2.1 Context

In several respects, modern society has strengthened the need for statistical analysis both from the applied and theoretical points of view. The genesis comes from the easier availability of data thanks to technological breakthroughs (storage, transfer, computing), and are now so widespread that they are no longer limited to large human organizations. The more or less conscious goal of such data availability is the expectation of improving the quality of “since the dawn of time” statistical stories which are namely discovering new knowledge or doing better predictions. These both central tasks can be referred to respectively as unsupervised learning or supervised learning, even if it is not limited to them or other names exist depending on communities. Somehow, it pursues the following hope: “more data for better quality and more numerous results”.

However, today's data are increasingly complex. They gather mixed type features (for instance continuous data mixed with categorical data), missing or partially missing items (like intervals) and numerous variables (high dimensional situation). As a consequence, the target “better quality and more numerous results” of the previous adage (both words are important: “better quality” and also “more numerous”) could not be reached through a somewhat “manual” way, but should inevitably rely on some theoretical formalization and guarantee. Indeed, data can be so numerous and so complex (data can live in quite abstract spaces) that the “empirical” statistician is quickly outdated. However, data being subject by nature to randomness, the probabilistic framework is a very sensible theoretical environment to serve as a general guide for modern statistical analysis.

2.2 Goals

Modal is a project-team working on today's complex data sets (mixed data, missing data, high-dimensional data), for classical statistical targets (unsupervised learning, supervised learning, regression, etc.) with approaches relying on the probabilistic framework. This latter can be tackled through both model-based methods (as mixture models for a generic tool) and model-free methods (as probabilistic bounds on empirical quantities). Furthermore, Modal is connected to the real world by applications, typically with biological ones (some members have this skill) but many other are also considered since the application coverage of the Modal methodology is very large. It is also important to note that, in return, applications are often real opportunities for initiating academic questioning for the statistician (case of some projects treated by Bilille platform and some bilateral contracts of the team).

From the academic communities point of view, Modal can be seen as belonging simultaneously to both the statistical learning and machine learning ones, as attested by its publications. Somewhere it is the opportunity to make a bridge between these two communities around a common but large probabilistic framework.

3.1 Research axis 1: Unsupervised learning

Scientific locks related to unsupervised learning are numerous, concerning the clustering outcome validity, the ability to manage different kinds of data, the missing data questioning, the dimensionality of the data set, etc. Many of them are addressed by the team, leading to publication achievements, often with a specific package delivery (sometimes upgraded as a software or even as a platform grouping several software). Because of the variety of the scope, it involves nearly all the permanent team members, often with PhD students and some engineers. The related works are always embedded inside a probabilistic framework, typically model-based approaches but also model-free ones like PAC-Bayes (PAC stands for Probably Approximately Correct), because such a mathematical environment offers both a well-posed problem and a rigorous answer.

3.2 Research axis 2: Performance assessment

One main concern of the Modal team is to provide theoretical justifications on the procedures which are designed. Such guarantees are important to avoid misleading conclusions resulting from any unsuitable use. For example, one ingredient in proving these guarantees is the use of the PAC framework, leading to finite-sample concentration inequalities. More precisely, contributions to PAC learning rely on the classical empirical process theory and the PAC-Bayesian theory. The Modal team exploits such non-asymptotic tools to analyze the performance of iterative algorithms (such as gradient descent), cross-validation estimators, online change-point detection procedures, ranking algorithms, matrix factorization techniques and clustering methods, for instance. The team also develops some expertise on the formal dynamic study of algorithms related to mixture models (important models used in the previous unsupervised setting), like degeneracy for expectation-maximization algorithm or also label switching for Gibbs algorithm.

3.3 Research axis 3: Functional data

Mainly due to technological advances, functional data are more and more widespread in many application domains. Functional data analysis (FDA) is concerned with the modeling of data, such as curves, shapes, images or a more complex mathematical object, though as smooth realizations of a stochastic process (an infinite dimensional data object valued in a space of eventually infinite dimension; space of squared integrable functions, etc.). Time series are an emblematic example even if it should not be limited to them (spectral data, spatial data, etc.). Basically, FDA considers that data correspond to realizations of stochastic processes, usually assumed to be in a metric, semi-metric, Hilbert or Banach space. One may consider, functional independent or dependent (in time or space) data objects of different types (qualitative, quantitative, ordinal, multivariate, time-dependent, spatial-dependent, etc.). The last decade saw a dynamic literature on parametric or non-parametric FDA approaches for different types of data and applications to various domains, such as principal component analysis, clustering, regression and prediction.

3.4 Research axis 4: Applications motivating research

The fourth axis consists in translating real application issues into statistical problems raising new (academic) challenges for models developed in Modal team. Cifre PhDs in industry and interdisciplinary projects with research teams in Health and Biology are at the core of this objective. The main originality of this objective lies in the use of statistics with complex data, including in particular ultra-high dimension problems. We focus on real applications which cannot be solved by classical data analysis.

