3.3.1 Modelling extremal events

Extreme value theory is a branch of statistics dealing with the extreme deviations from the bulk of probability distributions. More specifically, it focuses on the limiting distributions for the minimum or the maximum of a large collection of random observations from the same arbitrary distribution. Let $X_{1,n}\le ...\le X_{n,n}$ denote $n$ ordered observations from a random variable $X$ representing some quantity of interest. A $p_n$-quantile of $X$ is the value $x_{p_n}$ such that the probability that $X$ is greater than $x_{p_n}$ is $p_n$, i.e.$P(X>x_{p_n})=p_n$. When $p_n<1/n$, such a quantile is said to be extreme since it is usually greater than the maximum observation $X_{n,n}$.

To estimate such quantiles therefore requires dedicated methods to extrapolate information beyond the observed values of $X$. Those methods are based on Extreme value theory. This kind of issue appeared in hydrology. One objective was to assess risk for highly unusual events, such as 100-year floods, starting from flows measured over 50 years. To this end, semi-parametric models of the tail are considered:

where both the extreme-value index $\theta >0$ and the function $\ell \left(x\right)$ are unknown. The function $\ell$ is a slowly varying function i.e. such that

for all $t>0$. The function $\ell \left(x\right)$ acts as a nuisance parameter which yields a bias in the classical extreme-value estimators developed so far. Such models are often referred to as heavy-tail models since the probability of extreme events decreases at a polynomial rate to zero. It may be necessary to refine the model (2,3) by specifying a precise rate of convergence in (3). To this end, a second order condition is introduced involving an additional parameter $\rho \le 0$. The larger $\rho$ is, the slower the convergence in (3) and the more difficult the estimation of extreme quantiles.

More generally, the problems that we address are part of the risk assessment theory. For instance, in reliability, the distributions of interest are included in a semi-parametric family whose tails are decreasing exponentially fast. These so-called Weibull-tail distributions 8 are defined by their survival distribution function:

Gaussian, gamma, exponential and Weibull distributions, among others, are included in this family. An important part of our work consists in establishing links between models (2) and (4) in order to propose new estimation methods. We also consider the case where the observations were recorded with a covariate information 9. In this case, the extreme-value index and the $p_n$-quantile are functions of the covariate. We propose estimators of these functions by using moving window approaches, nearest neighbor methods, or kernel estimators.

3.3.2 Level sets estimation

Level sets estimation is a recurrent problem in statistics which is linked to outlier detection. In biology, one is interested in estimating reference curves, that is to say curves which bound $90\%$ (for example) of the population. Points outside this bound are considered as outliers compared to the reference population. Level sets estimation can be looked at as a conditional quantile estimation problem which benefits from a non-parametric statistical framework. In particular, boundary estimation, arising in image segmentation as well as in supervised learning, is interpreted as an extreme level set estimation problem. Level sets estimation can also be formulated as a linear programming problem. In this context, estimates are sparse since they involve only a small fraction of the dataset, called the set of support vectors.

3.3.3 Dimension reduction

Our work on high dimensional data requires that we face the curse of dimensionality phenomenon. Indeed, the modelling of high dimensional data requires complex models and thus the estimation of high number of parameters compared to the sample size. In this framework, dimension reduction methods aim at replacing the original variables by a small number of linear combinations with as small as a possible loss of information. Principal Component Analysis (PCA) is the most widely used method to reduce dimension in data. However, standard linear PCA can be quite inefficient on image data where even simple image distortions can lead to highly non-linear data. Two directions are investigated. First, non-linear PCAs can be proposed, leading to semi-parametric dimension reduction methods 88. Another field of investigation is to take into account the application goal in the dimension reduction step. One of our approaches is therefore to develop new Gaussian models of high dimensional data for parametric inference 1. Such models can then be used in a Mixtures or Markov framework for classification purposes. Another approach consists in combining dimension reduction, regularization techniques, and regression techniques to improve the Sliced Inverse Regression method 89.

7.1.1 Planet-GLLiM

• Name:
  Planet-GLLiM
• Keyword:
  Inverse problem
• Functional Description:
  The application implements the GLLiM statistical learning technique in its different variants for the inversion of a physical model of reflectance on spectro-(gonio)-photometric data. The latter are of two types: 1. laboratory measurements of reflectance spectra acquired according to different illumination and viewing geometries, 2. and 4D spectro-photometric remote sensing products from multi-angular CRISM or Pléiades acquisitions.
• URL:
  https://­gitlab.­inria.­fr/­kernelo-mistis/­planet-gllim-front-end/­-/­wikis/­Home
• Publications:
  insu-03705153, hal-02908364
• Contact:
  Sylvain Douté
• Participants:
  Florence Forbes, Benoit Kugler, Sami Djouadi, Samuel Heidmann, Stanislaw Borkowski
• Partner:
  Institut de Planétologie et d’Astrophysique de Grenoble

7.1.2 Kernelo

• Name:
  Kernelo-GLLiM
• Keywords:
  Inverse problem, Clustering, Regression, Gaussian mixture, Python, C++
• Scientific Description:
  Building a regression model for the purpose of prediction is widely used in all disciplines. A large number of applications consists of learning the association between responses and predictors and focusing on predicting responses for the newly observed samples. In this work, we go beyond simple linear models and focus on predicting low-dimensional responses using high-dimensional covariates when the associations between responses and covariates are non-linear.
• Functional Description:
  Kernelo-GLLiM is a Gaussian Locally-Linear Mapping (GLLiM) solver. Kernelo-GLLiM provides a C++ library and a python module for non linear mapping (non linear regression) using a mixture of regression model and an inverse regression strategy. The methods include the GLLiM model (Deleforge et al (2015) ) based on Gaussian mixtures.
• URL:
  https://­gitlab.­inria.­fr/­kernelo-mistis/­kernelo-gllim-is/­-/­wikis/­home
• Publications:
  hal-00863468, hal-02908364
• Contact:
  Florence Forbes
• Participants:
  Florence Forbes, Benoit Kugler, Sami Djouadi, Samuel Heidmann, Stanislaw Borkowski
• Partner:
  Institut de Planétologie et d’Astrophysique de Grenoble

8.1.1 An online Minorization-Maximization algorithm

Participants: Florence Forbes.

Joint work with: Hien Nguyen, University of Queensland, Brisbane Australia, Gersende Fort, IMT Toulouse and Olivier Cappé ENS Paris.

Modern statistical and machine learning settings often involve high data volume and data streaming, which require the development of online estimation algorithms. The online Expectation-Maximization (EM) algorithm extends the popular EM algorithm to this setting, via a stochastic approximation approach. We show that an online version of the Minorization-Maximization (MM) algorithm, which includes the online EM algorithm as a special case, can also be constructed in a similar manner. We demonstrate our approach via an application to the logistic regression problem and compare it to existing methods 36.

8.1.2 Global implicit function theorems and the online expectation-maximisation algorithm

Participants: Florence Forbes.

Joint work with: Hien Nguyen, University of Queensland, Brisbane Australia.

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 27.

8.1.3 Concentration results for approximate Bayesian computation without identifiability

Participants: Florence Forbes, Julyan Arbel, Trung Tin Nguyen.

Joint work with: Hien Nguyen, University of Queensland, Brisbane Australia.

We study the large sample behaviors of approximate Bayesian computation (ABC) posterior measures in situations when the data generating process is dependent on non-identifiable parameters. In particular, we establish the concentration of posterior measures on sets of arbitrarily small size that contain the equivalence set of the data generative parameter, when the sample size tends to infinity. Our theory also makes weak assumptions regarding the measurement of discrepancy between the data set and simulations, and in particular, does not require the use of summary statistics and is applicable to a broad class of kernelized ABC algorithms. We provide useful illustrations and demonstrations of our theory in practice, and offer a comprehensive assessment of the nature in which our findings complement other results in the literature.

8.1.4 Online EM algorithm for robust clustering

Participants: Florence Forbes, Geoffroy Oudoumanessah.

