly stands out for the mathematical tractability and interpretability of its predictive probabilities, which made it the natural candidate in several applications. Given a sample of size $n$, in this paper we show that the predictive probabilities of any Gibbs-type prior admit a large $n$ approximation, with an error term vanishing as $o(1/n)$, which maintains the same desirable features as the predictive probabilities of the Pitman–Yor process.

In 37, we study the prior distribution induced on the number of clusters, which is key for prior specification and calibration. However, evaluating this prior is infamously difficult even for moderate sample size. We evaluate several statistical approximations to the prior distribution on the number of clusters for Gibbs-type processes, a class including the Pitman-Yor process and the normalized generalized gamma process. We introduce a new approximation based on the predictive distribution of Gibbs-type process, which compares favourably with the existing methods. We thoroughly discuss the limitations of these various approximations by comparing them against an exact implementation of the prior distribution of the number of clusters.

We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a connection between Hurwitz zeta function and the cumulants of the exponential-beta distribution.

6.2.8 Concentration inequalities

Participant: Julyan Arbel, Stéphane Girard, Mariia Vladimirova.

Joint work with: Olivier Marchal from Université Jean Monnet and Hien Nguyen from La Trobe University Melbourne Australia.

In this work, we investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these questions is how to characterize the optimal sub-Gaussian proxy variance? Another question is how to characterize strict sub-Gaussianity, defined by a proxy variance equal to the (standard) variance? We address the questions in proposing conditions based on the study of functions variations. A particular focus is given to the relationship between strict sub-Gaussianity and symmetry of the distribution. In particular, we demonstrate that symmetry is neither sufficient nor necessary for strict sub-Gaussianity. In contrast, simple necessary conditions on the one hand, and simple sufficient conditions on the other hand, for strict sub-Gaussianity are provided. These results are illustrated via various applications to a number of bounded random variables, including Bernoulli, beta, binomial, uniform, Kumaraswamy, and triangular distributions.

In 34, we propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterized by a positive tail index θ and reduce to sub-Gaussian distributions for $\theta =1/2$ and to sub-Exponential distributions for $\theta =1$. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties of the class are studied. An estimation procedure for the tail parameter is proposed and is applied to an example stemming from Bayesian deep learning.

6.2.9 Applications of semi and non-parametric methods in ecology and genomics

Participant: Julyan Arbel, Daria Bystrova, Giovanni Poggiato.

Joint work with: Florian Privé and Bjarni Vilhjálmsson from National Center for Register-Based Research (Aarhus, Denmark), Billur Bektaş and Wilfried Thuiller from LECA - Laboratoire d'Ecologie Alpine, James S Clark from Nicholas School of the Environment, Duke University, USA, Alessandra Guglielmi from POLIMI - Dipartimento di Matematica - POLIMI, Politecnico di Milano.

In 21, we investigate modelling species distributions over space and time which is one of the major research topics in both ecology and conservation biology. Joint Species Distribution models (JSDMs) have recently been introduced as a tool to better model community data, by inferring a residual covariance matrix between species, after accounting for species' response to the environment. However, these models are computationally demanding, even when latent factors, a common tool for dimension reduction, are used. To address this issue, previous research proposed to use a Dirichlet process, a Bayesian nonparametric prior, to further reduce model dimension by clustering species in the residual covariance matrix. Here, we built on this approach to include a prior knowledge on the potential number of clusters, and instead used a Pitman-Yor process to address some critical limitations of the Dirichlet process. We therefore propose a framework that includes prior knowledge in the residual covariance matrix, providing a tool to analyze clusters of species that share the same residual associations with respect to other species. We applied our methodology to a case study of plant communities in a protected area of the French Alps (the Bauges Regional Park), and demonstrated that our extensions improve dimension reduction and reveal additional information from the residual covariance matrix, notably showing how the estimated clusters are compatible with plant traits, endorsing their importance in shaping communities.

In 31, we investigate modelling polygenic scores which have become a central tool in human genetics research. LDpred is a popular method for deriving polygenic scores based on summary statistics and a matrix of correlation between genetic variants. However, LDpred has limitations that may reduce its predictive performance. Here we present LDpred2, a new version of LDpred that addresses these issues. We also provide two new options in LDpred2: a "sparse" option that can learn effects that are exactly 0, and an "auto" option that directly learns the two LDpred parameters from data. We benchmark predictive performance of LDpred2 against the previous version on simulated and real data, demonstrating substantial improvements in robustness and predictive accuracy compared to LDpred1. We then show that LDpred2 also outperforms other polygenic score methods recently developed, with a mean AUC over the 8 real traits analyzed here of $65.1\%$, compared to $63.8\%$ for lassosum, $62.9\%$ for PRS-CS and $61.5\%$ for SBayesR. Note that LDpred2 provides more accurate polygenic scores when run genome-wide, instead of per chromosome. LDpred2 is implemented in R package bigsnpr.

6.3.1 Optimal shrinkage for robust covariance matrix estimators in a small sample size setting

Participants: Sophie Achard, Karina Ashurbekova, Florence Forbes, Antoine Usseglio Carleve.

When estimating covariance matrices, traditional sample covariance-based estimators are straightforward but suffer from two main issues: 1) a lack of robustness, which occurs as soon as the samples do not come from a Gaussian distribution or are contaminated with outliers and 2) a lack of data when the number of parameters to estimate is too large compared to the number of available observations, which occurs as soon as the covariance matrix dimension is greater than the sample size. The first issue can be handled by assuming samples are drawn from a heavy-tailed distribution, at the cost of more complex derivations, while the second issue can be addressed by shrinkage with the difficulty of choosing the appropriate level of regularization. In this work 48 we offer both a tractable and optimal framework based on shrinked likelihood-based M-estimators. First, a closed-form expression is provided for a regularized covariance matrix estimator with an optimal shrinkage coefficient for any sample distribution in the elliptical family. Then, a complete inference procedure is proposed which can also handle both unknown mean and tail parameter, in contrast to most existing methods that focus on the covariance matrix parameter requiring pre-set values for the others. An illustration on synthetic and real data is provided in the case of the t-distribution with unknown mean and degrees-of-freedom parameters.