4.1 Economic world

The Modal team applies its research to the economic world through CIFRE PhD supervision such as CACF (credit scoring), A-Volute (expert in 3D sound), Meilleur Taux (insurance comparator), Worldline. It also has several contracts with companies such as COLAS, Nokia-Apsys/Airbus, Safety Line (through the PERF-AI consortium), Agence d'Urbanisme Métropole Européenne de Lille, ASYGN SAS (MEMs, joint Cytomems ANR project), HORIBA France SAS (Raman spectrometry), Withings (medical devices), Seckiot (cyber-security).

4.2 Biology and health

The second main application domain of the team is biology and health. Some members of the team are involved in the direction of Bilille, the bioinformatics platform of Lille, and of OncoLille Institute. Some members of the team also co-supervise PhD students of Inserm teams.

6.1 Awards

• Christophe Biernacki was elected as Head of the SFdS (Société Française de Statistique) since July 2024, which is the French society specialized in statistics, whose mission is to promote the use of statistics and its understanding and to foster its methodological developments.
• Sophie Dabo got a CNRS chair (2024-2027) within a joint research program with Africa.
• Guilemette Marot is co-author of the paper "Data-driven cluster analysis identifies distinct types of metabolic dysfunction-associated steatotic liver disease", published in Nature Medicine.
• Sophie Dabo was elected on June 2024 vice-president of CIMPA (International Center of Pure and Applied Mathematics), whose mission is to promote the developments of Mathematics in the developping world. The nomination will be made official during the steering committee of January 2025.

7.1 New software

8.1 Axis 1: Dealing with Missing Data in Model-based Clustering through a MNAR Model

Participants: Christophe Biernacki.

Model-based unsupervised learning, as any learning task, stalls as soon as missing data occurs. This is even more true when the missing data are informative, or said missing not at random (MNAR). We propose model-based clustering algorithms designed to handle very general types of missing data, including MNAR data. To do so, we introduce a mixture model for different types of data (continuous, count, categorical and mixed) to jointly model the data distribution and the MNAR mechanism, remaining vigilant to the relative degrees of freedom of each. Several MNAR models are discussed, for which the cause of the missingness can depend on both the values of the missing variable themselves and on the class membership. However, we focus on a specific MNAR model, called MNARz, for which the missingness only depends on the class membership. We first underline its ease of estimation, by showing that the statistical inference can be carried out on the data matrix concatenated with the missing mask considering finally a standard MAR mechanism. Consequently, we propose to perform clustering using the Expectation Maximization algorithm, specially developed for this simplified reinterpretation. Finally, we assess the numerical performances of the proposed methods on synthetic data and on the real medical registry TraumaBase as well.

It is a joint work with Claire Boyer from Sorbonne Université, Gilles Celeux from Inria Saclay, Julie Josse from Inria Montpellier, Fabien Laporte from Institut Pasteur and Matthieu Marbac-Lourdelle from ENSAI.

See for more details 26.

8.2 Axis 1: Co-clustering as a (very) parsimonious clustering

Participants: Christophe Biernacki.

Standard model-based clustering is known to be very efficient for low-dimensional data sets, but it fails for properly addressing high dimension (HD) ones, where it suffers from both statistical and computational drawbacks. In order to counterbalance this curse of dimensionality, some proposals have been made to take into account redundancy and features utility, but related models are not suitable for too many variables. We advocate that co-clustering, an unsupervised mixture model learning method to define simultaneously groups of rows (individuals) and groups of columns (variables) on a data matrix, is of particular interest to perform high dimension (HD) clustering of individuals even if it is not its primary mission. Indeed, column clustering is recast as a strategy to control the variance of the estimation, the model dimension being driven by the number of groups of variables instead of the number of variables itself. However, the statistical counterpart of this important variance reduction brings naturally some important model bias.

A presentation at an international conference 29 advocates the ability of co-clustering to outperform simple mixture row-clustering, even if co-clustering clearly corresponds to a misspecified model situation, revealing a promising manner to efficiently address (very) HD clustering.

It is a joint work with Julien Jacques from University Lyon 2 and Christine Keribin from University Paris-Saclay.

8.3 Axis 1: An EM Stopping Rule for Avoiding Degeneracy in Gaussian-based Clustering with Missing Data

Participants: Christophe Biernacki.

Missing data frequency increases with the growing size of multivariate modern datasets. In Gaussian model-based clustering, the EM algorithm easily takes into account such data but the degeneracy problem is dramatically aggravated during the EM runs: parameter degeneracy is quite slow and also more frequent than with complete data. Consequently, parameter degenerated solutions may be confused with valuable parameter solutions and, in addition, computing time may be wasted through wrong runs. In this work, a simple and low informational condition on the latent partition allows to propose a very simple partition-based stopping rule of EM which shows good behavior on numerical experiments.

This work has been presented to an international conference 30, to a national conference 28 and also to the “séminaire parisien de statistique’’ 44.

It is a joint work with Vincent Vandewalle from University Côte d'Azur.