Joint work with: Hien Nguyen, University of Queensland, Australia and Michel Dojat Grenoble Institute of Neurosciences.

A popular way to approach clustering tasks is via a parametric mixture model. The vast majority of the work on such mixtures has been based on Gaussian mixture models. However, in some applications the tails of Gaussian distributions are shorter than appropriate or parameter estimations are affected by atypical observations (outliers). To address this issue, mixtures of so-called multiple scale Student distributions have been proposed and used for clustering. In contrast to the Gaussian case, no closed-form solution exists for such mixtures but tractability is maintained via the use of the expectation-maximisation (EM) algorithm. However, such mixtures require more parameters than the standard Student or Gaussian mixtures and the EM algorithm used to estimate the mixture parameters involves more complex numerical optimizations. Consequently, when the number of samples to be clustered becomes large, applying EM on the whole data set (Batch EM) may become costly both in terms of time and memory requirements. A natural approach to bypass this issue is to consider an online version of the algorithm, that can incorporate the samples incrementally or in mini batches. In this work, we proposed to design a tractable online EM for mixtures of multiple scale Student distributions in order to use it then to detect subtle brain anomalies from MR brain scans for patients suffering from Parkinson disease. The application to Parkinson disease will be carried out jointly with Grenoble Institute of Neuroscience.

8.1.5 A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models

Participants: Florence Forbes, Trung Tin Nguyen.

Joint work with: Faicel Chamroukhi, University of Caen and Hien Nguyen, University of Queensland, Brisbane, Australia.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper 84 is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

8.1.6 Bayesian mixture models (in)consistency for the number of clusters

Participants: Julyan Arbel, Louise Alamichel, Daria Bystrova.

Joint work with: Guillaume Kon Kam King (INRAE).

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, their application for clustering has some limitations. Recent results proved posterior inconsistency of the number of clusters when the true number of clusters is finite for the Dirichlet process and Pitman–Yor process mixture models. In 68, we extend these results to additional Bayesian nonparametric priors such as Gibbs-type processes and finite-dimensional representations thereof. The latter include the Dirichlet multinomial process, the recently proposed Pitman–Yor, and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a post-processing algorithm introduced for the Dirichlet process can be extended to more general models and provides a consistent method to estimate the number of components.

8.1.7 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 16.

8.2.1 Extreme events and neural networks

Participants: Stephane Girard.

Joint work with: M. Allouche and E. Gobet (CMAP, Ecole Poytechnique)

Feedforward neural networks based on Rectified linear units (ReLU) cannot efficiently approximate quantile functions which are not bounded, especially in the case of heavy-tailed distributions. We thus propose a new parametrization for the generator of a Generative adversarial network (GAN) adapted to this framework, basing on extreme-value theory. We provide an analysis of the uniform error between the extreme quantile and its GAN approximation. It appears that the rate of convergence of the error is mainly driven by the second-order parameter of the data distribution. The above results are illustrated on simulated data and real financial data 13.

A similar investigation has been conducted to simulate fractional Brownian motion with ReLU neural networks 12.

In 69, we propose new parametrizations for neural networks in order to estimate extreme quantiles in both non-conditional and conditional heavy-tailed settings. All proposed neural network estimators feature a bias correction based on an extension of the usual second-order condition to an arbitrary order. The convergence rate of the uniform error between extreme log-quantiles and their neural network approximation is established. The finite sample performances of the non-conditional neural network estimator are compared to other bias-reduced extreme-value competitors on simulated data. It is shown that our method outperforms them in difficult heavy-tailed situations where other estimators almost all fail. Finally, the conditional neural network estimators are implemented to investigate the behaviour of extreme rainfalls as functions of their geographical location in the southern part of France. The results are submitted for publication.

8.2.2 Estimation of extreme risk measures

Participants: Stephane Girard.

Joint work with: J. El-Methni (Univ. Paris Cité), G. Stupfler (Univ. Angers) and A. Usseglio-Carleve (Univ. Avignon).

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. Weissman extrapolation device for estimating extreme quantiles (when $\alpha \to 0$) from heavy-tailed distributions is based on two estimators: an order statistic to estimate an intermediate quantile and an estimator of the tail-index. The common practice is to select the same intermediate sequence for both estimators. In 11, we show how an adapted choice of two different intermediate sequences leads to a reduction of the asymptotic bias associated with the resulting refined Weissman estimator. This new bias reduction method is fully automatic and does not involve the selection of extra parameters. Our approach is compared to other bias reduced estimators of extreme quantiles both on simulated and real data.

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.

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 3. The novel expectile-based risk measures satisfy all coherence requirements. Currently available estimators of extreme expectiles are typically biased and hence may show poor finite-sample performance even in fairly large samples. In 22, 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.

8.2.3 Conditional extremal events

Participants: Stephane Girard.

As explained in Paragraph 8.2.2, 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.

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 21. The extension to functional covariates is investigated in 20.

8.2.4 Estimation of multivariate risk measures

Participants: Julyan Arbel, Stephane Girard.

Joint work with: H. Nguyen, Universityof Queensland, Brisbane, Australia and A. Usseglio-Carleve (Univ. Avignon).

Expectiles form a family of risk measures that have recently gained interest over the more common value-at-risk or return levels, primarily due to their capability to be determined by the probabilities of tail values and magnitudes of realisations at once. However, a prevalent and ongoing challenge of expectile inference is the problem of uncertainty quantification, which is especially critical in sensitive applications, such as in medical, environmental or engineering tasks. In 14, we address this issue by developing a novel distribution, termed the multivariate expectilebased distribution (MED), that possesses an expectile as a closed-form parameter. Desirable properties of the distribution, such as log-concavity, make it an excellent fitting distribution in multivariate applications. Maximum likelihood estimation and Bayesian inference algorithms are described. Simulated examples and applications to expectile and mode estimation illustrate the usefulness of the MED for uncertainty quantification.

8.2.5 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 15.

8.2.6 Bayesian inference for extreme values

Participants: Julyan Arbel, Theo Moins, Stephane Girard.

Joint work with: A. Dutfoy (EDF R&D).

Combining extreme value theory with Bayesian methods offers several advantages, such as a quantification of uncertainty on parameter estimation or the ability to study irregular models that cannot be handled by frequentist statistics. However, it comes with many options that are left to the user concerning model building, computational algorithms, and even inference itself. Among them, the parameterization of the model induces a geometry that can alter the efficiency of computational algorithms, in addition to making calculations involved. In 75, we focus on the Poisson process characterization of extremes and outline two key benefits of an orthogonal parameterization addressing both issues. First, several diagnostics show that Markov chain Monte Carlo convergence is improved compared with the original parameterization. Second, orthogonalization also helps deriving Jeffreys and penalized complexity priors, and establishing posterior propriety. The analysis is supported by simulations, and our framework is then applied to extreme level estimation on river flow data. The results are submitted for publication.

8.2.7 Diagnosing convergence of Markov chain Monte Carlo

Participants: Julyan Arbel, Theo Moins, Stephane Girard.

Joint work with: A. Dutfoy (EDF R&D).

Diagnosing convergence of Markov chain Monte Carlo (MCMC) is crucial in Bayesian analysis. Among the most popular methods, the potential scale reduction factor (commonly named $\widehat{R}$) is an indicator that monitors the convergence of output chains to a stationary distribution, based on a comparison of the between- and within-variance of the chains. Several improvements have been suggested since its introduction in the 90'ss. We analyse some properties of the theoretical value $R$ associated to $\widehat{R}$ in the case of a localized version that focuses on quantiles of the distribution. This leads to proposing a new indicator, which is shown to allow both for localizing the MCMC convergence in different quantiles of the distribution, and at the same time for handling some convergence issues not detected by other $\widehat{R}$ versions. This work is submitted for publication 74.

8.2.8 Dimension reduction with Sliced Inverse Regression

Participants: Stephane Girard.

Joint work with: H. Lorenzo and J. Saracco (Inria Bordeaux Sud-Ouest).

