2.1 Outline of the research project

The highly interconnected contemporary world is faced with an immense range of serious challenges in statistical learning, engineering and information sciences which make the development of statistical and stochastic methods for complex estimation problems and decision making critical. The most significant challenges arise in risk analysis, in environmental and statistical analysis of massive data sets, as well as in defense systems. From both the numerical and the theoretical viewpoints, there is a need for unconventional statistical and stochastic methods that go beyond the current frontier of knowledge.

Our approach to this interdisciplinary challenge is based on recent developments in statistics and stochastic computational methods. We propose a work programme which will lead to significant breakthroughs in fundamental and applied mathematical research, as well as in advanced engineering and information sciences with industrial applications with a particular focus on defence applications, in collaboration with Naval Group.

Many real-world systems and processes are dynamic and essentially random. Examples can be found in many areas like communication and information systems, biology, geophysics, finance, economics, production systems, maintenance, logistics and transportation. These systems require dynamic and stochastic mathematical representations with discrete and/or continuous state variables in possibly infinite dimensional space. Their dynamics can be modeled in discrete or continuous time according to different time scales and are governed by different types of processes such as stochastic differential equations, piecewise deterministic processes, jump-diffusion processes, branching and mean field type interacting processes, reinforced processes and self-interacting Markov processes, to name a few. Our interdisciplinary project draws knowledge from information science, signal processing, control theory, statistics and applied probability including numerical and mathematical analysis. The idea is to work across these scientific fields in order to enhance their understandings and to offer an original theory or concept.

Our group mainly focuses on the development of advanced statistical and probabilistic methods for the analysis and the control of complex stochastic systems, as outlined in the following three topics.

• Statistical and Stochastic modeling: Design and analysis of realistic and tractable statistical and stochastic models, including measurement models, for complex real-life systems taking into account various random phenomena. Refined qualitative and quantitative mathematical analysis of the stability and the robustness of statistical models and stochastic processes.
• Estimation/Calibration: Theoretical methods and advanced computational methodologies to estimate the parameters and the random states of the model given partial and noisy measurements as well as statistical data sets. Refined mathematical analysis of the performance and the convergence of statistical and stochastic learning algorithms.
• Decision and Control: Theoretical methods and advanced computational methodologies for solving regulation and stochastic optimal control problems, including optimal stopping problems and partially observed models. Refined mathematical analysis of the long time behavior and the robustness of decision and control systems.

These three items are by no means independent.

• Regarding the interdependence between the modeling aspects and the estimation/calibration/control aspects, it must be emphasized that when optimizing the performance of a partially observed/known stochastic system, the involved mathematical techniques will heavily depend on the underlying mathematical characteristics and complexity of the model of the state process and the model of the observation process. The main difficulty here is to find a balance between complexity and feasibility/solvability. The more sophisticated a model is, the more complicated the statistical inference and optimization problems will be to solve.
• The interdependence that arises between estimation/calibration and the optimal control can be summarised as follows. When the decision-maker has only partial information on the state process, it is necessary to assume that the admissible control policies will depend on the filtration generated by the observation process. This is a particularly difficult optimisation problem to solve. Roughly speaking, by introducing the conditional distribution of the state process, the problem can then be reformulated in terms of a fully observed control problem. This leads to a separation of estimation and control principle, i.e. the estimation step is carried out first and then the optimisation. The price to be paid for this new formulation is an enlarged state space of infinite dimension. More precisely, in addition to the observable part of the state, a probability distribution enters the new state space which defines the conditional distribution of the unobserved part of the state given the history of the observations.

Solving such global optimization problems remain an open problem and is recognized in the literature as a very difficult challenge to meet.

One of the fundamental challenges we will address is to develop estimation/calibration and optimal control techniques related to general classes of stochastic processes in order to deal with real-world problems. Our research results will combine, mathematical rigour (through the application of advanced tools from probability, statistics, measure theory, functional analysis and optimization) with computational efficiency (providing accurate and applicable numerical methods with a refined analysis of the convergence). Thus, the results that we will obtain in this research programme will be of interest to researchers in the fields of stochastic modeling, statistics and control theory both for the theoretical and the applied communities. Moreover, the topics studied by Naval Group, such as target detection, nonlinear filtering, multi-object tracking, trajectory optimization and navigation systems, provide a diverse range of application domains in which to implement and test the methodologies we wish to develop.

The final goal is to develop a series of reliable and robust softwares dedicated to statistical and stochastic learning, as well as automated decision and optimal control processes. The numerical codes are required to be both accurate and fast since they are often elements of real time estimation and control loops in automation systems. In this regard, the research topics proposed by Naval Group will provide a natural framework for testing the efficiency and robustness of the algorithms developed by the team.

From our point of view, this collaboration between the INRIA project team and Naval Group offers new opportunities and strategies to design advanced cutting-edge estimation and control methodologies.

2.2 Approach and methodologies

The types of learning and control methodologies developed by the team differ in their approach as well as in the problems that they are intended to solve. They can be summarised by the following three sets of interdependent methodologies.