8.4 Axis 4: Estimating Substitution for Optimised Replenishment with Slow Movers Products

Participants: Christophe Biernacki, Axel Potier.

In Retail, inventory optimisation is a common problem targeting a trade-off between the risk of stock-out and the risk of overstocking, in order to reach an optimal global profit. This inventory optimisation task is however very challenging in case of products that are sold in low quantity (so-called slow movers in Retail). Indeed, estimating properly the related future sales, especially after discretisation, usually suffers from high relative standard deviation, from which the optimal replenishment solution inherits to the point of being usefulness in practice. Nevertheless, slow movers in many companies, as ADEO (French holding company selling consumer goods for decoration), are sufficiently numerous to represent a significant portion of the sales and of the stock. Consequently, concerned items are difficult to be optimally replenished, and even a small improvement of the replenishment process may have a significant positive effect on the whole global profit. For bridging the gap, we reformulate the slow movers optimal replenishment problem as a substitution probability estimation problem between items. When a product is out of stock, a client may alternatively choose another item (a so-called substitute product), avoiding to definitively loose the intended initial sale. As a consequence, instead of choosing the optimal quantity to replenish separately for each item (classical approach), we leverage that additional information that a group of items products can be substituted for each other allows to more efficiently estimate the optimal replenished quantity of the whole group of items. Obviously, such a substitution process occurs only with a certain probability, (1) that we have to estimate and (2) then we have to properly use through the optimal replenishment calculation. Notice fundamentally that the discrete nature of the stock quantity is expected to provide a better relative improvement in terms of profit in the case of slow movers compared to the case of fast movers (the contrary of slow movers), which justifies the special interest of our approach for slow movers.

This thesis has been defended this year 36 and a associated preprint is under preparation for submission to an international journal of statistics.

It is a joint work with Vincent Vandewalle from University Côte d'Azur, Matthieu Marbac-Lourdelle from ENSAI and Julien Favre from the ADEO company.

8.5 Axis 4: Testing Abnormality of a Sequence of Graphs: Application to Cybersecurity

Participants: Christophe Biernacki, Clarisse Boinay, Cristian Preda.

The increasing number of cyber attacks on industrial networks puts human life and economies at risk. Firms usually implement fixed rules rather than anomaly detection to prevent such attacks. However, anomaly detection methods would allow for a more flexible grasp of deviations from normal behaviour. For instance, anomaly detection in graphs modeling industrial networks can sense changes in the behaviour of machines. In this work, we seek to establish whether the number of messages sent from one or more machines to one or more machines is normal or not. To this end, we first model interactions between IP addresses with dynamical graphs. Then, we construct a test statistic based on the lihelihood of a graph computed thanks to generative models such as the stochastic block model and kernel estimators. Finally, we evaluate the power of the test in realistic and generic attack scenarios.

This work has been presented to a specialized seminar in Cybersecurity at Campus Cyber – La Défense 43.

8.6 Axis 4: Comparative study of clustering models of multivariate time series from connected medical objects

Participants: Christophe Biernacki, Violaine Courrier, Cristian Preda.

In healthcare, patient data are often collected as multivariate time series, providing a comprehensive view of a patient’s health status over time. These data are typically sparse and episodic. However, connected medical devices can increase the frequency of data. The goal is to create patient profiles from these time series in an unsupervised manner. In the absence of labels, a predictive model can be used to predict future values while forming a latent cluster space, evaluated based on predictive performance. Using real-world data from Withings, we compare the static clustering approaches MAGMACLUST, which creates a cluster across the entire time series, and dynamic clustering approaches DGM2, which allows an individual’s membership in a group to change over time.

This work has been presented to a national conference 33.

It is a joint work with Benjamin Vittrant from the Withings company.

8.7 Axis 2: Anomaly detection in time series using breakpoint detection and multiple testing

Participants: Etienne Krönert, Alain Celisse.

The purpose of this work is to develop new methods in the field of anomaly detection. An anomaly detector should identify data points that have been generated by a process different from the reference process. In general, anomaly detectors are trained on past data and only consider the reference distribution given in the training set. Alternatively, the detector is updated in real time from a fixed length sliding window. Neither approach takes into account the true dynamics of the time series, leading to false positives when the reference distribution changes.The proposed approach consists in detecting these distribution changes upstream, using breakpoint detectors. Anomalies are then retrieved within the identified homogeneous segments.The advantage of this approach for a company like Worldline is that it can quickly detect incidents in its system, while reducing the number of false alarms.In addition, care is taken to theoretically control the number of false positives through the False Detection Rate (FDR).The first step is an attempt to develop a new estimator of the p-value. After comparison with existing estimators, this new estimator turns out to be too complex, with no real gain. The empirical p-value estimator is then used.Then, the problem of anomaly detection on iid series is studied theoretically. A procedure is developed to control the FDR of a series of infinite length by controlling a variant of the FDR on subseries of fixed length. Empirical experiments show under which conditions this control is achieved in practice. Finally, our new anomaly detector based on breakpoints is introduced for piecewise iid series. It is shown that the FDR control procedure is effective in this new context. However, the use of a breakpoint detector leads to two difficulties: small segment length and breakpoint detection delays. To overcome these difficulties, a confidence score is introduced. The detector is empirically evaluated to show the relevance and limitations of our approach. See for more details 35.