Since its introduction in the early 90's, the Sliced Inverse Regression (SIR) methodology has evolved adapting to increasingly complex data sets in contexts combining linear dimension reduction with non linear regression. The assumption of dependence of the response variable with respect to only a few linear combinations of the covariates makes it appealing for many computational and real data application aspects. In 19, we propose an overview of the most active research directions in SIR modeling from multivariate regression models to regularization and variable selection.

8.2.9 Latent factor models: a tool for dimension reduction in joint species distribution models

Participant: Julyan Arbel, Daria Bystrova, Giovanni Poggiato.

Joint work with: Wilfried Thuiller, LECA - Laboratoire d'Ecologie Alpine.

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. A book chapter describing latent factor models as a tool for dimension reduction in joint species distribution models is aslo available.

8.3.1 A Pre-Screening Approach for Faster Bayesian Network Structure Learning

Participants: Florence Forbes.

Joint work with: Thibaud Rahier from Criteo and Sylvain Marié from Schneider.

Learning the structure of Bayesian networks from data is a NP-Hard problem that involves optimization over a super-exponential sized space. Still, in many real-life datasets a number of the arcs contained in the final structure correspond to strongly related pairs of variables and can be identified efficiently with information-theoretic metrics. In this work, we propose a meta-algorithm to accelerate any existing Bayesian network structure learning method. It contains an additional arc pre-screening step allowing to narrow the structure learning task down to a subset of the original variables, thus reducing the overall problem size. We conduct extensive experiments on both public benchmarks and private industrial datasets, showing that this approach enables a significant decrease in computational time and graph complexity for little to no decrease in performance score 37.

8.3.2 Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis.

Participants: Florence Forbes, Benjamin Lambert.

Joint work with: Senan Doyle, Alan Tucholka from Pixyl and Michel Dojat from Grenoble Institute of Neurosciences.

The full acceptance of Deep Learning (DL) models in the clinical field is rather low with respect to the quantity of high-performing solutions reported in the literature. Particularly, end users are reluctant to rely on the rough predictions of DL models. Uncertainty quantification methods have been proposed in the literature as a potential response to reduce the rough decision provided by the DL black box and thus increase the interpretability and the acceptability of the result by the final user. In this review, we propose an overview of the existing methods to quantify uncertainty associated to DL predictions. We focus on applications to medical image analysis, which present specific challenges due to the high dimensionality of images and their quality variability, as well as constraints associated to real-life clinical routine. We then discuss the evaluation protocols to validate the relevance of uncertainty estimates. Finally, we highlight the open challenges of uncertainty quantification in the medical field 72.

8.3.3 Beyond Voxel Prediction Uncertainty: Identifying brain lesions you can trust.

Participants: Florence Forbes, Benjamin Lambert.

Joint work with: Senan Doyle, Alan Tucholka from Pixyl and Michel Dojat from Grenoble Institute of Neurosciences.

Deep neural networks have become the gold-standard approach for the automated segmentation of 3D medical images. Their full acceptance by clinicians remains however hampered by the lack of intelligible uncertainty assessment of the provided results. Most approaches to quantify their uncertainty, such as the popular Monte Carlo dropout, restrict to some measure of uncertainty in prediction at the voxel level. In addition not to be clearly related to genuine medical uncertainty, this is not clinically satisfying as most objects of interest (e.g. brain lesions) are made of groups of voxels whose overall relevance may not simply reduce to the sum or mean of their individual uncertainties. In this work, we propose to go beyond voxel-wise assessment using an innovative Graph Neural Network approach, trained from the outputs of a Monte Carlo dropout model. This network allows the fusion of three estimators of voxel uncertainty: entropy, variance, and model's confidence; and can be applied to any lesion, regardless of its shape or size. We demonstrate the superiority of our approach for uncertainty estimate on a task of Multiple Sclerosis lesions segmentation 35.

8.3.4 Multi-Scale Evaluation of Uncertainty Quantification Techniques for Deep Learning based MRI Segmentation.

Participants: Florence Forbes, Benjamin Lambert.

Joint work with: Senan Doyle, Alan Tucholka from Pixyl and Michel Dojat from Grenoble Institute of Neurosciences.

Deep Learning (DL) techniques have become the gold standard for biomedical image segmentation. Although extensively used, they tend to be considered as black-boxes, preventing their full acceptance in clinical routine. This opacity is partly due to the inability of neural networks to express the uncertainty in their predictions. In recent years, tremendous work has been carried out to alleviate this limitation and develop models that know when they don't know 1. In this work, we propose an in-depth evaluation of 3 state-of-the-art approaches to quantify uncertainty attached to DL predictions : Monte- Carlo Dropout, Deep Ensemble, and Heteroscedastic network. We performed a multi-scale analysis of these techniques by evaluating uncertainty estimates at the voxel, lesion and image levels. We illustrate this comparison on an automatic segmentation task to detect White-Matter Hyperintensities (WMH) from T2-weighted FLAIR MRI sequences of multiple sclerosis patients 56.

8.3.5 Improving Uncertainty-based Out-of-Distribution detection for medical image segmentation .

Participants: Florence Forbes, Benjamin Lambert.

Joint work with: Senan Doyle, Alan Tucholka from Pixyl and Michel Dojat from Grenoble Institute of Neurosciences.

Deep Learning models are easily disturbed by variations in the input images that were not seen during training, resulting in unpredictable behaviours. Such Out-of-Distribution (OOD) images represent a significant challenge in the context of medical image analysis, where the range of possible abnormalities is extremely wide, including artifacts, unseen pathologies, or different imaging protocols. In this work, we evaluate various uncertainty frameworks to detect OOD inputs in the context of Multiple Sclerosis lesions segmentation. By implementing a comprehensive evaluation scheme including 14 sources of OOD of various nature and strength, we show that methods relying on the predictive uncertainty of binary segmentation models often fails in detecting outlying inputs. On the contrary, learning to segment anatomical labels alongside lesions highly improves the ability to detect OOD inputs.

8.3.6 Brain subtle anomaly detection based on Auto-Encoders latent space analysis: Application to de novo Parkinson patients

Participants: Florence Forbes, Geoffroy Oudoumanessah.

Joint work with: Michel Dojat from Grenoble Institute of Neurosciences, Carole Lartizien, Nicolas Pinon, Robin Trombetta from Creatis.

Neural network-based anomaly detection remains challenging in clinical applications with little or no supervised information and subtle anomalies such as hardly visible brain lesions. Among unsupervised methods, patch-based auto-encoders with their efficient representation power provided by their latent space, have shown good results for visible lesion detection. However, the commonly used reconstruction error criterion may limit their performance when facing less obvious lesions. In this work, we design two alternative detection criteria. They are derived from multivariate analysis and can more directly capture information from latent space representations. Their performance compares favorably with two additional supervised learning methods, on a difficult de novo Parkinson Disease (PD) classification task.

8.3.7 Bayesian nonparametric models for hidden Markov random fields on count variables and application to traffic accidents

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

Joint work with: Hien Nguyen from University of Queensland Brisbane Australia and Fatoumata Dama, Laboratoire des Sciences du Numérique de Nantes, 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 90 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 17. 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.Further 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.

8.3.8 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) 91, but we used hidden semi-Markov models for better characterization of phase length distributions (Olivier et al., 2021) 29. 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.

As a perspective of this work, the segmentation induced by our eye-movement model could be used 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.

The results of this study have been partially included in a dissemination work at Inria Interstice journal. 85.

8.3.9 Estimation of leaf area densities in tropical forests

Participants: Jean-Baptiste Durand, Florence Forbes, Yuchen Bai.

Joint work with: Grégoire Vincent, IRD, AMAP, Montpellier, France.

Covering just 7% of the Earth’s land surface, tropical forests play a disproportionate role in the biosphere: they store about 25% of the terrestrial carbon and contribute to over a third of the global terrestrial productivity. They also recycle about a third of the precipitations through evapotranspiration and thus contribute to generate and maintain a humid climate regionally, with positive effects also extending well beyond the tropics. However, the seasonal variability in fluxes between tropical rainforests and atmosphere is still poorly understood. Better understanding the processes underlying flux seasonality in tropical forests is thus critical to improve our predictive ability on global biogeochemical cycles. Leaf area, one key variable controlling water efflux and carbon influx, is poorly characterized. To monitor evolutions of biomass, leaf area density (LAD) or gas exchange, aerial and terrestrial laser scanner (LiDAR) measurements have been frequently used.