• Statistical learning: Regression, clustering, volume and dimensionality reduction, classification, data mining, training sets analysis, supervised and unsupervised learning, active and online learning, reinforcement learning, identification, calibration, Bayesian inference, likelihood optimisation, information processing and computational data modeling.
• Stochastic learning: Advanced Monte Carlo methods, reinforcement learning, local random searches, stochastic optimisation algorithms, stochastic gradients, genetic programming and evolutionary algorithms, interacting particle and ensemble methodologies, uncertainty propagation, black box inversion tools, uncertainty propagation in numerical codes, rare event and default tree simulation, nonlinear and high dimensional filtering, prediction and smoothing.
• Decision and control: Markov decision processes, piecewise deterministic Markov processes, stability, robustness, regulation, optimal stopping, impulse control, stochastic optimal control including partially observed problems, games, linear programming approaches, dynamic programming techniques.

All team members of the project work at the interface of the these three areas. This joint research project between INRIA and Naval Group is a natural and unprecedented opportunity to embrace and push the frontiers of the applied and theoretical sides of these research topics in a common research team.

Despite some recent advances, the design and the mathematical analysis of statistical and stochastic learning tools, as well as automated decision processes, is still a significant challenge. For example, since the mid-1970s nonlinear filtering problems and stochastic optimal control problems with partial observations have been the subject of several mathematical studies, however very few numerical solutions have been proposed in the literature.

Conversely, since the mid-1990s, there has been a virtual explosion in the use of stochastic particle methods as powerful tools in real-word applications of Monte Carlo simulation; to name a few, particle filters, evolutionary and genetic algorithms and ensemble Kalman filters. Most of the applied research in statistics, information theory and engineering sciences seems to be developed in a completely blind way with no apparent connections to the mathematical counterparts.

This lack of communication between the fields often produces a series of heuristic techniques often tested on reduced or toy models. In addition, most of these methodologies do not have a single concrete industrial application nor do they have any connection with physical problems.

As such, there exists a plethora of open mathematical research problems related to the analysis of statistical learning and decision processes. For instance, a variety of theoretical studies on particle algorithms, including particle filters and sequential Monte Carlo models are often based on ad-hoc and practically unrealistic assumptions for the kinds of complex models that are increasingly emerging in applications.

The aim of this project is to fill these gaps with an ambitious programme at the intersection of probability, statistics, engineering and information sciences.

One key advantage of the project is its interdisciplinary nature. Combining techniques from pure and applied mathematics, applied probability and statistics, as well as computer science, machine learning, artificial intelligence and advanced engineering sciences enables us to consider these topics holistically, in order to deal with real industrial problems in the context of risk management, data assimilation, tracking applications and automated control systems. The overarching aim of this ambitious programme is to make a breakthrough in both the mathematical analysis and the numerical aspects of statistical learning and stochastic estimation and control.

2.3 Innovation and industrial transfer

Fundamentally, our team is not driven by a single application. The reasons are three-fold. Firstly, the robustness and transferability of our approaches means that the same statistical or stochastic learning algorithms can be used in a variety of application areas. On the other hand every application domain offers a series of different perspectives that can be used to improve the design and performances of our techniques and algorithms. Last but not least, industrial applications, including those that arise in defence, require specific attention. As such, we use a broad set of stochastic and statistical algorithms to meet these demands.

This research programme is oriented towards concrete applications with significant potential industrial transfers on three central problems arising in engineering and information and data sciences, namely, risk management and uncertainty propagation, process automation, and data assimilation, tracking and guidance. Our ultimate goal is to bring cutting edge algorithms and advanced statistical tools to industry and defence. The main application domains developed by the team are outlined below:

• Risk management and uncertainty propagation: Industrial and environmental risks, fault diagnostics, phase changes, epidemiology, nuclear plants, financial ruin, systemic risk, satellite debris collisions.
• Process automation: Production maintenance and manufacturing planing, default detection, integrated dynamics and control of distributed dynamical systems, multi-object coordination, automatic tuning of cochlear implants, classification of EGG signals.
• Data assimilation, tracking and guidance: Target detection and classification, nonlinear filtering and multi-object tracking, multiple sensor fusions, motion planning, trajectory optimization, design of navigation systems.

The main objectives and challenges related to the three application domains discussed above will be developed in section 4. The latter application domain will be developed in collaboration with Naval Group. The reader is refereed to section 4.1 for a description of this collaboration and to sections 3.2 and 3.3 for the theoretical aspects that will be carried out by the team in relation to these topics. Specific details on the particular techniques used to tackle the estimation and tracking problems in the context of the collaboration with Naval Group will remain confidential.

3.1 Statistical learning

Permanent researchers: M. Chavent, P. Del Moral, F. Dufour, A. Genadot, P. Legrand, J. Saracco.