6.3.2 Bayesian nonparametric models for hidden Markov random fields on non-Gaussian variables and applications

Participants: Julyan Arbel, Jean-Baptiste Durand, Florence Forbes.

Joint work with: Hien Nguyen from La Trobe University Melbourne Australia and Grégoire Vincent from IRD, AMAP, Montpellier, France

Hidden Markov random fields (HMRFs) have been widely used in image segmentation and more generally, for clustering of data indexed by graphs. Dependent hidden variables (states) represent the cluster identities and determine their interpretations. Dependencies between state variables are induced by the notion of neighborhood in the graph. A difficult and crucial problem in HMRFs is the identification of the number of possible states $K$. Recently, selection methods based on Bayesian non parametric priors (Dirichlet processes) have been developed. They do not assume that $K$ is bounded a priori, thus allowing its adaptive selection with respect to the quantity of available data and avoiding costly systematic estimation and comparison of models with different fixed values for $K$. Our previous work 27 has focused on Bayesian nonparametric priors for HMRFs and continuous, Gaussian observations. In this work, we consider extensions to non-Gaussian observed data. A first case is discrete data, typically issued from counts. A second is exponential-distributed data. We defined and implemented Bayesian nonparametric models for HMRFs with Poisson- and exponential-distributed observations. Inference is achieved by Variational Bayesian Expectation Maximization (VBEM).

We proposed an application of the discrete-data model to a new risk mapping model for traffic accidents in the region of Victoria, Australia 54. The partition into regions using labels yielded by HMRFs was interpreted using covariates, which showed a good discrimination with regard to labels.

As a perspective, Bayesian nonparametric models for hidden Markov random fields could be extended to non-Poissonian models (particularly to account for zero-inflated and over-/under-dispersed cases of application) and to regression models.

The exponential model was applied to leaf density estimation in forests and isolated trees subjected to laser scans. The data are lengths of portions of laser beams between two hits of translucent materials (mainly, leaves). The sampling space is discretized into voxels and under some specific assumptions, the lengths have an exponential distribution with possible censoring if the beam leaves the voxel. The added-value of HMRFs is to go beyond the assumption of independent voxels and taking into account spatial dependencies between them, which are due to the underlying geometric structure of trees.

Current perspectives of this work include the improvement of the convergence in the VBEM algorithm, since however the KL divergence between the posterior distribution and its approximation converges, the sequence of optimizing parameters is shown to diverge in our current approach.

6.3.3 Bayesian nonparametric spatial prior for traffic crash risk mapping: a case study of Victoria, Australia

Participants: Jean-Baptiste Durand, Florence Forbes.

Joint work with: Hien Nguyen, Long Truong, Q. Phan from La Trobe University Melbourne Australia.

We investigate the use of Bayesian nonparametric (BNP) models coupled with Markov random fields (MRF) in a risk mapping context, to build partitions of the risk into homogeneous spatial regions. In contrast to most existing methods, the proposed approach does not require an arbitrary commitment to a specified number of risk classes and determines their risk levels automatically. We consider settings in which the relevant information are counts and propose a so called BNP Hidden MRF (BNP-HMRF) model that is able to handle such data. The model inference is carried out using a variational Bayes Expectation–Maximisation algorithm and the approach is illustrated on traffic crash data in the state of Victoria, Australia. The obtained results corroborate well with the traffic safety literature. More generally, the model presented here for risk mapping offers an effective, convenient and fast way to conduct partition of spatially localised count data. Details can be found in 54.

6.3.4 Hidden Markov models for the analysis of eye movements

Participants: Jean-Baptiste Durand, Sophie Achard.

Joint work with: Anne Guérin-Dugué (GIPSA-lab) and Benoit Lemaire (Laboratoire de Psychologie et Neurocognition)

This research theme is supported by a LabEx PERSYVAL-Lab project-team grant.

In the last years, GIPSA-lab has developed computational models of information search in web-like materials, using data from both eye-tracking and electroencephalograms (EEGs). These data were obtained from experiments, in which subjects had to decide whether a text was related or not to a target topic presented to them beforehand. In such tasks, reading process and decision making are closely related. Statistical analysis of such data aims at deciphering underlying dependency structures in these processes. Hidden Markov models (HMMs) have been used on eye-movement series to infer phases in the reading process that can be interpreted as strategies or steps in the cognitive processes leading to decision. In HMMs, each phase is associated with a state of the Markov chain. The states are observed indirectly though eye-movements. Our approach was inspired by Simola et al. (2008) 70, but we used hidden semi-Markov models for better characterization of phase length distributions (Olivier et al., 2017) 69. The estimated HMM highlighted contrasted reading strategies, with both individual and document-related variability. New results were obtained in the standalone analysis of the eye-movements: 1) a statistical comparison between the effects of three types of texts was performed, considering texts either closely related, moderately related or unrelated to the target topic; 2) a characterization of the effects of the distance to trigger words on transition probabilities and 3) highlighting a predominant intra-individual variability in scanpaths.

Our goal for this coming year is to use the segmentation induced by our eye-movement model to obtain a statistical characterization of functional brain connectivity through simultaneous EEG recordings. This should lead to some integrated models coupling EEG and eye movements within one single HMM for better identification of strategies.

6.3.5 Assessing spatial dependencies in the effect of treatment on neurite growth

Participants: Jean-Baptiste Durand, Sophie Achard, Jiajie Li.