8.8 Axis 2: Breakpoint based online anomaly detection

Participants: Etienne Krönert, Alain Celisse.

This work proposes a new online anomaly detector for time series. Classically, anomaly detectors do not adapt well in real time to changes in the reference distribution. The novelty of our approach is to use breakpoint detection to adapt online to the new reference behavior of the time series. The statistical performance of the detector is theoretically ensured by a control on the FDR. The anomaly detector is empirically evaluated in depth to assess its capabilities and limitations. See for more details 39.

8.9 Axis 1&2: Seeded graph matching for the correlated Gaussian Wigner model via the projected power method

Participants: Ernesto Araya, Guillaume Braun, Hemant Tyagi.

In the graph matching problem we observe two graphs $G,H$ and the goal is to find an assignment (or matching) between their vertices such that some measure of edge agreement is maximized. We assume in this work that the observed pair $G,H$ has been drawn from the Correlated Gaussian Wigner (CGW) model – a popular model for correlated weighted graphs – where the entries of the adjacency matrices of $G$ and $H$ are independent Gaussians and each edge of $G$ is correlated with one edge of $H$ (determined by the unknown matching) with the edge correlation described by a parameter $\sigma \in [0,1)$. In this paper, we analyse the performance of the projected power method (PPM) as a seeded graph matching algorithm where we are given an initial partially correct matching (called the seed) as side information. We prove that if the seed is close enough to the ground-truth matching, then with high probability, PPM iteratively improves the seed and recovers the ground-truth matching (either partially or exactly) in $𝒪(logn)$ iterations. Our results prove that PPM works even in regimes of constant $\sigma$, thus extending the analysis in (Mao et al.,2021) for the sparse Correlated Erdös-Renyi (CER) model to the (dense) Wigner model. As a byproduct of our analysis, we see that the PPM framework generalizes some of the state-of-art algorithms for seeded graph matching. We support and complement our theoretical findings with numerical experiments on synthetic data.

This work has been published in the Journal of Machine Learning Research (JMLR) (11).

8.10 Axis 1&2: Graph Matching via convex relaxation to the simplex

Participants: Ernesto Araya, Hemant Tyagi.

This paper addresses the Graph Matching problem, which consists of finding the best possible alignment between two input graphs, and has many applications in computer vision, network deanonymization and protein alignment. A common approach to tackle this problem is through convex relaxations of the NP-hard Quadratic Assignment Problem (QAP). Here, we introduce a new convex relaxation onto the unit simplex and develop an efficient mirror descent scheme with closed-form iterations for solving this problem. Under the correlated Gaussian Wigner model, we show that the simplex relaxation admits a unique solution with high probability. In the noiseless case, this is shown to imply exact recovery of the ground truth permutation. Additionally, we establish a novel sufficiency condition for the input matrix in standard greedy rounding methods, which is less restrictive than the commonly used `diagonal dominance' condition. We use this condition to show exact one-step recovery of the ground truth (holding almost surely) via the mirror descent scheme, in the noiseless setting. We also use this condition to obtain significantly improved conditions for the GRAMPA algorithm [Fan et al. 2019] in the noiseless setting. Our method is evaluated on both synthetic and real data, demonstrating superior statistical performance compared to existing convex relaxation methods with similar computational costs.

This work appeared in the journal Foundations of Data Science 11.

8.11 Axis 2: Learning linear dynamical systems under convex constraints

Participants: Hemant Tyagi.

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where no structural assumption is made on the system matrix $A^{*}\in R^{n\times n}$, and have consequently analyzed the ordinary least squares (OLS) estimator in detail. We assume prior structural information on $A^{*}$ is available, which can be captured in the form of a convex set $𝒦$ containing $A^{*}$. For the solution of the ensuing constrained least squares estimator, we derive non-asymptotic error bounds in the Frobenius norm that depend on the local size of $𝒦$ at $A^{*}$. To illustrate the usefulness of these results, we instantiate them for three examples, namely when (i) $A^{*}$ is sparse and $𝒦$ is a suitably scaled ${\ell }_1$ ball; (ii) $𝒦$ is a subspace; (iii) $𝒦$ consists of matrices each of which is formed by sampling a bivariate convex function on a uniform $n\times n$ grid (convex regression). In all these situations, we show that $A^{*}$ can be reliably estimated for values of $T$ much smaller than what is needed for the unconstrained setting.

This work is currently under review in a journal 41 and is joint work with Denis Efimov (Inria Lille, Valse team).

8.12 Axis 2: Joint Learning of Linear Dynamical Systems under Smoothness Constraints

Participants: Hemant Tyagi.