Regarding statistical learning, some of the objectives of the team is to develop dimension reduction models, data visualization, non-parametric estimation methods, genetic programming and artificial evolution. These models/methodologies provide a way to understand and visualize the structure of complex data sets. Furthermore, they are important tools in several different areas of research, such as data analysis and machine learning, that arise in many applications in biology, genetics, environment and recommendation systems. Of particular interest is the analysis of classification and clustering approaches and semi-parametric modeling that combines the advantages of parametric and non-parametric models, amongst others. One major challenge is to tackle both the complexity and the quantity of data when working on real-world problems that emerge in industry or other scientific fields in academia. Of particular interest is to find ways to handle high-dimensional data with irrelevant and redundant information.

Another challenging task is to take into account successive arrivals of information (data stream) and to dynamically refine the implemented estimation algorithms, whilst finding a balance between the estimation precision and the computational cost. One potential method for this is to project the available information into suitably chosen lower dimensional spaces.

For regression models, sliced inverse regression (SIR) and related approaches have proven to be highly efficient methods for modeling the link between a dependent variable (which can be multidimensional) and multivariate covariates in several frameworks (data stream, big data, etc.). The underlying regression model is semi-parametric (based on a single index or on multiple indices that allow dimension reduction). Currently, these models only deal with quantitative covariates. One of the team’s goals is to extend these regression models to mixed data, i.e. models dealing with quantitative and categorical covariates. This generalization would allow one to propose discriminant analysis to deal with mixed data. Extension of sparse principal component analysis (PCA) to mixed data is also another challenge. One idea is to take inspiration from the underlying theory and method of recursive SIR and SIR approaches for data stream in order to adapt them to commonly used statistical methods in multivariate analysis (PCA, discriminant analysis, clustering, etc.). The common aim of all these approaches is to estimate lower dimensional subspaces whilst minimizing the loss of statistical information. Another important aspect of data stream is the possible evolution in time of the underlying model: we would like to study break(s) detection in semi-parametric regression model, the breakdown being susceptible to appear in the parametric part or in the functional part of the regression model. The question of selecting covariates in regression modelling when we deal with big data is a fundamental and difficult problem. We will address this challenge using genetic programming and artificial evolution. Several directions are possible: for instance, improve, via genetic algorithms, the exploration of the covariate space in closest submodel selection (CSS) method or study optimization problems that simultaneously take into account variable selection, efficiency of estimation and interpretability of the model. Another important question concerns the detection of outliers that will disturb the estimation of the model, and this is not an obvious problem to deal with when working with large, high dimensional data.

In multivariate data analysis, an objective of the team is to work on a new formulation/algorithm for group-sparse block PCA since it is always important to take into account group information when available. The advantage of the group-sparse block PCA is that, via the selection of groups of variables (based on the synthetic variables), interpretability of the results becomes easier. The underlying idea is to address the simultaneous determination of group-sparse loadings by block optimization, and the correlated problem of defining explained variance for a set of non-orthogonal components. The team is also interested in clustering of supervised variables, the idea being to construct clusters made up of variables correlated with each other, which are either well-linked or not-linked to the variable to be explained (which can be quantitative or qualitative).

Another way to study the links between variables is to consider conditional quantiles instead of conditional expectation as is the case in classical regression models. Indeed, it is often of interest to model conditional quantiles, particularly in the case where the conditional mean fails to take into account the impact of the covariates on the dependent variable. Moreover, the quantile regression function provides a much more comprehensive picture of the conditional distribution of a dependent variable than the conditional mean function. The team is interested in the non parametric estimation of conditional quantile estimation. New estimators based on quantization techniques have been introduced and studied in the literature for univariate conditional quantiles and multivariate conditional quantiles. However, there are still many open problems, such as combining information from conditional quantiles of different orders in order to refine the estimation of a conditional quantile of a given order.

Another topic of interest is genetic programming (GP) and Artificial Evolution. GP is an evolutionary computation paradigm for automatic program induction. GP has produced impressive results but there are still some practical limitations, including its high computational cost, overfitting and excessive code growth. Recently, many researchers have proposed fitness-case sampling methods to overcome some of these problems, with mixed results in several limited tests. Novelty Search (NS) is a unique approach towards search and optimization, where an explicit objective function is replaced by a measure of solution novelty. While NS has been mostly used in evolutionary robotics, the team would like to explore its usefulness in classic machine learning problems.

Another important objective of the team is to implement new R (Matlab/Python) packages or to enrich those existing in the literature with the methods we are going to develop in order to make them accessible to the scientific community.

With respect to our statistical learning research program, the objectives of the team can be divided into mid- and long-term works. Mid-term objectives focus on sparsity in SIR (via soft thresholding for instance) and group-sparse block PCA, the underlying idea being to make the selection of variables or blocks of variables in the regression model or in the data. Taking into account multi-block data in regression models via data-driven sparse partial least squares is also at the heart of our concerns. Coupling genetic algorithms and artificial evolution with statistical modeling issues is also planned. The team has several long-term projects associated with the notion of data stream. Many theoretical and practical problems arise from the possible evolution of the information contained in the data: break detection in the underlying model, balance between precision and computational cost. Another scientific challenge is to extend certain approaches such as SIR to the case of mixed data by incorporating the information provided by the qualitative variables in the associated low dimensional subspaces. Moreover, the team has already worked on clustering of variables for mixed data and the clustering of supervised variables is now planned. Finally the idea of combining information from conditional quantiles of different orders in order to refine the estimation of a given order conditional quantile is still relevant today. It should be noted that other research themes may appear or become a priority depending on the academic or industrial collaborations that may emerge during the next evaluation period.