Joint work with: Stéphane Belin, Homaira Nawabi, Sabine Chierici from Grenoble Institute of Neuroscience.

The World Health Organization estimates that 250 000 to 500 000 new cases of spinal cord injuries occur each year. People suffering from those lesions endure irreversible disabilities, as no treatment is available to counteract the regenerative failure of mature Central Nervous System (CNS). Thus, promoting neuronal growth, repair and functional recovery remains one of the greatest challenges for neurology, patients and public health. Our partners at GIN (Grenoble Institute for Neurosciences) demonstrated that doublecortin is a key factor for axon regeneration and neuronal survival. Short peptides could be used as a treatment to enhance axon outgrowth. To test their potential effect on axonal growth, embryonic neurons in culture are treated with those peptides. Neurons are then imaged and neurite length is quantified automatically. The analysis of such data raises statistical questions to avoid bias in testing the relevance of a given peptide. All neuronal cultures are not the same. Particularly, the proximity between neurons is variable and likely to influence its intrinsic capability to grow. In such contexts, the usual test-based methodology to compare treatments cannot be applied and has to be adapted.

In this work, we highlighted the first-order spatial stationarity of neurite lengths within a same experiment, using HMRF models depicted in Subsection 6.3.3. Then we investigate spatial dependencies between lengths of close neurites, highlighting the relevance of CAR models of J. Besag to account for the effect of neighbours' lengths. This raises the question of choosing a relevant graph of dependencies in CAR and several types of graphs were compared.

6.3.6 Modelling the effects of cultivars and treatments on the structure of apple trees

Participants: Jean-Baptiste Durand.

Joint work with: Evelyne Costes, INRAE, AGAP, Montpellier, France and Martin Mészáros, Research and Breeding Institute of Pomology Holovousy Ltd., Hořice, Czech Republic.

This study aims at characterizing the effects of cultivars and treatments on the structure of apple trees. More specifically, tree trunks are issued from the following cultivars Rubinola, Topaz and Golden Delicious. Each tree is fertilized one among these different nitrogen (N) doses: I) untreated (control), II) treated with 20 g N/tree/year, and III) treated with 30 g N/tree/year. We developed a modelling strategy inspired by Meszaros in 2020: it is assumed that in every cultivar under every treatment, there exists an underlying common sequence of development, which is indirectly observed through the following features attached to each metamer (elementary entity) of the trunk: length class of axillary shoots, together with their lateral and terminal flowering. This sequence is modelled by successions of zones along the trunks (zone lengths, transitions and distributions of features within each zone). These assumptions lead to estimated hidden semi-Markov chain (HSMC) models with similar definitions as in Subsection 6.3.4.

It now remains to model how the HSMC parameters depend on cultivars and treatments, which is planned to be handled with generalized linear models.

6.3.7 Splitting models for multivariate count data

Participants: Jean-Baptiste Durand.

Joint work with: Jean Peyhardi, Institut Montpelliérain Alexander Grothendieck, Montpellier, France and Pierre Fernique, CIRAD, Agap, Montpellier, France

Modelling multivariate count data and their dependencies is a difficult problem, in absence of a reference probabilistic model equivalent to the multivariate Gaussian in the continuous case, which allows modelling arbitrary marginal and conditional independence properties among those representable by graphical models while keeping probabilistic computations tractable (or even better, explicit).

In this work, we investigated the class of splitting distributions as the composition of a singular multivariate distribution and a univariate distribution. It was shown that most common parametric count distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate negative hypergeometric, ...) can be written as splitting distributions with separate parameters for both components, thus facilitating their interpretation, inference, the study of their probabilistic characteristics and their extensions to regression models. We highlighted many probabilistic properties deriving from the compound aspect of splitting distributions and their underlying algebraic properties. Parameter inference and model selection are thus reduced to two separate problems, preserving time and space complexity of the base models. Based on this principle, we introduced several new distributions. In the case of multinomial splitting distributions, conditional independence and asymptotic normality properties for estimators were obtained. Mixtures of splitting regression models were used on a mango tree dataset in order to analyse its patchiness.

Conditional independence properties of estimators were obtained for sum and singular distribution parameters for MLE and Bayesian estimators in the framework of multinomial splitting distributions 29. As a perspective, similar properties remain to be investigated for other cases of splitting (or possibly sum) distributions and regression models. Moreover, this work could be used for learning graphical models with discrete variables, which is an open issue. Although the graphical models for usual additive convolution splitting distributions are trivial (either complete or empty), they could be used as building blocks for partially directed acyclic graphical models. Therefore, some existing procedures for learning partially directed acyclic graphical models could be used for learning those based on convolution splitting distributions and regressions. Such approaches could be used for instance to infer gene co-expression network from RNA seq data sets.

6.3.8 Bayesian neural networks

Participants: Julyan Arbel, Mariia Vladimirova.

Joint work with: Pablo Mesejo from University of Granada, Spain, Jakob Verbeek from Inria Grenoble Rhône-Alpes, France.

We investigate deep Bayesian neural networks with Gaussian priors on the weights and ReLU-like nonlinearities, shedding light on novel sparsity-inducing mechanisms at the level of the units of the network, both pre- and post-nonlinearities. The main thrust of the paper is to establish that the units prior distribution becomes increasingly heavy-tailed with depth. We show that first layer units are Gaussian, second layer units are sub-Exponential, and we introduce sub-Weibull distributions to characterize the deeper layers units. Bayesian neural networks with Gaussian priors are well known to induce the weight decay penalty on the weights. In contrast, our result indicates a more elaborate regularisation scheme at the level of the units. This result provides new theoretical insight on deep Bayesian neural networks, underpinning their natural shrinkage properties and practical potential.

6.3.9 Brain connectivity

Participants: Sophie Achard.