We consider the problem of joint learning of multiple linear dynamical systems. This has received significant attention recently under different types of assumptions on the model parameters. The setting we consider involves a collection of $m$ linear systems each of which resides on a node of a given undirected graph $G=\left(\right[m],ℰ)$. We assume that the system matrices are marginally stable, and satisfy a smoothness constraint w.r.t $G$ – the smoothness measured in a manner akin to the quadratic variation of a signal on a graph. Given access to the states of the nodes over $T$ time points, we then propose two estimators for joint estimation of the system matrices, along with non-asymptotic error bounds on the mean-squared error (MSE). In particular, we show conditions under which the MSE converges to zero as $m$ increases, typically polynomially fast w.r.t $m$. The results hold under mild (i.e., $T\sim logm$), or sometimes, even no assumption on $T$ (i.e. $T\ge 2$).

This work is currently under review in a journal 42.

8.13 Axis 1&2: Dynamic angular synchronization under smoothness constraints

Participants: Ernesto Araya, Mihai Cucuringu, Hemant Tyagi.

Given an undirected measurement graph $\mathscr{H}=\left(\right[𝓃],ℰ)$, the classical angular synchronization problem consists of recovering unknown angles ${\theta }_{1^{*}},\cdots ,{\theta }_{n^{*}}$ from a collection of noisy pairwise measurements of the form $({\theta }_i^{*}-{\theta }_j^{*})mod2\pi$, for all $i,j\in ℰ$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from pairwise comparisons. In this paper, we consider a dynamic version of this problem where the angles, and also the measurement graphs evolve over $T$ time points. Assuming a smoothness condition on the evolution of the latent angles, we derive three algorithms for joint estimation of the angles over all time points. Moreover, for one of the algorithms, we establish non-asymptotic recovery guarantees for the mean-squared error (MSE) under different statistical models. In particular, we show that the MSE converges to zero as $T$ increases under milder conditions than in the static setting. This includes the setting where the measurement graphs are highly sparse and disconnected, and also when the measurement noise is large and can potentially increase with $T$. We complement our theoretical results with experiments on synthetic data.

This work is currently under review in a journal 37.

8.14 Axis 2: A shared-frailty spatial scan statistic model for time-to-event data

Participants: Sophie Dabo-Niang.

This paper presents a scan statistic based on a Cox model with shared frailty that takes into account the spatial correlation between spatial units. In simulation studies, we have shown that (i) classical models of spatial scan statistics for time-to-event data fail to maintain the type I error in the presence of intra-spatial unit correlation, and (ii) our model performs well in the presence of both intra-spatial unit correlation and inter-spatial unit correlation. Our method has been applied to epidemiological data and to the detection of spatial clusters of mortality in patients with end-stage renal disease in northern France.

It is a joint work with with Camille Frévent, Mohamed Salem Ahmed and Michael Genin (University of Lille, CERIM) 16.

8.15 Axis 2: A Markov-switching spatio-temporal ARCH model

Participants: Sophie Dabo-Niang.

This paper proposes a Markov switching framework of the spatio-temporal log-ARCH model. We investigate the estimation procedure and the smooth inferences of the regimes. The Monte-Carlo simulation studies show that the maximum likelihood estimation method for our proposed model has good finite sample properties. The proposed model was applied to 28 stock indices data that were presumably affected by the 2015-2016 Chinese stock market crash. The results showed that our model is a better fit compared to that of the one-regime counterpart. Furthermore, the smoothed inference of the data indicated the approximate periods where structural breaks occurred. This model can capture structural breaks that simultaneously occur in nearby locations.

It is a joint work with with Tzung Hsuen Khoo, Dharini Pathmanathan (Malaya University, Malaysia), Philipp Otto (University of Glasgow) 19.

8.16 Axis 2: Automatic geomorphological mapping using ground truth data with coverage sampling and random forest algorithms

Participants: Sophie Dabo-Niang.

This work provides statistical learning approaches based framework to build automatically geomorphological maps. We used bathymetric data to build Digital Bathymetric Model (DBM) and compute terrain attributes characteristic of seafloor geomorphology. Then, we used clustering based algorithms to select automatically ground truth locations from a reference geomorphological map manually made. Finally a supervised classification model random forest based was used to build predictive models for seafloor geomorphology typologies. Subsequently we studied the effect of DBM resolution, sample size and sampling method of the ground truth locations, in the quality of map production via a series of simulations. Results showed that the proposed framework allowed to build efficiently relevant seafloor geomorphological maps. The best compromise between the sampling effort and the quality of the resulting maps was obtained with 100 m DBM resolution, 200 data points sample size and using a complexity-dependent sampling method and led to a map matching at 90% the reference one.

It is a joint work with with Paul Aimé Latsouck Faye, Elodie Brunel, Thomas Claverie, Solym Mawaki Manou-Abi (University of Montpellier 2) 15.

8.17 Axis 2: FDR control for Online Anomaly Detection

Participants: Etienne Krönert, Alain Célisse, Dalila Hattab.