The principle is, for different LiDAR shoots assumed as independent, to measure the portions of beam lengths between successive hits. Possible censoring comes from beams not being intercepted within a given voxel. Current approaches aim at connecting LAD to the distribution of beam lengths through some statistical model. Such a simplified model does not currently take into account several effects that may impact either LAD or beam lengths: heterogeneity and dependencies in the vegetation properties in different voxels on the one hand and the nature of hit material on the other hand: wood vs. leaves, leading to biases or deteriorated uncertainty in estimation.

This collaboration, supported by Y. Bai's PhD work, aims at developping machine learning methods to address these issues.Current work is now focusing on 1) Applying 3D point convolution neural network to discriminate wood from leaves 2) Modeling the effect of underdetection of vegetal elements due to gradual loss of laser power through different censoring assumptions and validating these assumptions on simulated and real data sets.

8.3.10 Bayesian neural networks

Participants: Julyan Arbel, Pierre Wolinski, Konstantinos Pitas.

The study of feature propagation at initialization in neural networks lies at the root of numerous initialization designs. An assumption very commonly made in the field states that the pre-activations are Gaussian. Although this convenient Gaussian hypothesis can be justified when the number of neurons per layer tends to infinity, it is challenged by both theoretical and experimental works for finite-width neural networks. In 79, our major contribution of this work is to construct a family of pairs of activation functions and initialization distributions that ensure that the pre-activations remain Gaussian throughout the network's depth, even in narrow neural networks. In the process, we discover a set of constraints that a neural network should fulfill to ensure Gaussian pre-activations. Additionally, we provide a critical review of the claims of the Edge of Chaos line of works and build an exact Edge of Chaos analysis. We also propose a unified view on pre-activations propagation, encompassing the framework of several well-known initialization procedures. Finally, our work provides a principled framework for answering the much-debated question: is it desirable to initialize the training of a neural network whose pre-activations are ensured to be Gaussian?

We also investigate the cold posterior effect through the lens of PAC-Bayes generalization bounds. We argue that in the non-asymptotic setting, when the number of training samples is (relatively) small, discussions of the cold posterior effect should take into account that approximate Bayesian inference does not readily provide guarantees of performance on out-of-sample data. Instead, out-of-sample error is better described through a generalization bound. In this context, we explore the connections of the ELBO objective from variational inference and the PAC-Bayes objectives. We note that, while the ELBO and PAC-Bayes objectives are similar, the latter objectives naturally contain a temperature parameter $\lambda$ which is not restricted to be $\lambda =1$. For classification tasks, in the case of Laplace approximations to the posterior, we show how this PAC-Bayesian interpretation of the temperature parameter captures important aspects of the cold posterior effect.

8.3.11 Graph comparisons

Participants: Sophie Achard, Lucrezia Carboni.

Joint work with: Michel Dojat from GIN, Univ. Grenoble Alpes

In recent accepted publication, we worked on the notion of graph comparisons. Node role explainability in complex networks is very difficult, yet is crucial in different application domains such as social science, neurosciences or computer science. Many efforts have been made on the quantification of hubs revealing particular nodes in a network using a given structural property. Yet, in several applications, when multiple instances of networks are available and several structural properties appear to be relevant, the identification of node roles remains largely unexplored. Inspired by the node automorphically equivalence relation, we define an equivalence relation on graph's nodes associated with any collection of nodal statistics (i.e. any functions on the node set). This allows us to define new graph global measures, the power coefficient and the orthogonality score to evaluate the collection parsimony and heterogeneity of a given nodal statistics collection. In addition, we introduce a new method based on structural patterns to compare graphs that have the same vertices set. This methods assigns a value to a node to determine its role distinctiveness in a graph family. Extensive numerical results of our method are conducted on both generative graph models and real data concerning human brain functional connectivity. The differences in nodal statistics are shown to be dependent on the underlying graph structure. Comparisons between generative models and real networks combining two different nodal statistics reveal the complexity of human brain functional connectivity with differences at both global and nodal levels. Using a group of 200 healthy controls connectivity networks, our method is able to compute high correspondence scores among the whole population, to detect homotopy, and finally to quantify differences between comatose patients and healthy controls.

8.3.12 Spatio-temporal data

Participants: Sophie Achard, Hana Lbath.

Joint work with: Alex Petersen, Brigham Young University, US and Wendy Meiring, University Santa Barbara California, US

A novel non-parametric estimator of the correlation between regions, or groups of arbitrarily dependent variables, is proposed in the presence of noise. The challenge resides in the fact that both noise and low intra-regional correlation lead to inconsistent inter-regional correlation estimation using classical approaches. While some existing methods handle one of these issues or the other, none tackle both at the same time. To address this problem, we propose a trade-off between two approaches: correlating regional averages, which is not robust to low average intra-regional correlation, and averaging pairwise inter-regional correlations, which is not robust to high noise. To that end, we project the data onto a space where the Euclidean distance can be used as a proxy for the sample correlation. We then leverage hierarchical clustering to gather together highly correlated variables within each region prior to averaging. We prove our estimator is consistent for an appropriate cut-off height of the dendogram. We also empirically show our approach surpasses popular estimators in terms of quality and provide illustrations on real-world datasets that further demonstrate its usefulness. 54

8.4.1 Sequential Bayesian experimental design for inverse problems.

Participants: Florence Forbes, Jacopo Iollo.

Bayesian Optimal Experimental Design is a technique that allows practitioners to efficiently make use of limited experimental resources. In the sequential case however, we often have to run from start computationally intensive inference techniques such as Markov Chain Monte Carlo or Variational Inference to obtain the current estimate of the posterior. In this study, we show how we can leverage Sequential Monte Carlo Samplers in order to simultaneously estimate the best possible design and the current posterior. This iterative procedure make use of past information in order to avoid to have to run an inference algorithm from start at each iteration. We demonstrate its applicability in a source location inverse problem.

8.4.2 Bayesian nonparametric mixture of experts for high-dimensional inverse problems.

Participants: Julyan Arbel, Florence Forbes, Trung Tin Nguyen.

A wide class of problems can be formulated as inverse problems where the goal is to find parameter values that best explain some observed measures. Typical constraints in practice are that relationships between parameters and observations are highly nonlinear, with high-dimensional observations and multi-dimensional correlated parameters. To handle these constraints, we consider probabilistic mixtures of locally linear models, which can be seen as particular instances of mixtures of experts (MoE). We have shown in previous studies that such models had a good approximation ability provided the number of experts was large enough. This contribution is to propose a general scheme to design a tractable Bayesian nonparametric (BNP) MoE model to avoid any commitment to an arbitrary number of experts. A tractable estimation algorithm is designed using a variational approximation and theoretical properties are derived on the predictive distribution and the number of components. Illustrations on simulated and real data show good results in terms of selection and computing time compared to more traditional model selection procedures.

8.4.3 Hierarchical Bayesian models for simulation-based inference

Participants: Pedro Rodrigues, Julia Linhart.

Joint work with: Thomas Moreau and Alexandre Gramfort from Inria Saclay and Gilles Louppe from Université de Liège

Inferring the parameters of a stochastic model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e. when distinct sets of parameters yield identical observations. This arises in many practical situations, such as when inferring the distance and power of a radio source (is the source close and weak or far and strong?) or when estimating the amplifier gain and underlying brain activity of an electrophysiological experiment. In a recent work, we have proposed the hierarchical neural posterior estimation (HNPE), a novel method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters. This method extends recent developments in simulation-based inference (SBI) based on normalizing flows to Bayesian hierarchical models. We validated HNPE quantitatively on a motivating example amenable to analytical solutions and then applied it to invert a well known non-linear model from computational neuroscience, using both simulated and real EEG data.