Joint work with: Emmanuel Barbier from GIN and Guillaume Becq from GIPSA-lab, Univ. Grenoble Alpes

In two recent publications 16 and 16, we evaluated the reliability of graph connectivity estimations using wavelets. Under anesthesia, systemic variables and CBF are modified. How does this alter the connectivity measures obtained with rs-fMRI? To tackle this question, we explored the effect of four different anesthetics on Long Evans and Wistar rats with multimodal recordings of rs-fMRI, systemic variables and CBF. After multimodal signal processing, we show that the blood-oxygen-level-dependent (BOLD) variations and functional connectivity (FC) evaluated at low frequencies (0.031–0.25 Hz) do not depend on systemic variables and are preserved across large interval of baseline CBF values. Based on these findings, we found that most brain areas remain functionally active under any anesthetics, i.e. connected to at least one other brain area, as shown by the connectivity graphs. In addition, we quantified the influence of nodes by a measure of functional connectivity strength to show the specific areas targeted by anesthetics and compare correlation values of edges at different levels. These measures enable us to highlight the specific network alterations induced by anesthetics. Altogether, this suggests that changes in connectivity could be evaluated under anesthesia, routinely used in the control of neurological injury.

8.1.1 Inria International Labs

Statify is involved in the Inria associate team SIMERG2E (Statistical Inference for the Management of Extreme Risks, Genetics and Global Epidemiology) headed by Stéphane Girard, 2015-2020, part of the LIRIMA international lab, and together with LERSTAD, Université Gaston Berger (Senegal). Two research axes are explored: 1) Spatial extremes, application to management of extreme risks. We address the definition of new risk measures, the study of their properties in case of extreme events and their estimation from data and covariate information. Our goal is to obtain estimators accounting for possible variability, both in terms of space and time, which is of prime importance in many hydrological, agricultural and energy contexts. 2) Classification, application to genetics and global epidemiology. We address the challenge to build statistical models in order to test association between diseases and human host genetics in a context of genome-wide screening. Adequate models should allow to handle complexity in genomic data (correlation between genetic markers, high dimensionality) and additional statistical issues present in data collected from a family-based longitudinal survey (non-independence between individuals due to familial relationship and non-independence within individuals due to repeated measurements on a same person over time).

8.1.2 Inria associate team not involved in an IIL

LANDER: Title: Latent Analysis, Adversarial Networks, and DimEnsionality Reduction - International Partner (Institution - Laboratory - Researcher): Start year: 2019. See also: https://team.inria.fr/mistis/projects/lander/

The collaboration is based on three main points, in statistics, machine learning and applications: 1) clustering and classification (mixture models), 2) regression and dimensionality reduction (mixture of regression models and non parametric techniques) and 3) high impact applications (neuroimaging and MRI). Our overall goal is to collectively combine our resources and data in order to develop tools that are more ubiquitous and universal than we could have previously produced, each on our own. A wide class of problems from medical imaging can be formulated as inverse problems. Solving an inverse problem means recovering an object from indirect noisy observations. Inverse problems are therefore often compounded by the presence of errors (noise) in the data but also by other complexity sources such as the high dimensionality of the observations and objects to recover, their complex dependence structure and the issue of possibly missing data. Another challenge is to design numerical implementations that are computationally efficient. Among probabilistic models, generative models have appealing properties to meet all the above constraints. They have been studied in various forms and rather independently both in the statistical and machine learning literature with different depths and insights, from the well established probabilistic graphical models to the more recent (deep) generative adversarial networks (GAN). The advantages of the latter being primarily computational and their disadvantages being the lack of theoretical statements, in contrast to the former. The overall goal of the collaboration is to build connections between statistical and machine learning tools used to construct and estimate generative models with the resolution of real life inverse problems as a target. This induces in particular the need to help the models scale to high dimensional data while maintaining our ability to assess their correctness, typically the uncertainty associated to the provided solutions.

8.1.3 Participation in other international programs

Sophie Achard is coPI of the ANR project (PRCI) QFunC in partnership with University of Santa Barbara (USA) and Université de Lausanne (Switzerland). The aim of the project is to build spatio-temporal models for brain connectivity. The financial support for Statify is 260000 euros.

ANR

Statify is involved in the 4-year ANR project ExtremReg (2019-2023) hosted by Toulouse University. This research project aims to provide new adapted tools for nonparametric and semiparametric modeling from the perspective of extreme values. Our research program concentrates around three central themes. First, we contribute to the expanding literature on non-regular boundary regression where smoothness and shape constraints are imposed on the regression function and the regression errors are not assumed to be centred, but one-sided. Our second aim is to further investigate the study of the modern extreme value theory built on the use of asymmetric least squares instead of traditional quantiles and order statistics. Finally, we explore the less-discussed problem of estimating high-dimensional, conditional and joint extremes

The financial support for Statify is about 15.000 euros.

Statify is also involved in the ANR project GAMBAS (2019-2023) hosted by Cirad, Montpellier. The project Generating Advances in Modeling Biodiversity And ecosystem Services (GAMBAS) develops statistical improvements and ecological relevance of joint species distribution models. The project supports the PhD thesis of Giovanni Poggiato.

Grenoble Idex projects

Statify is involved in a transdisciplinary project NeuroCoG and in a newly accepted cross-disciplinary project (CDP) Risk@UGA. F. Forbes is also a member of the executive committee and responsible for the Data Science for life sciences work package in another project entitled Grenoble Alpes Data Institute.