The goal of anomaly detection is to identify observations generated by a process that is different from a reference one. An accurate anomaly detector must ensure low false positive and false negative rates. However in the online context such a constraint remains highly challenging due to the usual lack of control of the False Discovery Rate (FDR). In particular the online framework makes it impossible to use classical multiple testing approaches such as the Benjamini-Hochberg (BH) procedure. Our strategy overcomes this difficulty by exploiting a local control of the "modified FDR" (mFDR). An important ingredient in this control is the cardinality of the calibration set used for computing empirical p-values, which turns out to be an influential parameter. It results a new strategy for tuning this parameter, which yields the desired FDR control over the whole time series. The statistical performance of this strategy is analyzed by theoretical guarantees and its practical behavior is assessed by simulation experiments which support our conclusions. See for more details 38.

8.18 Axis 3: Uncovering Data Across Continua : An Introduction to Functional Data Analysis

Participants: Sophie Dabo-Niang.

This article introduces FDA, merging statistics with real-world complexity, ideal for those with mathematical skills but no FDA background.

It is a joint work with Camille Frévent (University of Lille, METRICS). It bas been published in the AMS (American Mathematical Society) Notices (13).

8.19 Axis 3: Principal Component Analysis of Multivariate Spatial Functional Data

Participants: Sophie Dabo-Niang.

This paper is devoted to the study of dimension reduction techniques for multivariate spatially indexed functional data and d­efined on different domains. We present a method called Spatial Multivariate Functional Principal Component Analysis (SMFPCA), which performs principal component analysis for multivariate spatial functional data. In contrast to Multivariate Karhunen-Loève approach for independent data, SMFPCA is notably adept at effectively capturing spatial dependencies among multiple functions. SMFPCA applies spectral functional component analysis to multivariate functional spatial data, focusing on data points arranged on a regular grid. The methodological framework and algorithm of SMFPCA have been developed to tackle the challenges arising from the lack of appropriate methods for managing this type of data. The performance of the proposed method has been veri­fied through finite sample properties using simulated datasets and sea-surface temperature dataset. Additionally, we conducted comparative studies of SMFPCA against some existing methods providing valuable insights into the properties of multivariate spatial functional data within a finite sample.

It is a joint work with IdrisSi-ahmeda, Leila Hamdad (ESI, Algeria) Christelle Judith Agonkoui (IMSP, Benin) and Yoba Kande (IRD, Senegal and University of Lille). For more details, see 25.

8.20 Axis 3: Forecasting mortality rates with functional signatures

Participants: Sophie Dabo-Niang.

This study introduces an innovative methodology for mortality forecasting, which integrates signature-based methods within the functional data framework of the Hyndman-Ullah (HU) model. This new approach, termed the Hyndman-Ullah with truncated signatures (HUts) model, aims to enhance the accuracy and robustness of mortality predictions. By utilizing signature regression, the HUts model is able to capture complex, nonlinear dependencies in mortality data which enhances forecasting accuracy across various demographic conditions. The model is applied to mortality data from 12 countries, comparing its forecasting performance against variants of the HU models across multiple forecast horizons. Our findings indicate that overall the HUts model not only provides more precise point forecasts but also shows robustness against data irregularities, such as those observed in countries with historical outliers. The integration of signature-based methods enables the HUts model to capture complex patterns in mortality data, making it a powerful tool for actuaries and demographers. Prediction intervals are also constructed with bootstrapping methods.

It is a joint work with Zhong Jing Yap, Dharini Pathmanathan (University of Malaya, Malaysia).

For more details, see 27.

8.21 Axis 3: PLS regression approach for multivariate functional data with different domains

Participants: Issam Moindjie, Sophie Dabo, Cristian Preda.

Multivariate functional data are considered as sample paths of a multivariate valued stochastic process, $X=(X_1,...,X_d)$. In this setting, each dimension $X_i$, $i=1,...,d$, is a stochastic process, $X_i=\{X_i\left(t\right),t\in {ℐ}_i\}$, where ${ℐ}_i$ is some compact domaine of $ℝ$. The problems of linear regression and binary classification are addressed by PLS regularization techniques. For application purposes, decision tree methods combined with functional PLS regression are proposed. For more details, see 20.

8.22 Axis 3: Group lasso regression for spatially dependent functional data

Participants: Issam Moindjie, Sophie Dabo, Cristian Preda.

Multivariate functional data is considered under the assumption of spatially dependence between dimensions. Each dimension is associated to some (spatial) clusters with potentially different effect on a response variable. In the context of linear regression with multivariate functional data, a natural assumption is to consider the same regression coefficient (slope) function for all dimensions belonging to the same cluster. Fused and group lasso techniques are extended for this purpose. This work was published in the CSDA journal 40.

8.23 Axis 3: Statistical learning with categorical functional data

Participants: Cristian Preda, Quentin Grimonprez.

We introduce unsupervised and supervised models for categorical functional data. Multiple correspondence analysis is extended to categorical functional data and principal components are used as latent variables for clustering and regression models. An application on the DAMAGE medical dataset is presented. A presentation of these models is done in 34.