8.4.4 Bayesian inference on a large-scale brain simulator

Participants: Pedro Rodrigues.

Joint work with: Nicholas Tolley and Stephanie Jones from Brown University, Alexandre Gramfort from Inria Saclay

The Human Neocortical Neurosolver (HNN) is a framework whose foundation is a cortical column model with cell and circuit level detail designed to connect macroscale signals to meso/microcircuit level phenomena. We apply this model to study the cellular and circuit mechanisms of beta generation using local field potential (LFP) recordings from the non-human primate (NHP) motor cortex. To characterize beta producing mechanisms, we employ simulation based inference (SBI) in the HNN modeling tool. This framework leverages machine learning techniques and neural density estimators to characterize the relationship between a large space of model parameters and simulation output. In this setting, Bayesian inference can be applied to models with intractable likelihood functions (Gonçalves 2020, Papamakarios 2021). The main goal of this project is to provide a set of guidelines for scientists that wish to apply simulation-based inference to their neuroscience studies with a large-scale simulator such as HNN. This involves developing new methods for extracting summary features, checking the quality of the posterior approximation, etc. This work is mostly carried out by the Ph.D. student Nicholas Tolley from Brown University.

10.1.1 Inria associate team not involved in an IIL or an international program

Participants: Florence Forbes, Julyan Arbel, Jean-Baptiste Durand, Stephane Girard, Trung Tin Nguyen.

LANDER stands for "Latent Analysis, Adversarial Networks, and DimEnsionality Reduction" and is an associate team with researchers in Australia that has started in 2019. Details can be found at Lander website.

During the year, a number of journal publications have been finalized on subjects directly linked to the project, mixture of expert models and variants related to high dimensional regression, distributions and properties for non-Gaussian data, clustering and classification, Approximate Bayesian Computation (ABC), Bayesian non parametrics and Markov random fields, Expectiles, etc. The corresponding publications and working papers are listed on the website.

All this work served as a basis for a new submission to the Australian Research Council (ARC), which has been recently granted.

10.2.1 Visits of international scientists

10.2.2 Visits to international teams

ANR

• statify is 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.
• an ANR project RADIO-AIDE (2022-26) for Radiation induced neurotoxicity assessed by Spatio-temporal modeling and AI after brain radiotherapy coordinated by S.Ancelet from IRSN has been granted for 4 years starting from April 2022. It involves statify, Grenoble Insitute of Neurosciences, Pixyl, ICANS, APHP, ICM and ENS P.Saclay. The available funding for statify is 94K euros.
• ANR project PEG2 (2022-26) on Predictive Ecological Genomics: statify is involved in this 4-year project recently accepted in July 2022. The PI is prof. Olivier Francois who spent 2 years (2021-22) in the team on a Delegation position.
• Julyan Arbel is coPI of the Bayes-Duality project launched with a funding of $2.76 millions by Japan JST - French ANR for a total of 5 years starting in October 2021. The goal is to develop a new learning paradigm for Artificial Intelligence that learns like humans in an adaptive, robust, and continuous fashion. On the Japan side the project is led by Mohammad Emtiyaz Khan as the research director, and Kenichi Bannai and Rio Yokota as Co-PIs.
• 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.

Grenoble Idex projects

• MIAI, Multidisciplinary Institute in Artificial Intelligence: In the context of the MIAI institute, S. Achard is co-PI of a chair (2020-23) on Toward Robust and Understandable Neuromorphic Systems funding one PhD student and several post-doc fellows.
• MIAI: Pedro Rodrigues was awarded 13K euros for his project on Machine Learning for Experimental Data via the IRGA 2022 call for projects.
• MIAI: F. Forbes, J-B. Durand and Y. Bai were awarded 4.5K euros for their project on Developing IA for estimating leaf area density area in tropical forests from LiDAR data, Nov. 2022.

10.3.1 Networks

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

11.1.1 Scientific events: organisation

11.1.2 Scientific events: selection

11.1.3 Journal

11.1.4 Invited talks

• F. Forbes, Automatic learning of functional summary statistics for approximate Bayesian computation, O’Bayes 2022 - Objective Bayes Methodology Conference, Santa Cruz, United States, September 2022, 46.
• F. Forbes, Learning approaches for Bayesian inverse problems, UGA-McMaster joint workshop 2022, Hamilton, Canada, June 2022, 47.
• F. Forbes, Online Majorization Minimization algorithms, CIRM Workshop on Computational Methods for Unifying Multiple Statistical Analyses (Fusion), Luminy, France, October 2022, 49.
• F. Forbes, Simulation based inference for high dimensional inverse problems: application to magnetic resonance fingerprinting, Colloque Intelligence Artificielle et santé : approches interdisciplinaires 2022, Nantes, France, June 2022, 50.
• A. Usseglio-Carleve, S. Girard, G. Stuplfer, Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models, Insurance Data Science Conference 2022, Milano, Italy, June 2022.
• S. Achard, Statistical comparisons of spatio-temporal networks, CIRM Workshop on GraphLearn: Machine Learning and Signal Processing on Graphs, Luminy, France, November 2022,

11.1.5 Research administration

• S. Achard, since Nov. 2020, has been elected as the head of Pole MSTIC (with J.P. Jamont,K. Altisen and C. Lescop) at University of Grenoble. Before she was co-director of pole MSTIC since 2017.
• Julyan Arbel, Member of the scientific committee of the Data Science axis of Persyval Labex.
• Julyan Arbel, Board of Directors member of ISBA, the International Society for Bayesian Analysis, 2022-2025.
• F. Forbes is a member of the advisory committee of the Helmholtz AI Cooperation Unit since 2019.
• F. Forbes is Scientific Advisor since March 2015 for the Pixyl company.
• F. Forbes and S. Achard are members of the EURASIP Technical Area Committee BISA (Biomedical Image & Signal Analytics) since January 2021 for a 3 years duration.
• J. Arbel has been a member of the Comit´e des Emplois Scientifiques at Inria Grenoble since 2019.
• P. Rodrigues is a member of the Comit´e D´eveloppement Technologique, a committee for evaluating software development projects, at Inria Grenoble since 2021.
• F. Forbes is a member of the Comite d’organisation strategique of Inria Grenoble since 2017.
• F. Forbes was deputy head of science at Inria Grenoble, from Sep. 2021 to Sep. 2022.

11.2.1 Teaching

• Master: Stéphane Girard, Statistique Inférentielle Avancée, 18 ETD, M1 level, Ensimag. Grenoble-INP, France.
• Master: Stéphane Girard, Introduction to Extreme-Value Analysis, 18 ETD, M2 level, Univ-Grenoble Alpes (UGA), France.
• Master: 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.
• Master: Julyan Arbel, Bayesian deep learning, Master Intelligence Artificielle, Systèmes, Données (IASD), Université PSL (Paris Sciences & Lettres), 12 ETD.
• Master, Julyan Arbel, Bayesian machine learning, Master Mathématiques Vision et Apprentissage (MVA), École normale supérieure Paris-Saclay, 36 ETD.
• Master, Julyan Arbel, Bayesian statistics, Ensimag Grenoble INP, 27 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.