• The main objective of the Risk@UGA project is to provide some innovative tools both for the management of risk and crises in areas that are made vulnerable because of strong interdependencies between human, natural or technological hazards, in synergy with the conclusions of Sendai conference. The project federates a hundred researchers from Human and Social Sciences, Information & System Sciences, Geosciences and Engineering Sciences, already strongly involved in the problems of risk assessment and management, in particular natural risks. The PhD thesis of Meryem Bousebata is one of the eleven PhDs funded by this project.
• The NeuroCoG project aims at understanding the biological, neurophysiological and functional bases of behavioral and cognitive processes in normal and pathological conditions, from cells to networks and from individual to social cognition. No decisive progress can be achieved in this area without an aspiring interdisciplinary approach. The interdisciplinary ambition of NeuroCoG is particularly strong, bringing together the best scientists, engineers and clinicians at the crossroads of experimental and life sciences, human and social sciences and information and communication sciences, to answer major questions on the workings of the brain and of cognition. One of the work package entitled InnobioPark is dedicated to Parkinson's Disease. The PhD thesis of Veronica Munoz Ramirez is one of the three PhDs in this work package.
• The Grenoble Alpes Data Institute aims at undertaking groundbreaking interdisciplinary research focusing on how data change science and society. It combines three fields of data-related research in a unique way: data science applied to spatial and environmental sciences, biology, and health sciences; data-driven research as a major tool in Social Sciences and Humanities; and studies about data governance, security and the protection of data and privacy. In this context, a 2-year multi-disciplinary projects has been granted in November 2018 to Mistis in collaboration with the Grenoble Institute of Neuroscience. The objective of this project is to develop a statistical learning technique that is able to solve a problem of tracking and analyzing a large population of single molecules. The main difficulties are: 1) the large number of observations to analyse, 2) the noisy nature of the signals, 3) the definition of a quality index to allow the elimination of poor-quality data and false positive signals. We also aim at providing a powerful, well-documented and open-source software, that will be user-friendly for non-specialists.

In the context of the Idex associated with the Université Grenoble Alpes, Alexandre Constantin was awarded half a PhD funding from IRS (Initiatives de Recherche Stratégique), 50 keuros.

In the context of the MIAI (Multidisciplinary Institute in Artificial Intelligence) institute and its open call to sustain the development and promotion of AI, Stéphane Girard was awarded a grant of 4500 euros for his project "Simulation of extreme values by AI generative models. Application to banking risk" joint with CMAP, Ecole Polytechnique.

In the context of the MIAI (Multidisciplinary Institute in Artificial Intelligence) institute and its open call to sustain the development and promotion of AI, Julyan Arbel was awarded a grant of 5000 euros for his project "Bayesian deep learning".

Julyan Arbel was awarded a grant of 10000 euros for his project "Bayesian nonparametric modeling".

8.2.1 Networks

MSTGA and AIGM INRA (French National Institute for Agricultural Research) networks: F. Forbes and J.B Durand are members of the INRA network called AIGM (ex MSTGA) network since 2006, http://carlit.toulouse.inra.fr/AIGM, on Algorithmic issues for Inference in Graphical Models. It is funded by INRA MIA and RNSC/ISC Paris. This network gathers researchers from different disciplines. mistis co-organized and hosted 2 of the network meetings in 2008 and 2015 in Grenoble.

9.1.1 Scientific events: organisation

9.1.2 Journal

9.1.3 Invited talks

• Julyan Arbel was an invited speaker at 13th International Conference of Computational and Methodological Statistics (CMStat), University of London, UK, December.
• Julyan Arbel was an invited speaker at Statistics Seminar Series in the School of Mathematics & Statistics, University College Dublin, November 23.
• Stéphane Girard was an invited speaker at StressTest-2020: International Workshop on Stress Test and Risk Management 42.
• Florence Forbes was an invited speaker at the AppliBUGS group Seminar (link).

9.1.4 Scientific expertise

• Julyan Arbel is a scientific committee member of the Data Science axis of Persyval Labex (Machine learning: fundamentals and applications, and Data linking, sharing and privacy), since 2019.
• Stéphane Girard was a member of the committee in charge of hiring a Professor at LJK, Université Grenoble-Alpes.
• Stéphane Girard acted as an expert of NWO projects evaluation (Netherlands Organisation for Scientific Research).
• Florence Forbes was a member of the committee in charge of hiring professors and teaching assistants at Ecole Polytechnique, Paris.
• Florence Forbes acted as an expert for the tenure application of Lo Bin Chang at Ohio University, USA.
• Florence Forbes acted as a reviewer for Charles University, Prague.
• Florence Forbes is a member of the Helmholtz AI Cooperation Unit advisory committee (link), 2019-present.
• Florence Forbes is a member of the EURASIP Technical Area Committee BISA (Biomedical Image & Signal Analytics) since January 2021 for a 3 years duration.

9.2.1 Teaching

• Licence : Stéphane Girard, Principe et Méthodes Statistiques, 18 ETD, L3 level, Ensimag. Grenoble-INP, France.
• Master : Stéphane Girard, Statistique Inférentielle Avancée, 18 ETD, M1 level, Ensimag. Grenoble-INP, France.
• Master and PhD course: Julyan Arbel, Bayesian nonparametrics and Bayesian deep learning, Master Mathématiques Apprentissage et Sciences Humaines (M*A*S*H), Université PSL (Paris Sciences & Lettres), 25 ETD. Bayesian deep learning, Master Intelligence Artificielle, Systèmes, Données (IASD), Université PSL (Paris Sciences & Lettres), 12 ETD.
• Master and PhD course: Julyan Arbel, Bayesian machine learning, Master Mathématiques Vision et Apprentissage Master MVA, École normale supérieure Paris-Saclay, 36 ETD.
• Master: Jean-Baptiste Durand, Statistics and probability, 192H, M1 and M2 levels, Ensimag Grenoble INP, France. Head of the MSIAM M2 program, in charge of the data science track.
• Jean-Baptiste Durand is a faculty member at Ensimag, Grenoble INP.
• Sophie Achard M1 course Théorie des graphes et réseaux sociaux, M1 level, MIASHS, Université Grenoble Alpes (UGA), 14 ETD.