8.24 Axis 4: Data-driven cluster analysis identifies distinct types of metabolic dysfunction-associated steatotic liver disease.

Participants: Guillemette Marot.

Metabolic dysfunction-associated steatotic liver disease (MASLD) exhibits considerable variability in clinical outcomes. Identifying specific phenotypic profiles within MASLD is essential for developing targeted therapeutic strategies. Here we investigated the heterogeneity of MASLD using partitioning around medoids clustering based on six simple clinical variables in a cohort of 1,389 individuals living with obesity. The identified clusters were applied across three independent MASLD cohorts with liver biopsy (totaling 1,099 participants), and in the UK Biobank to assess the incidence of chronic liver disease, cardiovascular disease and type 2 diabetes. Results unveiled two distinct types of MASLD associated with steatohepatitis on histology and liver imaging. The first cluster, liver-specific, was genetically linked and showed rapid progression of chronic liver disease but limited risk of cardiovascular disease. The second cluster, cardiometabolic, was primarily associated with dysglycemia and high levels of triglycerides, leading to a similar incidence of chronic liver disease but a higher risk of cardiovascular disease and type 2 diabetes. Analyses of samples from 831 individuals with available liver transcriptomics and 1,322 with available plasma metabolomics highlighted that these two types of MASLD exhibited distinct liver transcriptomic profiles and plasma metabolomic signatures, respectively. In conclusion, these data provide preliminary evidence of the existence of two distinct types of clinically relevant MASLD with similar liver phenotypes at baseline, but each with specific underlying biological profiles and different clinical trajectories, suggesting the need for tailored therapeutic strategies. This work was published in Nature Medicine 24.

8.25 Axis 4: Assessing the multi-dimensional effects of air pollution on maternal complications and birth outcomes : A structural equation modeling approach

Participants: Sophie Dabo-Niang.

This cross-sectional study aims to investigate the direct and indirect relationships between exposure to a metal mixture in air and adverse pregnancy outcomes across gestational stages. It reveals time-dependent associations between a metal mixture in $P{M}_{2.5}$ exposure and adverse pregnancy outcomes, highlights the need to address dust in $P{M}_{2.5}$, and provides additional evidence for understanding the pathway of the pollution effects on fetal health. This work is a result of a visit of Boubakari Ibrahimou (Florida International University, Miami, FL, USA) to Modal and university of Lille during two months.

It is a joint work with Ning Sun and Boubakari Ibrahimou (Florida International University, Miami, FL, USA) 17.

8.26 Axis 4: Demonstrating the relevance of spatial-functional statistical analysis in marine ecological studies : The case of environmental variations in micronektonic layers

Participants: Sophie Dabo-Niang.

In this study, we conducted an analysis of a multifrequency acoustics dataset acquired from scientific echosounders in the West African water. Our objective was to explore the spatial arrangement of marine organism aggregations. We investigated various attributes of these intricate biological entities, such as thickness, relative density, and depth, in relation to their surroundings. These environmental conditions were represented at a fine scale using a towed multiparameter system. This study is closely intertwined with two key domains: Fisheries acoustics techniques and functional data analysis. Fisheries acoustics techniques facilitate the collection of high-resolution spatial and temporal data concerning marine organisms at various depths and spatial scales, all without causing any disturbance. On the other hand, spatial-functional data analysis is a statistical approach for examining data characterised by functional attributes distributed across a spatial domain. This analysis encompasses dimension reduction techniques, as well as supervised and unsupervised methods, which take into consideration spatial dependencies within extensive dataset.

See for more details 18.

It is a joint work with Yoba Kande (IRD Senegal nd University of Lille), Ndague Diogoul, Patrice Brehmer and Yannick Perrot (IRD, Senegal) and Papa Ngom (University of Dakar, Senegal).

8.27 Axis 4: Aspects of the gender gap in Mathematics

Participants: Sophie Dabo-Niang.

As a contribution to some aspects of the gender gap in mathematics, this paper provides a detailed analysis of mathematicians answers to the Global Survey of Scientists. The questions we address are the following: are the answers from all sciences and the answers of mathematics or applied mathematics similar? In which cases is the situation in mathematics or in applied mathematics different from the situation in all sciences? Better or worse?

For more details, see 12. It is a joint work with Maria Esteban (University of Paris Dauphine, France), Colette Guillopé (Université Paris-Est Créteil) and Marie-Françoise Roy (Université de Rennes I).

8.28 Axis 4: Functional data geometric morphometrics with machine learning for craniodental shape classification in shrews

Participants: Sophie Dabo-Niang.