11.2.2 Supervision

• Stéphane Girard was co-supervisor of the PhD thesis of Michaël Allouche (with Emmanuel Gobet, Ecole Polytechnique) "Contributions to generative modeling and dictionary learning: Theory and application”, Institut Polytechnique de Paris, defended on December, 2022.
• Stéphane Girard was co-supervisor of the PhD thesis of Meryem Bousebata (with Geoffroy Enjolras, UGA), "Bayesian estimation of extreme risk measures: Implication for the insurance of natural disasters", UGA, defended on March 2022.
• Julyan Arbel was supervisor of the PhD thesis of Mariia Vladimirova, "Bayesian Neural Networks' Distributional Properties", Inria, defended on March 2022.
• 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: 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: 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.
• PhD in progress: Hana Lbath, "Advanced Spatiotemporal Statistical Models for Quantification and Estimation of Functional Connectivity", started in October 2020, supervised by Sophie Achard and Alex Petersen (Brigham Young University, Utah, USA).
• PhD in progress: Lucrezia Carboni, "Graph embedding for brain connectivity", started in October 2020, supervised by Sophie Achard and Michel Dojat (GIN).
• PhD in progress: Louise Alamichel. "Bayesian Nonparametric methods for complex genomic data" Inria, started in October 2021, advised by Julyan Arbel and Guillaume Kon Kam King (INRAE).
• PhD in progress: Julien Zhou. "Learning combinatorial bandit models under privacy constraints" Inria-Criteo, started in November 2022, advised by Julyan Arbel, Pierre Gaillard and Thibaud Rahier.
• PhD in progress: Mohamed-Bahi Yahiaoui. "Computation time reduction and efficient uncertainty propagation for fission gas simulation" CEA Cadarache-Inria, started in October 2021, advised by Julyan Arbel, Loïc Giraldi, Geoffrey Daniel.
• PhD in progress: Yuchen Bai, "Hierarchical Bayesian Modelling of leaf area density from UAV-lidar", started in October 2021, supervised by Jean-Baptiste Durand, Florence Forbes and Gregoire Vincent (IRD, Montpellier).
• PhD in progress: Julia Linhart, "Simulation based inference with neural networks: applications to computational neuroscience", started in November 2021, supervised by Pedro Rodrigues and Alexandre Gramfort (DR Inria Saclay).
• PhD in progress: Jacopo Iollo, started in January 2022, supervised by F. Forbes, P. Alliez (DR Inria Sophia) and C. Heinkele (Cerema, Strasbourg).
• PhD in progress: Geoffroy Oudoumanessah, started in October 2022, supervised by F. Forbes, C. Lartizien (Creatis, Lyon) and M. Dojat (GIN).
• PhD in progress: Theo Sylvestre, started in October 2022, supervised by F. Forbes and S. Ancelet (IRSN).
• PhD in progress: Benjamin Lambert, started in January 2022, supervised by F. Forbes and M. Dojat (GIN).

11.2.3 Juries

• Stéphane Girard, Member of the PhD thesis committee of Gloria Buritica, "Assessing the time dependence of multivariate extremes for heavy rainfall modeling", Sorbonne Université, May 2022.
• Julyan Arbel, Rapporteur of the PhD thesis of Gabriel Ducrocq, Institut Polytechnique de Paris, France.
• Julyan Arbel, Rapporteur of the PhD thesis of Ioanni Mitro, University College Dublin, Ireland.
• Julyan Arbel, Rapporteur of the PhD thesis of Yuqing Hu, IMT Atlantique & Orange, France.
• Julyan Arbel, Member of the PhD thesis of Meryem Bousebata, Inria Grenoble, France.
• F. Forbes, Member of the PhD thesis of Grégoire Aufort, "Statistique Computationnelle Bayésienne pour l’étude des Distributions Spectrales d’énergie des galaxies", October 2022, University Aix-Marseille.
• F. Forbes, Reviewer for the Master Thesis of John Davey from Adelaide University, Australia, July 2022.
• F. Forbes, Reviewer for the CSI, mid-term examination, for the PhD thesis of Thomas Coudert, GIN, University of Grenoble, October 2022.

11.3.1 Articles and contents

S. Achard and J-B. Durand published an illustration of the process of statistical modeling, in the Inria journal for popularization of science (in French). The topic was illustrated through the analysis of eye movements to infer cognitive processes.

International journals

• 11 articleM.Michaël Allouche, J.Jonathan El Methni and S.Stéphane Girard. A refined Weissman estimator for extreme quantiles.Extremes2022
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• 12 articleM.Michaël Allouche, S.Stéphane Girard and E.Emmanuel Gobet. A generative model for fBm with deep ReLU neural networks.Journal of Complexity73December 2022, 101667
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• 13 articleM.Michaël Allouche, S.Stéphane Girard and E.Emmanuel Gobet. EV-GAN: Simulation of extreme events with ReLU neural networks.Journal of Machine Learning Research231502022, 1--39
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• 14 articleJ.Julyan Arbel, S.Stéphane Girard, H. D.Hien Duy Nguyen and A.Antoine Usseglio-Carleve. Multivariate expectile-based distribution: properties, Bayesian inference, and applications.Journal of Statistical Planning and Inference2252023, 146-170
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• 15 articleM.Meryem Bousebata, G.Geoffroy Enjolras and S.Stéphane Girard. Extreme Partial Least-Squares.Journal of Multivariate Analysis1942023, 105101
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• 16 articleA.Alexandre Constantin, M.Mathieu Fauvel and S.Stéphane Girard. Mixture of multivariate Gaussian processes for classification of irregularly sampled satellite image time-series.Statistics and Computing322022, 79
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• 17 articleJ.-B.Jean-Baptiste Durand, F.Florence Forbes, C. D.Cong Duc Phan, L.Long Truong, H. D.Hien D Nguyen and F.Fatoumata Dama. Bayesian nonparametric spatial prior for traffic crash risk mapping: a case study of Victoria, Australia.Australian and New Zealand Journal of Statistics642June 2022, 171-204
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• 18 articleF.Florence Forbes, H. D.Hien Duy Nguyen, T. T.Trung Tin Nguyen and J.Julyan Arbel. Summary statistics and discrepancy measures for ABC via surrogate posteriors.Statistics and Computing32852022
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• 19 articleS.Stéphane Girard, H.Hadrien Lorenzo and J.Jérôme Saracco. Advanced topics in Sliced Inverse Regression.Journal of Multivariate Analysis1882022, 104852
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• 20 articleS.Stéphane Girard, G.Gilles Stupfler and A.Antoine Usseglio-Carleve. Functional estimation of extreme conditional expectiles.Econometrics and Statistics 21January 2022, 131-158
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• 21 articleS.Stéphane Girard, G.Gilles Stupfler and A.Antoine Usseglio-Carleve. Nonparametric extreme conditional expectile estimation.Scandinavian Journal of Statistics491March 2022, 78-115
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• 22 articleS.Stéphane Girard, G.Gilles Stupfler and A.Antoine Usseglio-Carleve. On automatic bias reduction for extreme expectile estimation.Statistics and Computing32August 2022, 64
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• 23 articleM.Maëliss Jallais, P. L.Pedro Luiz Coelho Rodrigues, A.Alexandre Gramfort and D.Demian Wassermann. Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements.Journal of Machine Learning for Biomedical ImagingMay 2022, 1-27
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• 24 articleB.Benoit Kugler, F.Florence Forbes and S.Sylvain Douté. Fast Bayesian Inversion for high dimensional inverse problems.Statistics and Computing3231March 2022
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• 25 articleT.Thomas Mistral, P.Pauline Roca, C.Christophe Maggia, A.Alan Tucholka, F.Florence Forbes, S.Senan Doyle, A.Alexandre Krainik, D.Damien Galanaud, E.Emmanuelle Schmitt, S.Stéphane Kremer, A.Adrian Kastler, I.Irène Troprès, E.Emmanuel Barbier, J.-F.Jean-François Payen and M.Michel Dojat. Automated Quantification of Brain Lesion Volume From Post-trauma MR Diffusion-Weighted Images.Frontiers in Neurology12February 2022, 740603
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• 26 articleV.Verónica Muñoz-Ramírez, V.Virgilio Kmetzsch, F.Florence Forbes, S.Sara Meoni, E.Elena Moro and M.Michel Dojat. Subtle anomaly detection: Application to brain MRI analysis of <i>de novo</i> Parkinsonian patients.Artificial Intelligence in Medicine125March 2022, 102251
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• 27 articleH. D.Hien Duy Nguyen and F.Florence Forbes. Global implicit function theorems and the online Expectation-Maximisation algorithm.Australian and New Zealand Journal of Statistics642June 2022, 255-281
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• 28 articleH. D.Hien Duy Nguyen, S.Sharon Lee and F.Florence Forbes. A Festschrift for Geoff McLachlan.Australian and New Zealand Journal of Statistics642June 2022, 111 - 116
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• 29 articleB.Brice Olivier, A.Anne Guérin-Dugué and J.-B.Jean-Baptiste Durand. Hidden Semi-Markov Models to Segment Reading Phases from Eye Movements.Journal of Eye Movement Research154September 2022, 5
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• 30 articleS. M.Sandra M. Potin, S.Sylvain Douté, B.Benoit Kugler and F.Florence Forbes. The impact of asteroid shapes and topographies on their reflectance spectroscopy.Icarus376April 2022, 114806:1-24
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• 31 articleE.E. Roger, L.Lilian Rodrigues de Almeida, H.Hélène Loevenbruck, M.Marcela Perrone-Bertolotti, E.Emilie Cousin, J.-L.Jean-Luc Schwartz, P.Pascal Perrier, M.Marion Dohen, A.Anne Vilain, P.Pierre Baraduc, S.Sophie Achard and M.Monica Baciu. Unraveling the functional attributes of the language connectome: crucial subnetworks, flexibility and variability.NeuroImage263November 2022, 119672
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• 32 articleS.Sahar Yassine, U.Ute Gschwandtner, M.Manon Auffret, S.Sophie Achard, M.Marc Verin, P.Peter Fuhr and M.Mahmoud Hassan. Functional Brain Dysconnectivity in Parkinson's Disease: A 5-Year Longitudinal Study.Movement Disorders377July 2022, 1444-1453
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International peer-reviewed conferences