9.2.2 Supervision

• PhD defended: Aboubacrène Ag Ahmad "Modélisation semi-paramétrique des extrêmes conditionnels", 46, September 2020, Stéphane Girard and Alio Diop, Université Gaston Berger, Sénégal.
• PhD defended: Veronica Munoz,"Extraction de signatures dans les données IRM de patients parkinsoniens de novo", Florence Forbes and Michel Dojat, Université Grenoble Alpes, December 2020.
• PhD defended: Fabien Boux,"Développement de méthodes statistiques pour l’imagerie IRM fingerprinting", Florence Forbes and Emmanuel Barbier, Université Grenoble Alpes, December 2020.
• PhD in progress: Benoit Kugler, "Massive hyperspectral images analysis by inverse regression of physical models", Florence Forbes and Sylvain Douté, Université Grenoble Alpes, started on October 2018.
• PhD in progress: Mariia Vladimirova, “Prior specification for Bayesian deep learning models and regularization implications”, started on October 2018, Julyan Arbel and Jakob Verbeek, Université Grenoble Alpes.
• PhD in progress: Théo Moins "Quantification bayésienne des limites d’extrapolation en statistique des valeurs extrêmes", started on October 2020, Stéphane Girard and Julyan Arbel, Université Grenoble Alpes.
• PhD in progress: Michael Allouche "Simulation d’extrêmes par modèles génératifs et applications aux risques bancaires", started on April 2020, Stéphane Girard and Emmanuel Gobet, Ecole Polytechnique.
• PhD in progress: Meryem Bousebata "Bayesian estimation of extreme risk measures: Implication for the insurance of natural disasters", started on October 2018, Stéphane Girard and Geffroy Enjolras, Université Grenoble Alpes.
• PhD in progress: Alexandre Constantin "Analyse de séries temporelles massives d'images satellitaires : Applications à la cartographie des écosystèmes", started on November 2018, Stéphane Girard and Mathieu Fauvel, Université Grenoble Alpes.
• PhD in progress: Daria Bystrova, “Joint Species Distribution Modeling: Dimension reduction using Bayesian nonparametric priors”, started on October 2019, Julyan Arbel and Wilfried Thuiller, Université Grenoble Alpes.
• PhD in progress: Giovanni Poggiatto, “Scalable Approaches for Joint Species Distribution Modeling”, started on November 2019, Julyan Arbel and Wilfried Thuiller, Université Grenoble Alpes.
• PhD in progress: Minh Tri Lê, “Constrained signal processing using deep neural networks for MEMs sensors based applications.”, started on September 2020, Julyan Arbel and Etienne de Foras, Université Grenoble Alpes, CIFRE Invensense.

9.2.3 Juries

• Florence Forbes has been reviewer for the PhD thesis of Faustine Bousquet (Universite de Montpellier), Raphaelle Momal (Université Paris-Saclay), Nikola Hrelja (Ecole Polytechnique), Maxime Vono (Université de Toulouse) and Thi Khuyen Le (Université Aix-Marseille).
• Florence Forbes has been a member of the PhD committee of Bruno Meriaux (Université Paris-Saclay) and of the HDR committee of Jean-Baptiste Durand (Université Grenoble Alpes).
• Sophie Achard has been reviewer for the HDR of Julien Modolo (Université Rennes 1).