3.2 Stochastic learning

Permanent researchers: M. Chavent, P. Del Moral, F. Dufour, A. Genadot, D. Laneuville, P. Legrand, A. Nègre, J. Saracco.

Stochastic particle methodologies have become one of the most active intersections between pure and applied probability theory, Bayesian inference, statistical machine learning, information theory, theoretical chemistry, quantum physics, financial mathematics, signal processing, risk analysis, and several other domains in engineering and computer sciences.

Since the mid-1990s, rapid developments in computer science, probability and statistics have led to new generations of interacting particle learning/sampling type algorithms, such as:

Particle and bootstrap filters, sequential Monte Carlo methods, self-interacting and reinforced learning schemss, sequentially interacting Markov chain Monte Carlo, genetic type search algorithms, island particle models, Gibbs cloning search techniques, interacting simulated annealing algorithms, importance sampling methods, branching and splitting particle algorithms, rare event simulations, quantum and diffusion Monte Carlo models, adaptive population Monte Carlo sampling models, Ensemble Kalman filters and interacting Kalman filters.

Since computations are nowadays much more affordable, the aforementioned particle methods have become revolutionary for solving complex estimation and optimization problems arising in engineering, risk analysis, Bayesian statistics and information sciences. The books 40, 44, 47,62 provide a rather complete review on these application domains.

These topics have constituted some of the main research axes of several of the ASTRAL team members since the beginning of the 1990s. To the best of our knowledge, the first rigorous study on particle filters and the convergence of genetic algorithms as the size of the population tends to infinity seems to be the article 46, published in 1996 in the journal Markov Processes and Related Fields. This paper has opened an avenue of research questions in stochastic analysis and particle methods applications. The uniform convergence of particle filters and ensemble Kalman filters with respect to the time horizon was first seen in 41, 42, 45 and in the more recent article 48. The first use of particle algorithms and Approximated Bayesian Computation type methodologies in nonlinear filtering seems to have started in 43. Last but not least, the development of sequential Monte Carlo methodology in statistics was introduced in the seminal article 39.

Despite some recent advances, the mathematical foundation and the design and the numerical analysis of stochastic particle methods is still a significant challenge. For instance, particle filter technology is often combined with Metropolis-Hastings type techniques, or with Expectation Maximization type algorithms. The resulting algorithms are intended to solve high dimensional hidden Markov chain problems with fixed parameters. In this context (despite some recent attempts) the refined convergence analysis of the resulting particle algorithms, including exponential concentration estimates, remains to be developed.

Last but not least, the expectations of their performances are constantly rising in a variety of application domains. These particle methodologies are now expected to deal with increasingly sophisticated models in high dimensions, whilst also allowing for the variables to evolve at different scales. The overarching aim of this aspect of the programme is to make a breakthrough in both the mathematical analysis and the numerical simulation of stochastic and interacting particle algorithms.

Today, partly because of the emergence of new mean field simulation methodologies and partly because of the importance of new and challenging high-dimensional problems arising in statistical machine learning, engineering sciences and molecular chemistry, we are observing the following trends:

$•$ A need to better calibrate their performance with respect to the size of the systems and other tuning parameters, including cooling decay rates, local random search strategies, interacting and adaptive search criteria, and population size parameters. One of the main and central objectives is to obtain uniform and non asymptotic precision estimates with respect to the time parameter. These types of uniform estimates need to be developed, supporting industrial goals of enhanced design and confidence of algorithms, risk reduction and improved safety.

$•$ A need for new stochastic and adaptive particle methods for solving complex estimation models. Such models arise in a range of application areas including forecasting, data assimilation, financial risk management and analysis of critical events. This subject is also crucial in environmental studies and in the reliability analysis of engineering automated systems. The complexity of realistic stochastic models in advanced risk analysis requires the use of sophisticated and powerful stochastic particle models. These models go far beyond Gaussian models, taking into account abrupt random changes, as well as non nonlinear dynamics in high dimensional state spaces.

$•$ A need to find new mathematical tools to analyze the stability and robustness properties of sophisticated, nonlinear stochastic models involving space-time interaction mechanisms. Most of the theory on the stability of Markov chains is based on the analysis of the regularity properties of linear integral semigroups. To handle these questions, the interface between the theory of nonlinear dynamical systems and the analysis of measure valued processes needs to be further developed.

From a purely probabilistic point of view, the fundamental and the theoretical aspects of our research projects are essentially based on the stochastic analysis of the following three classes of interacting stochastic processes: Spatial branching processes and mean-field type interacting particle systems, reinforced and self-interacting processes, and finally random tree based search/smoothing learning processes.