• 33 inproceedingsS.Sophie Achard, I.Irène Gannaz and K.Kévin Polisano. Génération de modèles graphiques.GRETSI 2022 - XXVIIIème Colloque francophone de traitement du signal et des imagesNancy, France2022, 1-3
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• 34 inproceedingsG.-P. J.Guillaume Jean-Paul Claude Becq, A.Argheesh Bhanot, C.Céline Meillier, S.Sophie Achard and E. L.Emmanuel L. Barbier. Effect of filtering on the evaluation of dynamic functional connectivity and application to data from functional MRI of rats.28e Colloque sur le traitement du signal et des imagesGretsi 2022 - 28° Colloque sur le traitement du signal et des imagesNancy, FranceSeptember 2022
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• 35 inproceedingsB.Benjamin Lambert, F.Florence Forbes, S.Senan Doyle, A.Alan Tucholka and M.Michel Dojat. Beyond Voxel Prediction Uncertainty: Identifying brain lesions you can trust.Lecture Notes in Computer ScienceiMIMIC 2022 - Workshop on Interpretability of Machine Intelligence in Medical Image Computing13611Singapore, SingaporeOctober 2022, 61-70
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• 36 inproceedingsH. D.Hien Duy Nguyen, F.Florence Forbes, G.Gersende Fort and O.Olivier Cappé. An online Minorization-Maximization algorithm.17th Conference of the International Federation of Classification SocietiesProceedings of the 17th Conference of the International Federation of Classification SocietiesPorto, PortugalJuly 2022
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• 37 inproceedingsT.Thibaud Rahier, S.Sylvain Marié and F.Florence Forbes. A Pre-Screening Approach for Faster Bayesian Network Structure Learning.ECML-PKDD 2022 - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in DatabasesECML-PKDDGrenoble, FranceSeptember 2022, 1-16
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Conferences without proceedings

• 38 inproceedingsL.Louise Alamichel, D.Daria Bystrova, J.Julyan Arbel and G.Guillaume Kon Kam King. On the consistency of Bayesian nonparametric mixtures for the number of clusters.ISBA 2022 - World Meeting International Society for Bayesian AnalysisMontreal, CanadaJune 2022
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• 39 inproceedingsM.Michaël Allouche, J.Jonathan El Methni and S.Stéphane Girard. A refined Weissman estimator for extreme quantiles.EcoSta 2022 - 5th International Conference on Econometrics and StatisticsKyoto, JapanJune 2022
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• 40 inproceedingsM.Michaël Allouche, J.Jonathan El Methni and S.Stéphane Girard. A refined Weissman estimator for extreme quantiles.Compstat 2022 - 24th International Conference on Computational StatisticsBologna, ItalyAugust 2022
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• 41 inproceedingsM.Michaël Allouche, S.Stéphane Girard and E.Emmanuel Gobet. EV-GAN: Simulation of extreme events with ReLU neural networks.EcoSta 2022 - 5th International Conference on Econometrics and StatisticsKyoto, JapanJune 2022
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• 42 inproceedingsM.Michaël Allouche, S.Stéphane Girard and E.Emmanuel Gobet. Estimation of extreme quantiles from heavy-tailed distributions with neural networks.CMStatistics 2022 - 15th International Conference of the ERCIM WG on Computational and Methodological StatisticsLondon, United KingdomDecember 2022
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• 43 inproceedingsS.Stan Borkowski, S.Sylvain Douté, F.Florence Forbes and S.Samuel Heidmann. Planet-GLLiM: software for scalable Bayesian analysis of multidimensional data in astrophysics.Journées de l'Action Spécifique Numérique Astrophysique (ASNUM 2022)Lyon, FranceDecember 2022
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• 44 inproceedingsM.Meryem Bousebata, S.Stéphane Girard and G.Geoffroy Enjolras. Extreme partial least-squares.EcoSta 2022 - 5th International Conference on Econometrics and StatisticsKyoto, JapanJune 2022
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• 45 inproceedingsJ.Jonathan El Methni and S.Stéphane Girard. A refined extreme quantiles estimator of Weibull tail-distributions.CMStatistics 2022 - 15th International Conference of the ERCIM WG on Computational and Methodological StatisticsLondon, United KingdomDecember 2022
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• 46 inproceedingsF.Florence Forbes. Automatic learning of functional summary statistics for approximate Bayesian computation.O'Bayes 2022 - Objective Bayes Methodology ConferenceSanta Cruz, United StatesSeptember 2022
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• 47 inproceedingsF.Florence Forbes. Learning approaches for Bayesian inverse problems.UGA-McMaster joint workshop 2022Hamilton, CanadaJune 2022
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• 48 inproceedingsF.Florence Forbes, H. D.Hien Duy Nguyen, T.Trungtin Nguyen and J.Julyan Arbel. Mixture of expert posterior surrogates for approximate Bayesian computation.SFdS 2022 - 53èmes Journées de Statistique de la Société Française de StatistiqueLyon, FranceJune 2022, 1-6
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• 49 inproceedingsF.Florence Forbes. Online Majorization Minimization algorithms.CIRM Workshop on Computational Methods for Unifying Multiple Statistical Analyses (Fusion)Luminy, FranceOctober 2022
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• 50 inproceedingsF.Florence Forbes. Simulation based inference for high dimensional inverse problems: application to magnetic resonance fingerprinting.Colloque  Intelligence Artificielle et santé : approches interdisciplinaires 2022Nantes, FranceJune 2022
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• 51 inproceedingsF.Florence Forbes. Simulation-based approaches to Bayesian inverse problems.ICMS workshop on Interfacing Bayesian statistics, machine learning, applied analysis, and blind and semi-blind imaging inverse problemsEdimburgh, United KingdomJanuary 2023
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• 52 inproceedingsF.Florence Forbes. Summary statistics and discrepancy measures for approximate Bayesian computation via surrogate posteriors.BayesComp 2023Levi, FinlandMarch 2023
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• 53 inproceedingsH.Hanâ LBATH, A.Alexander Petersen and S.Sophie Achard. Large-Scale Correlation Screening Under Dependence for Brain Functional Connectivity Inference.JSM 2022 - Joint Statistical MeetingsWashington, United StatesAugust 2022
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• 54 inproceedingsH.Hanâ LBATH, A.Alexander Petersen, W.Wendy Meiring and S.Sophie Achard. Clustering-Based Inter-group Correlation Estimation.ICSDS 2022- IMS International Conference on Statistics and Data ScienceFlorence, ItalyDecember 2022
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• 55 inproceedingsB.Benjamin Lambert, F.Florence Forbes, S.Senan Doyle, A.Alan Tucholka and M.Michel Dojat. Fast Uncertainty Quantification for Deep Learning-based MR Brain Segmentation.EGC 2022 - Conference francophone pour l'Extraction et la Gestion des ConnaissancesBlois, FranceJanuary 2022, 1-12
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• 56 inproceedingsB.Benjamin Lambert, F.Florence Forbes, A.Alan Tucholka, S.Senan Doyle and M.Michel Dojat. Multi-Scale Evaluation of Uncertainty Quantification Techniques for Deep Learning based MRI Segmentation.ISMRM-ESMRMB & ISMRT 2022 - 31st Joint Annual Meeting International Society for Magnetic Resonance in MedecineLondon, United KingdomMay 2022, 1-3
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• 57 inproceedingsJ.Julia Linhart, P. L.Pedro Luiz Coelho Rodrigues, T.Thomas Moreau, G.Gilles Louppe and A.Alexandre Gramfort. Neural Posterior Estimation of hierarchical models in neuroscience.GRETSI 2022 - XXVIIIème Colloque Francophone de Traitement du Signal et des ImagesNancy, FranceSeptember 2022, 1-3
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• 58 inproceedingsJ.Julia Linhart, A.Alexandre Gramfort and P. L.Pedro Luiz Coelho Rodrigues. Validation Diagnostics for SBI algorithms based on Normalizing Flows.NeurIPS 2022 - the 36th conference on Neural Information Processing Systems - Machine Learning and the Physical Sciences workshopNew Orleans, United StatesNovember 2022, 1-7
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• 59 inproceedingsT.Théo Moins, J.Julyan Arbel, A.Anne Dutfoy and S.Stéphane Girard. A local version of R-hat for MCMC convergence diagnostic.SFdS 2022 - 53èmes Journées de Statistique de la Société Française de StatistiqueLyon, FranceJune 2022, 1-6
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• 60 inproceedingsT.Théo Moins, J.Julyan Arbel, A.Anne Dutfoy and S.Stéphane Girard. Improving MCMC convergence diagnostic with a local version of R-hat.CMStatistics 2022 - 15th International Conference of the ERCIM WG on Computational and Methodological StatisticsLondon, United KingdomDecember 2022
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• 61 inproceedingsT.Théo Moins, J.Julyan Arbel, A.Anne Dutfoy and S.Stéphane Girard. On the use of a local R-hat to improve MCMC convergence diagnostic.Energy Forecasting Innovation Conference 2022Londres, United KingdomMay 2022
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• 62 inproceedingsT.Trungtin Nguyen, F.Faicel Chamroukhi, H. D.Hien Duy Nguyen and F.Florence Forbes. Model selection by penalization in mixture of experts models with a non-asymptotic approach.JDS 2022 - 53èmes Journées de Statistique de la Société Française de Statistique (SFdS)Lyon, FranceJune 2022, 1-6
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• 63 inproceedingsJ.Jérôme Saracco, H.Hadrien Lorenzo and S.Stéphane Girard. Advanced topics in Sliced Inverse Regression V2.JMVA 2022 - 50th Anniversary JubileeVirtual Meeting, United StatesApril 2022
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• 64 inproceedingsA.Antoine Usseglio-Carleve, S.Stéphane Girard and G.Gilles Stupfler. Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models.Insurance Data Science Conference 2022Milan, ItalyJune 2022, 1-65
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• 65 inproceedingsP.Pierre Wolinski and J.Julyan Arbel. Imposing Gaussian Pre-Activations in a Neural Network.JDS 2022 - 53es Journées de Statistique de la Société Française de Statistiques (SFdS)Lyon, FranceJune 2022
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Edition (books, proceedings, special issue of a journal)