International journals

• 11 articleAboubacrèneA. Ag Ahmad, HadjiH. Deme, AliouA. Diop, StephaneS. Girard and AntoineA. Usseglio-Carleve. Estimation of extreme quantiles from heavy-tailed distributions in a location-dispersion regression modelElectronic journal of statistics 1422020, 4421--4456
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• 12 articleClémentC. Albert, AnneA. Dutfoy, LaurentL. Gardes and StéphaneS. Girard. An extreme quantile estimator for the log-generalized Weibull-tail modelEconometrics and Statistics 13January 2020, 137-174
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• 13 articleClémentC. Albert, AnneA. Dutfoy and StéphaneS. Girard. Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantilesExtremes23June 2020, 349-380
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• 14 articleJulyanJ. Arbel, RiccardoR. Corradin and BernardoB. Nipoti. Dirichlet process mixtures under affine transformations of the dataComputational Statistics36March 2021, 577-601
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• 15 article JulyanJ. Arbel, OlivierO. Marchal and BernardoB. Nipoti. On the Hurwitz zeta function with an application to the exponential-beta distribution Journal of Inequalities and Applications February 2020
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• 16 articleGuillaume Jean-Paul ClaudeG.-P. Becq, Emmanuel LucE. Barbier and SophieS. Achard. Brain networks of rats under anesthesia using resting-state fMRI: comparison with dead rats, random noise and generative models of networksJournal of Neural Engineering174August 2020, 045012
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• 17 articleGuillaume Jean-Paul ClaudeG.-P. Becq, TarikT. Habet, NoraN. Collomb, MargauxM. Faucher, ChantalC. Delon-Martin, VéroniqueV. Coizet, SophieS. Achard and Emmanuel LucE. Barbier. Functional connectivity is preserved but reorganized across several anesthetic regimesNeuroImage219October 2020, 116945
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• 18 article FabienF. Boux, FlorenceF. Forbes, JulyanJ. Arbel, BenjaminB. Lemasson and Emmanuel L.E. Barbier. Bayesian inverse regression for vascular magnetic resonance fingerprinting IEEE Transactions on Medical Imaging 2021
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• 19 article FabienF. Boux, FlorenceF. Forbes, NoraN. Collomb, emmae. zub, LucileL. Maziere, FrédericF. Bock, MarineM. Blaquière, VasileV. Stupar, AntoineA. Depaulis, NicolaN. Marchi and EmmanuelE. Barbier. Neurovascular multiparametric MRI defines epileptogenic and seizure propagation regions in experimental mesiotemporal lobe epilepsy Epilepsia April 2021
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• 20 article ClémentC. Brossard, OlivierO. Montigon, FabienF. Boux, AurélienA. Delphin, ThomasT. Christen, Emmanuel LE. Barbier and BenjaminB. Lemasson. MP3: Medical software for Processing multi-Parametric images Pipelines Frontiers in Neuroinformatics 14 November 2020
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• 21 articleDariaD. Bystrova, GiovanniG. Poggiato, BillurB. Bektaş, JulyanJ. Arbel, James SJ. Clark, AlessandraA. Guglielmi and WilfriedW. Thuiller. Clustering species with residual covariance matrix in Joint Species Distribution modelsFrontiers in Ecology and Evolution2021, 1-20
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• 22 articleAbdelaatiA. Daouia, StephaneS. Girard and GillesG. Stupfler. ExpectHill estimation, extreme risk and heavy tailsJournal of Econometrics2020, 1-54
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• 23 articleAbdelaatiA. Daouia, StephaneS. Girard and GillesG. Stupfler. Tail expectile process and risk assessmentBernoulli2612020, 531-556
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• 24 article LaurentL. Gardes and StéphaneS. Girard. On the estimation of the variability in the distribution tail Test 2021
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• 25 articleLaurentL. Gardes, StephaneS. Girard and GillesG. Stupfler. Beyond tail median and conditional tail expectation: extreme risk estimation using tail $L^p$−optimisation'Scandinavian Journal of Statistics473September 2020, 922--949
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• 26 article StephaneS. Girard, GillesG. Stupfler and AntoineA. Usseglio-Carleve. Nonparametric extreme conditional expectile estimation Scandinavian Journal of Statistics 2020
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• 27 articleHongliangH. Lu, JulyanJ. Arbel and FlorenceF. Forbes. Bayesian nonparametric priors for hidden Markov random fieldsStatistics and Computing302020, 1015-1035
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• 28 articleHien DH. Nguyen, FlorenceF. Forbes and Geoffrey JG. Mclachlan. Mini-batch learning of exponential family finite mixture modelsStatistics and Computing30July 2020, 731–748
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• 29 articleJeanJ. Peyhardi, PierreP. Fernique and Jean-BaptisteJ.-B. Durand. Splitting models for multivariate count dataJournal of Multivariate Analysis181January 2021, 104677
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• 30 article GiovanniG. Poggiato, TamaraT. Münkemüller, DariaD. Bystrova, JulyanJ. Arbel, JamesJ. Clark and WilfriedW. Thuiller. On the interpretations of joint modelling in community ecology Trends in Ecology and Evolution 2021
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• 31 article FlorianF. Privé, JulyanJ. Arbel and Bjarni JB. Vilhjálmsson. LDpred2: better, faster, stronger Bioinformatics December 2020
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• 32 articleFélixF. Renard, ChristianC. Heinrich, MarineM. Bouthillon, MalekaM. Schenck, FrancisF. Schneider, StéphaneS. Kremer and SophieS. Achard. A covariate-constraint method to map brain feature space into lower dimensional manifoldsNetwork Neuroscience51January 2021, 252-273
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• 33 articleMilanM. Stehlik, JozefJ. Kiseľák, MarijusM. Vaičiulis, Pavlina KalchevaP. Jordanova, Ludy NunezL. Soza, ZdeněkZ. Fabián, PhilippP. Hermann, LubošL. Střelec, AndresA. Rivera, StéphaneS. Girard and SebastiánS. Torres. Priority statement and some properties of t-lgHill estimatorExtremes233September 2020, 393--399
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• 34 article MariiaM. Vladimirova, StéphaneS. Girard, HienH. Nguyen and JulyanJ. Arbel. Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions Stat October 2020
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• 35 articleFeiF. Zheng, ManonM. Jalbert, FlorenceF. Forbes, StephaneS. Bonnet, AnneA. Wojtusciszyn, SandrineS. Lablanche and Pierre-YvesP.-Y. Benhamou. Characterization of Daily Glycemic Variability in Subjects with Type 1 Diabetes Using a Mixture of MetricsDiabetes Technology and Therapeutics224April 2020, 301-313
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International peer-reviewed conferences

• 36 inproceedingsMeryemM. Bousebata, GeoffroyG. Enjolras and StéphaneS. Girard. The dependence structure between yields and prices: A copula-based model of French farm incomeAAEA 2020 - Annual Meeting of the Agricultural and Applied Economics AssociationVirtuel, United StatesAugust 2020, 1-15
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• 37 inproceedingsDariaD. Bystrova, JulyanJ. Arbel, GuillaumeG. Kon Kam King and FrançoisF. DESLANDES. Approximating the clusters' prior distribution in Bayesian nonparametric modelsAABI 2020 - 3rd Symposium on Advances in Approximate Bayesian InferenceOnline, United StatesJanuary 2021, 1-16
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• 38 inproceedingsGuillaumeG. Cathelain, BertrandB. Rivet, SophieS. Achard, JeanJ. Bergounioux and FrancoisF. Jouen. Smart ballistocardiography front-endI2MTC 2020 - IEEE International Instrumentation and Measurement Technology Conference (I2MTC)Dubrovnik (online), CroatiaIEEEMay 2020, 1-6
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• 39 inproceedingsGuillaumeG. Cathelain, BertrandB. Rivet, SophieS. Achard, JeanJ. Bergounioux and FrancoisF. Jouen. U-Net Neural Network for Heartbeat Detection in BallistocardiographyEMBC 2020 - CMBEC 2020 - 42nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society - 43rd Annual Conference of the Canadian Medical and Biological Engineering SocietyMontreal (virtual), CanadaIEEEJuly 2020, 465-468
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Conferences without proceedings