This work proposes a functional data analysis approach for morphometrics in classifying three shrew species (S. murinus, C. monticola, and C. malayana) from Peninsular Malaysia. Functional data geometric morphometrics (FDGM) for 2D landmark data is introduced and its performance is compared with classical geometric morphometrics (GM). The FDGM approach converts 2D landmark data into continuous curves, which are then represented as linear combinations of basis functions. The landmark data was obtained from 89 crania of shrew specimens based on three craniodental views (dorsal, jaw, and lateral). Principal component analysis and linear discriminant analysis were applied to both GM and FDGM methods to classify the three shrew species. This study also compared four machine learning approaches (naïve Bayes, support vector machine, random forest, and generalised linear model) using predicted PC scores obtained from both methods (a combination of all three craniodental views and individual views). The analyses favoured FDGM and the dorsal view was the best view for distinguishing the three species.

It is a joint work with Aneesha Balachandran Pillay, Dharini Pathmanathan, Sophie Dabo-Niang, Arpah Abu and and Hasmahzaiti Omar from University of Malaya, Malaysia. See for more details 23.

8.29 Axis 4: A Novel Unstained Blood Smears Multispectral Images Normalization for automatic and rapid diagnosis of malaria

Participants: Sophie Dabo-Niang.

This work proposes a novel method for achieving this normalization, aiming to improve the accuracy and reliability of the diagnostic process. This method is based on estimating the Bright reference image, which captures the luminosity, and the contrast variability function from the background region of the image. This is achieved through two distinct resampling methodologies, namely Gaussian random field simulation by variogram analysis and Bootstrap resampling. A method for handling the intensity saturation issue of certain pixels is also proposed, which involves outlier imputation. Both of these proposed approaches for image normalization are demonstrated to outperform existing methods for multispectral and multimodal unstained blood smear images, as measured by the Structural Similarity Index Measure (SSIM), Mean Squared Error (MSE), Zero mean Sum of Absolute Differences (ZSAD), Peak Signal to Noise Ratio (PSNR), and Absolute Mean Brightness Error (AMBE). These methods not only improve the image contrast but also preserve its spectral footprint and natural appearance more accurately. The normalization technique employing Bootstrap resampling significantly reduces the acquisition time for multimodal and multispectral images by 66%. Moreover, the processing time for Bootstrap resampling is less than 4% of the processing time required for Gaussian random field simulation.

It is a joint work with Solange Doumun Oulai and Jérémie Zoueu from San Pedro Universuty (Ivory Coast). See for more details 14.

9.1 Bilateral contracts with industry

9.2 Bilateral grants with industry

10.1 International initiatives

10.2 International research visitors

10.3 National initiatives

11.1 Promoting scientific activities

11.2 Teaching - Supervision - Juries

11.3 Popularization

12.1 Major publications

• 1 articleP.Pierre Alquier and B.Benjamin Guedj. Simpler PAC-Bayesian Bounds for Hostile Data.Machine Learning2018HALDOI
• 2 articleP.Parmeet Bathia, S.Serge Iovleff and G.G. Govaert. An R Package and C++ library for Latent block models: Theory, usage and applications.Journal of Statistical Software2016HAL
• 3 articleC.Christophe Biernacki and A.Alexandre Lourme. Unifying Data Units and Models in (Co-)Clustering.Advances in Data Analysis and Classification1241May 2018HAL
• 4 articleA.Alain Celisse. Optimal cross-validation in density estimation with the L2-loss.The Annals of Statistics4252014, 1879--1910HAL
• 5 articleS.Sophie Dabo-Niang, C.Camille Ternynck and A.-F.Anne-Francoise Yao. Nonparametric prediction in the multivariate spatial context.Journal of Nonparametric Statistics2822016, 428-458HALDOI
• 6 articleJ.Julie Dubois, V.Vanessa Dubois, H.Hélène Dehondt, P.Parisa Mazrooei, C.Claire Mazuy, A. A.Aurélien A. Sérandour, C.Céline Gheeraert, P.Penderia Guillaume, E.Eric Baugé, B.Bruno Derudas, N.Nathalie Hennuyer, R.Réjane Paumelle, G.Guillemette Marot, J. S.Jason S. Carroll, M.Mathieu Lupien, B.Bart Staels, P.Philippe Lefebvre and J.Jerome Eeckhoute. The logic of transcriptional regulator recruitment architecture at cis -regulatory modules controlling liver functions.Genome Research276June 2017, 985--996HALDOI
• 7 inproceedingsG.Gaël Letarte, P.Pascal Germain, B.Benjamin Guedj and F.François Laviolette. Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks.NeurIPS 2019Vancouver, CanadaDecember 2019HAL
• 8 articleM.Matthieu Marbac, C.Christophe Biernacki and V.Vincent Vandewalle. Model-based clustering of Gaussian copulas for mixed data.Communications in Statistics - Theory and MethodsDecember 2016HAL
• 9 articleC.Cristian Preda, Q.Quentin Grimonprez and V.Vincent Vandewalle. Categorical Functional Data Analysis. The cfda R Package.Mathematics 923December 2021, 31HALDOI
• 10 articleH.Hemant Tyagi and J.Jan Vybiral. Learning general sparse additive models from point queries in high dimensions.Constructive ApproximationJanuary 2019HAL

12.2 Publications of the year