• 66 proceedingsL.Louise AlamichelJ.Julyan ArbelD.Daria BystrovaG.Guillaume Kon Kam KingBayesian nonparametric mixtures inconsistency for the number of clusters.June 2022
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Reports & preprints

• 67 miscS.Sophie Achard and I.Irène Gannaz. Whittle estimation with (quasi-)analytic wavelets.June 2022
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• 68 miscL.Louise Alamichel, D.Daria Bystrova, J.Julyan Arbel and G.Guillaume Kon Kam King. Bayesian mixture models (in)consistency for the number of clusters.November 2022
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• 69 miscM.Michaël Allouche, S.Stéphane Girard and E.Emmanuel Gobet. Estimation of extreme quantiles from heavy-tailed distributions with neural networks.2022
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• 70 reportP. A.Pascal Alain Dkengne Sielenou and S.Stéphane Girard. Estimation of upper bounds for return levels: Methodology and illustrations on univariate random sequences.Inria - Research Centre Grenoble – Rhône-AlpesFebruary 2022
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• 71 miscM. N.Mahouton Norbert Hounkonnou and P. D.Pascal Dkengne Sielenou. Conservation laws for under determined systems of differential equations.February 2022
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• 72 miscB.Benjamin Lambert, F.Florence Forbes, A.Alan Tucholka, S.Senan Doyle, H.Harmonie Dehaene and M.Michel Dojat. Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis.October 2022
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• 73 miscN.Norbert Mahouton and P. D.Pascal Dkengne Sielenou. Extremum conditions for functionals involving higher derivatives of several variable vector valued functions.February 2022
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• 74 miscT.Théo Moins, J.Julyan Arbel, A.Anne Dutfoy and S.Stéphane Girard. On the use of a local $\stackrel{}{R}$ to improve MCMC convergence diagnostic.March 2022
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• 75 miscT.Théo Moins, J.Julyan Arbel, S.Stéphane Girard and A.Anne Dutfoy. Reparameterization of extreme value framework for improved Bayesian workflow.October 2022
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• 76 miscM.Marc Ohlmann, G.Giovanni Poggiato, S.Stéphane Dray, W.Wilfried Thuiller, C.Catherine Matias and V.Vincent Miele. Quantifying the overall effect of biotic interactions on species distributions along environmental gradients.January 2023
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• 77 reportG.Geoffroy Oudoumanessah, M.Michel Dojat and F.Florence Forbes. Unsupervised scalable anomaly detection: application to medical imaging.Inria Grenoble - Rhône-Alpes; Grenoble Institut des neurosciencesOctober 2022, 1-43
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• 78 miscK.Konstantinos Pitas and J.Julyan Arbel. Cold Posteriors through PAC-Bayes.September 2022
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• 79 misc P.Pierre Wolinski and J.Julyan Arbel. Gaussian Pre-Activations in Neural Networks: Myth or Reality? December 2022
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Other scientific publications

• 80 inproceedingsL.Louise Alamichel, D.Daria Bystrova, J.Julyan Arbel and G.Guillaume Kon Kam King. Bayesian mixture models (in)consistency for the number of clusters.13th Bayesian nonparametrics (BNP) conferencePuerto Varas, ChileOctober 2022
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• 81 inproceedingsL.Lucrezia Carboni, M.Michel Dojat and S.Sophie Achard. Nodal statistics-based structural pattern detection for graph collections characterization.Conference of Complex SystemPalma de Mallorca, SpainOctober 2022
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• 82 inproceedingsT.Théo Moins, J.Julyan Arbel, S.Stéphane Girard and A.Anne Dutfoy. A Local Version of R to Improve MCMC Convergence Diagnostic.BAYSM 2022 - Bayesian Young Statisticians MeetingMontréal, CanadaJune 2022
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• 83 inproceedingsT.Théo Moins, J.Julyan Arbel, S.Stéphane Girard and A.Anne Dutfoy. A Local Version of R-hat to Improve MCMC Convergence Diagnostic.ISBA 2022 - World Meeting of the International Society for Bayesian AnalysisMontréal, CanadaJune 2022, 1-1
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Scientific popularization

• 84 articleT.Trungtin Nguyen, H. D.Hien Duy Nguyen, F.Faicel Chamroukhi and F.Florence Forbes. A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models.Electronic Journal of Statistics 162September 2022, 4742 - 4822
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