• 40 inproceedings Aboubacrène AgA. Ahmad, StéphaneS. Girard, AntoineA. Usseglio-Carleve, AliouA. Diop and EL HadjiE. Deme. Estimation of extreme quantiles from heavy-tailed distributions in a semi-parametric location-dispersion regression model Quatrièmes rencontres des jeunes chercheurs africains en France Virtual, France December 2020
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• 41 inproceedings FabienF. Boux, FlorenceF. Forbes, JulyanJ. Arbel, AurélienA. Delphin, ThomasT. Christen and EmmanuelE. Barbier. Dictionary-based Learning in MR Fingerprinting: Statistical Learning versus Deep Learning International Society for Magnetic Resonance in Medicine (ISMRM) Sidney, Australia August 2020
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• 42 inproceedings StéphaneS. Girard, Aboubacrène AgA. Ahmad, EL HadjiE. Deme, AliouA. Diop and AntoineA. Usseglio-Carleve. Estimation of extreme quantiles from heavy-tailed distributions in a location-dispersion regression model StressTest-2020 - International Workshop on Stress Test and Risk Management Paris / Virtual, France November 2020
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• 43 inproceedingsBenoitB. Kugler, FlorenceF. Forbes and SylvainS. Douté. An efficient Bayesian method for inverting physical models on massive planetary dataEPSC 2020 - Europlanet Science CongressGranada (Virtual meeting), SpainSeptember 2020, 1-4
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• 44 inproceedingsBenoitB. Kugler, FlorenceF. Forbes and SylvainS. Douté. First order Sobol indices for physical models via inverse regressionJDS 2020 - 52èmes Journées de Statistique de la Société Française de Statistique (SFdS)Nice, FranceJune 2021, 1-6
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• 45 inproceedings AntoineA. Usseglio-Carleve, StéphaneS. Girard and GillesG. Stupfler. On automatic bias reduction for extreme expectile estimation CMStatistics 2020 - 13th International Conference of the ERCIM WG on Computational and Methodological Statistics London / Virtual, United Kingdom December 2020
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Doctoral dissertations and habilitation theses

• 46 thesis Aboubacrène AgA. Ahmad. Semi-parametric modelling of conditional extremes Université Gaston Berger de Saint-Louis (Sénégal) September 2020
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Reports & preprints

• 47 misc SophieS. Achard, PierreP. Borgnat and IrèneI. Gannaz. Asymptotic control of FWER under Gaussian assumption: application to correlation tests July 2020
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• 48 misc KarinaK. Ashurbekova, AntoineA. Usseglio-Carleve, FlorenceF. Forbes and SophieS. Achard. Optimal shrinkage for robust covariance matrix estimators in a small sample size setting March 2021
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• 49 misc MeryemM. Bousebata, GeoffroyG. Enjolras and StéphaneS. Girard. Extreme Partial Least-Squares regression 2021
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• 50 misc DariaD. Bystrova, JulyanJ. Arbel and ThibaudT. Rahier. Contributed comment on Article by Hahn, Murray, and Carvalho August 2020
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• 51 misc DariaD. Bystrova, GiovanniG. Poggiato, JulyanJ. Arbel and WilfriedW. Thuiller. Latent factor models: a tool for dimension reduction in joint species distribution models February 2021
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• 52 misc AlexandreA. Constantin, MathieuM. Fauvel and StéphaneS. Girard. Joint Supervised Classification and Reconstruction of Irregularly Sampled Satellite Image Times Series 2020
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• 53 misc Pascal SielenouP. Dkengne, StéphaneS. Girard and SamiaS. Ahiad. An automatic procedure to select a block size in the continuous generalized extreme value model estimation September 2020
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• 54 misc Jean-BaptisteJ.-B. Durand, FlorenceF. Forbes, Cong DucC. Phan, LongL. Truong, Hien DH. Nguyen and FatoumataF. Dama. Bayesian nonparametric spatial prior for traffic crash risk mapping: a case study of Victoria, Australia February 2021
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• 55 misc FlorenceF. Forbes, Hien DuyH. Nguyen, Trung TinT. Nguyen and JulyanJ. Arbel. Approximate Bayesian computation with surrogate posteriors February 2021
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• 56 misc StéphaneS. Girard, GillesG. Stupfler and AntoineA. Usseglio-Carleve. An $Lp$ −quantile methodology for estimating extreme expectiles' April 2020
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• 57 misc StéphaneS. Girard, GillesG. Stupfler and AntoineA. Usseglio-Carleve. Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models April 2021
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• 58 misc StéphaneS. Girard, GillesG. Stupfler and AntoineA. Usseglio-Carleve. Functional estimation of extreme conditional expectiles March 2021
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• 59 misc StéphaneS. Girard, GillesG. Stupfler and AntoineA. Usseglio-Carleve. On automatic bias reduction for extreme expectile estimation January 2021
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• 60 misc BenoitB. Kugler, FlorenceF. Forbes and SylvainS. Douté. Fast Bayesian Inversion for high dimensional inverse problems July 2020
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• 61 misc VincentV. Miele, CatherineC. Matias, MarcM. Ohlmann, GiovanniG. Poggiato, StéphaneS. Dray and WilfriedW. Thuiller. Quantifying the overall effect of biotic interactions on species communities along environmental gradients March 2021
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• 62 misc Hien DuyH. Nguyen and FlorenceF. Forbes. Global implicit function theorems and the online expectation-maximisation algorithm January 2021
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• 63 report BriceB. Olivier, AnneA. Guérin-Dugué and Jean-BaptisteJ.-B. Durand. Hidden Semi-Markov Models to Segment Reading Phases from Eye Movements Inria Grenoble - Rhône-Alpes March 2021
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