The first class of particle models includes interacting jump-diffusions, discrete generation models, particle ensemble Kalman filters and evolutionary algorithms. This class of models refers to mean field type interaction processes with respect to the occupation measure of the population. For instance genetic-type branching-selection algorithms are built on the following paradigm: when exploring a state space with many particles, we duplicate better fitted individuals while particles with poor fitness die. The selection is made by choosing randomly better fitted individuals in the population. Our final aim is to develop a complete mean-field particle theory combining the stability properties of the limiting processes as the size of the system tends to infinity with the performance analysis of these particle sampling tools.

The second class of particle models refers to mean field type interaction processes with respect to the occupation measure of the past visited sites. This type of reinforcement is observed frequently in nature and society, where "beneficial" interactions with the past history tend to be repeated. Self interaction gives the opportunity to build new stochastic search algorithms with the ability to, in a sense, re-initialize their exploration from the past, re-starting from some better fitted previously visited initial value. In this context, we plan to explore the theoretical foundations and the numerical analysis of continuous time or discrete generation self-organized systems by combining spatial and temporal mean field interaction mechanisms.

The last generation of stochastic random tree models is concerned with biology-inspired algorithms on paths and excursions spaces. These genealogical adaptive search algorithms coincide with genetic type particle models in excursion spaces. They have been successfully applied in generating the excursion distributions of Markov processes evolving in critical and rare event regimes, as well as in path estimation and related smoothing problems arising in advanced signal processing. The complete mathematical analysis of these random tree models, including their long time behavior, their propagation of chaos properties, as well as their combinatorial structures are far from complete.

Our research agenda on stochastic learning is developed around the applied mathematical axis as well as the numerical perspective, including concrete industrial transfers with a special focus on Naval Group. From the theoretical side, mid-term objectives are centered around non asymptotic performance analysis and long time behavior of Monte Carlo methods and stochastic learning algorithms. We also plan to further develop the links with Bayesian statistical learning methodologies and artificial intelligence techniques, including the analysis of genetic programming discussed in section 3.1. We also have several long term projects. The first one is to develop new particle type methodologies to solve high dimensional data assimilation problems arising in forecasting and fluid mechanics, as well as in statistical machine learning. We also plan to design stochastic filtering-type algorithms to solve partially observed control problems such as those discussed in section 3.3.

3.3 Decision and stochastic control

Permanent researchers: P. Del Moral, F. Dufour, A. Genadot, D. Laneuville, O. Marceau, A. Nègre, J. Saracco.

Part of this research project is devoted to the analysis of stochastic decision models. Many real applications in dynamic optimization can be, roughly speaking, described in the following way: a certain system evolves randomly under the control of a sequence of actions with the objective to optimize a performance function. Stochastic decision processes have been introduced in the literature to model such situations and it is undoubtedly their generic capacity to model real life applications that leads to and continues to contribute to their success in many fields such as engineering, medicine and finance.

In this project we will focus on specific families of models that can be identified according to the following elements: the nature of the time variable (discrete or continuous), the type of dynamics (piecewise deterministic trajectories) and the numbers of decision makers. For one player, the system will be called a stochastic control process and for the case of several decision-makers, the name (stochastic) game will be used. For ease of understanding, we now provide an informal description of the classes of stochastic processes we are interested in, according to the nature of the time variable.

4.1 Naval Group research activities

Permanent researchers: P. Del Moral, F. Dufour, A. Genadot, D. Laneuville, O. Marceau, A. Nègre.

An important line of research of the team is submarine passive target tracking. This is a very complicated practical problem that combines both filtering and stochastic control topics. In the context of passive underwater acoustic warfare, let us consider a submarine, called the observer, equipped with passive sonars collecting noisy bearing-only measurements of the target(s). The trajectory of the observer has to be controlled in order to satisfy some given mission objectives. These can be, for example, finding the best trajectory to optimize the state estimation (position and velocity) of the targets, maximize the different targets' detection range and/or minimize its own acoustic indiscretion with respect to these targets, and reaching a way-point without being detected. Let us now describe in more detail some of the topics we intend to work on.

In the case of passive tracking problems, one of the main issues is that the observer must manoeuvre in order to generate observability. It turns out that these manoeuvres are actually necessary but not sufficient to guarantee that the problem becomes observable. In fact, a significant body of the literature pertains to attempting to understand whether this type of problem is solvable. Despite this observability analysis, the following practical questions, which we would like to address in this project, remain challenging: What kind of trajectory should the observer follow to optimize the estimation of the target’s motion? What is the accuracy of that estimate? How to deal with a multitarget environment? How to take into account some physical constraints related to the sonar?

Another aspect of target tracking is to take into account both the uncertainties on the target's measurement and also the signal attenuation due to acoustic propagation. To the best of our knowledge, there are few works focusing on the computation of optimal trajectories of underwater vehicles based on signal attenuation. In this context, we would like address the problem of optimizing the trajectory of the observer to maximize the detection of the acoustic signals issued by the targets. Conversely, given that the targets are also equipped with sonars, how can one optimize the trajectory of the observer itself to keep its own acoustic indiscretion as low as possible with respect to those targets.

It must be emphasized that a human operator can find a suitable trajectory for either of these objectives in the context of a single target. However, if both criteria and/or several targets are taken into account simultaneously, it is hardly possible for a human operator to find such trajectories. From an operational point of view, these questions are therefore of great importance.

Such practical problems are strongly connected to the mathematical topics described in sections 3.2 and 3.3. For example it is clearly related to partially observed stochastic control problems. The algorithmic solutions that we will develop in the framework of submarine passive target tracking will be evaluated on the basis of case studies proposed by Naval Group. Our short-term aim is to obtain explicit results and to develop efficient algorithms to solve the various problems described above.

4.2 Other collaborations

Permanent researchers: M. Chavent, P. Legrand and J. Saracco.

For several years, the team has also had strong collaborations with INRAE which is the French National Research Institute for Agriculture, Food and Environment. More precisely, consumer satisfaction when eating beef is a complex response based on subjective and emotional assessments. Safety and health are very important in addition to taste and convenience but many other parameters are also extremely important for breeders. Many models were recently developed in order to predict each quality trait and to evaluate the possible trade-off that could be accepted in order to satisfy all the operators of the beef chain at the same time. However, in none of these quality prediction systems are issues of joint management of the different expectations addressed. Thus, it is vital to develop a model that integrates the sensory quality of meat but also its nutritional and environmental quality, which are expectations clearly expressed by consumers. Our team are currently developing statistical models and machine learning tools in order to simultaneously manage and optimize the different sets of expectations. Combining dimension reduction methodologies, nonparametric quantiles estimation and “Pareto front’’ approaches could provide an interesting way to address this complex problem. These different aspects are currently in progress.

The team is currently initiating scientific collaboration with the Advanced Data Analytics Group of Sartorius Corporate Research which is an international pharmaceutical and laboratory equipment supplier, covering the segments of Bioprocess Solutions and Lab Products & Services. The current work concerns the development of a partial least squares (PLS) inspired method in the context of multiblocks of covariates (corresponding to different technologies and/or different sampling techniques and statistical procedures) and high dimensional datasets (with the sample size $n$ much smaller than the number of variables in the different blocks). The proposed method allows variable selection in the $X$ and in the $Y$ components thanks to interpretable parameters associated with the soft-thresholding of the empirical correlation matrices (between the $X$ ’s blocks and the $Y$ block) decomposed using singular values decomposition (SVD). In addition, the method is able to handle specific missing values (i.e. “missing samples’’ in some covariate blocks). The suggested ddsPLS + Koh Lanta methodology is computationally fast. Some technical and/or theoretical work on this methodology must be naturally pursued in order to further refine this approach. Moreover, another aspect of the future research with Sartorius consists of associating the structures of datasets with the real biological dynamics described, until now, by differential equations and for which the most advanced solutions do not merge with both high dimensional multiblock analysis and these differential equations. Combining these two approaches in a unified framework will certainly have many applications in industry and especially in the biopharmaceutical production.

Within the framework of the GIS ALBATROS, the team has initiated a scientific collaboration with IMS and THALES. The first topic is focused on the measurement of the cognitive load of a pilot through the development of methods for measuring the regularity of biological signals (Hölderian regularity, Detrended Fluctuation Analysis, etc.). The second topic is dedicated to the development of classification techniques of vessels. The different methods we proposed are based on deep learning, evolutionary algorithms and signal processing techniques and are compared to the approaches in the literature.

6.1 New software

7.1 Statistical learning

7.2 Stochastic learning

7.3 Stochastic control and games

7.4 Signal processing, artifical evolution and neural networks

8.1 Bilateral contracts with industry

8.2 Bilateral Grants with Industry

Participants: Francois Dufour, Pierre del Moral, Alexandre Genadot, Marie Chavent, Jérôme Saracco, Enzo Iglesis, Denis Arrivault, Pierrick Legrand.

9.1 International initiatives

Participants: Francois Dufour, Pierre del Moral, Alexandre Genadot, Marie Chavent, Jérôme Saracco, Enzo Iglesis, Denis Arrivault, Pierrick Legrand.

9.2 International research visitors

9.3 European initiatives

Participants: Francois Dufour, Pierre del Moral, Alexandre Genadot, Marie Chavent, Jérôme Saracco, Enzo Iglesis, Denis Arrivault, Pierrick Legrand.

9.4 National initiatives

10.1 Promoting scientific activities

Participants: Francois Dufour, Pierre del Moral, Alexandre Genadot, Marie Chavent, Jérôme Saracco, Enzo Iglesis, Denis Arrivault, Pierrick Legrand.

Vulgarisation scientifique, table ronde à la Data Party organisée par Bordeaux Metropole et l'association des petits débrouillards.

10.2 Teaching - Supervision - Juries

Participants: Francois Dufour, Pierre del Moral, Alexandre Genadot, Marie Chavent, Jérôme Saracco, Enzo Iglesis, Denis Arrivault, Pierrick Legrand.

10.3 Popularization

Participants: Francois Dufour, Pierre del Moral, Alexandre Genadot, Marie Chavent, Jérôme Saracco, Enzo Iglesis, Denis Arrivault, Pierrick Legrand.

11.1 Major publications

• 1 miscP.Pierre Del Moral and E.Emma Horton. A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters.July 2021HAL
• 2 miscF.François Dufour and T.Tomás Prieto-Rumeau. Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games.January 2022HAL
• 3 articleM.-P.Marie-Pierre Ellies-Oury, D.D. Durand, A.Anne Listrat, M.Marie Chavent, J.Jérôme Saracco and D.Dominique Gruffat. Certain relationships between Animal Performance, Sensory Quality and Nutritional Quality can be generalized between various experiments on animal of similar types.Livestock Science250August 2021, 104554HALDOI
• 4 thesisA.Alexandre Genadot. Contributions à l’étude des processus markoviens déterministes par morceaux et de décision ainsi qu’à l’étude de l’enquête Bourciez.Université de BordeauxOctober 2023HAL
• 5 inproceedings A.Alexandre Genadot. Quina metodologia per despolhar l'enquèsta Bourciez ? Ièr, deman : diga-m'o dins la lenga Montpellier, France November 2021 HAL
• 6 articleS.Stéphane Girard, H.Hadrien Lorenzo and J.Jérôme Saracco. Advanced topics in Sliced Inverse Regression.Journal of Multivariate Analysis1882022, 104852HALDOI
• 7 articleE.Eric Grivel, B.Bastien Berthelot, P.Pierrick Legrand and A.Audrey Giremus. DFA-based abacuses providing the Hurst exponent estimate for short-memory processes.Digital Signal Processing1162021HALDOI
• 8 bookP.Pierrick Legrand, A.Arnaud Liefooghe, E.Edward Keedwell, J.Julien Lepagnot, L.Lhassane Idoumghar, N.Nicolas Monmarché and E.Evelyne Lutton. Artificial Evolution, 15th International Conference, Evolution Artificielle, EA 2022, Exeter, UK, October 31 - November 2, 2022, Revised Selected Papers.14091Lecture Notes in Computer ScienceSpringer Nature SwitzerlandSeptember 2023HALDOI
• 9 articleH.Hadrien Lorenzo, O.Olivier Cloarec, R.Rodolphe Thiébaut and J.Jérôme Saracco. Data-Driven Sparse Partial Least Squares.Statistical Analysis and Data MiningDecember 2021HAL
• 10 articleA.Alexis Saadoun, A.Antoine Schein, V.Vincent Péan, P.Pierrick Legrand, L. S.Ludwig Serge Aho Glélé and A.Alexis Bozorg Grayeli. Frequency Fitting Optimization Using Evolutionary Algorithm in Cochlear Implant Users with Bimodal Binaural Hearing.Brain Sciences122February 2022, 253HALDOI
• 11 articleT.Tara Vanhatalo, P.Pierrick Legrand, M.Myriam Desainte-Catherine, P.Pierre Hanna, A.Antoine Brusco, G.Guillaume Pille and Y.Yann Bayle. A Review of Neural Network-Based Emulation of Guitar Amplifiers.Applied Sciences1212June 2022, 5894HALDOI

11.2 Publications of the year

11.3 Cited publications

• 34 bookE.E. Altman. Constrained Markov decision processes.Stochastic ModelingChapman & Hall/CRC, Boca Raton, FL1999, xii+242back to text
• 35 bookN.Nicole Bäuerle and U.Ulrich Rieder. Markov decision processes with applications to finance.UniversitextSpringer, Heidelberg2011, xvi+388URL: https://doi.org/10.1007/978-3-642-18324-9DOIback to text
• 36 bookD. P.Dimitri P. Bertsekas and S. E.Steven E. Shreve. Stochastic optimal control: The discrete time case.139Mathematics in Science and EngineeringNew YorkAcademic Press Inc.1978, xiii+323back to text
• 37 bookO. L.Oswaldo Luiz do Valle Costa and F.François Dufour. Continuous average control of piecewise deterministic Markov processes.SpringerBriefs in MathematicsSpringer, New York2013, xii+116URL: https://doi.org/10.1007/978-1-4614-6983-4DOIback to text
• 38 bookM. H.M. H. A. Davis. Markov models and optimization.49Monographs on Statistics and Applied ProbabilityChapman & Hall, London1993, xiv+295URL: http://dx.doi.org/10.1007/978-1-4899-4483-2DOIback to text
• 39 articleP.P Del Moral, A.A Doucet and J.Jasra A. Sequential Monte Carlo samplers.6832006, 411--436back to text
• 40 bookP.P Del Moral. Genealogical and interacting particle systems with applications.Probability and its ApplicationsSpringer-Verlag, New York2004, 573back to textback to text
• 41 articleP.P Del Moral and A.A Guionnet. On the stability of Measure Valued Processes with Applications to filtering.1999, 429--434back to textback to text
• 42 articleP.P Del Moral and A.A Guionnet. On the stability of interacting processes with applications to filtering and genetic algorithms.3722001, 155-194back to text
• 43 articleP.P Del Moral, J.J Jacod and P.P Protter. The Monte-Carlo method for filtering with discrete-time observations.12032001, 346--368back to textback to text
• 44 bookP.P Del Moral. Mean field simulation for Monte Carlo integration.Monographs on Statistics and Applied ProbabilityChapman and Hall2013, URL: http://www.crcpress.com/product/isbn/9781466504059back to textback to text
• 45 bookP.P Del Moral and L.L Miclo. Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering.1729Séminaire de Probabilités XXXIVEd. J. Azéma and M. Emery and M. Ledoux and M. Yor, Lecture Notes in Mathematics, Springer-Verlag Berlin2000, 1--145back to textback to text
• 46 articleP.Pierre Del Moral. Non Linear Filtering: Interacting Particle Solution.241996, 555--580back to textback to textback to text
• 47 bookP.P Del Moral and S.S Penev. Stochastic Processes: From Applications to Theory.Chapman and Hall/CRC2017back to textback to text
• 48 articleP.P Del Moral and J.J Tugaut. On the stability and the uniform propagation of chaos properties of ensemble Kalman-Bucy filters.2822018, 790--850back to text
• 49 bookE.E.B. Dynkin and A.A.A. Yushkevich. Controlled Markov processes.235Grundlehren der Mathematischen WissenschaftenBerlinSpringer-Verlag1979, xvii+289back to text
• 50 bookJ.J. Filar and K.K. Vrieze. Competitive Markov decision processes.New YorkSpringer-Verlag1997, xii+393back to text
• 51 bookX.Xianping Guo and O.Onésimo Hernández-Lerma. Continuous-time Markov decision processes.62Stochastic Modelling and Applied ProbabilityTheory and applicationsSpringer-Verlag, Berlin2009, xviii+231URL: https://doi.org/10.1007/978-3-642-02547-1DOIback to text
• 52 bookO.O. Hernández-Lerma. Adaptive Markov control processes.79Applied Mathematical SciencesNew YorkSpringer-Verlag1989, xiv+148back to text
• 53 bookO.Onésimo Hernández-Lerma and J.-B.Jean-Bernard Lasserre. Discrete-time Markov control processes: Basic optimality criteria.30Applications of MathematicsNew YorkSpringer-Verlag1996, xiv+216back to text
• 54 bookO.Onésimo Hernández-Lerma and J.-B.Jean-Bernard Lasserre. Further topics on discrete-time Markov control processes.42Applications of MathematicsNew YorkSpringer-Verlag1999, xiv+276back to text
• 55 bookK.K. Hinderer. Foundations of non-stationary dynamic programming with discrete time parameter.Lecture Notes in Operations Research and Mathematical Systems, Vol. 33Springer-Verlag, Berlin-New York1970, vi+160back to text
• 56 articleA.Arie Hordijk and F. A.Frank A. van der Duyn Schouten. Discretization and weak convergence in Markov decision drift processes.Math. Oper. Res.911984, 112--141URL: http://dx.doi.org/10.1287/moor.9.1.112DOIback to text
• 57 articleA.Arie Hordijk and F.Frank van der Duyn Schouten. Markov decision drift processes: conditions for optimality obtained by discretization.Math. Oper. Res.1011985, 160--173URL: https://doi.org/10.1287/moor.10.1.160DOIback to text
• 58 bookA. B.A. B. Piunovskiy. Examples in Markov decision processes.2Imperial College Press Optimization SeriesImperial College Press, London2013, xiv+293back to text
• 59 bookA. B.A. B. Piunovskiy. Optimal control of random sequences in problems with constraints.410Mathematics and its ApplicationsWith a preface by V. B. Kolmanovskii and A. N. ShiryaevKluwer Academic Publishers, Dordrecht1997, xii+345URL: https://doi.org/10.1007/978-94-011-5508-3DOIback to text
• 60 bookT.Tomás Prieto-Rumeau and O.Onésimo Hernández-Lerma. Selected topics on continuous-time controlled Markov chains and Markov games.5ICP Advanced Texts in MathematicsImperial College Press, London2012, xii+279URL: https://doi.org/10.1142/p829DOIback to text
• 61 bookM.M.L. Puterman. Markov decision processes: discrete stochastic dynamic programming.Wiley Series in Probability and Mathematical Statistics: Applied Probability and StatisticsA Wiley-Interscience PublicationNew YorkJohn Wiley & Sons Inc.1994, xx+649back to text
• 62 articleV.V.N. kolokoltsov. Nonlinear Markov Processes and Kinetic Equations.2010back to text