Project-team positioning:

Some topics of the INRIA project teams (STATIFY, CELESTE, MODAL, SEQUEL, CLASSIC) are close to the ASTRAL objectives such as non parametric view of high dimensional data, statistical/machine learning, model selection, clustering, sequential learning algorithms, or multivariate data analysis for complex data. While certain ASTRAL objectives are similar to those of these teams, our approaches are significantly different. For example, in multivariate data analysis of complex data including clustering, our team mainly focuses on a geometric approach for mixed data. We also consider the case of successive arrivals of information in SIR both from the theoretical and numerical point of view. Currently there is no direct competition between our team and other INRIA project teams. However, interactions between ASTRAL and other INRIA teams exist. For instance, ASTRAL and STATIFY collaborations are fruitful with common publications, in particular with S. Girard (STATIFY project team).

In the field of multivariate data analysis, the team have interesting discussions with Agrocampus Ouest (Rennes, France) and with H.A.L. Kiers (Groningen University) on a mixed data approach for dimension reduction. Conditional and regression quantiles are very active research fields in France (University of Toulouse, Toulouse School of Economics, University of Montpellier) and around the world (ULB, Belgium; University of Illinois Urbana-Champaign, USA; Open University, UK; Brunel University, UK). The ASTRAL team has for the last four-year period collaborated with D. Paindaveine (ULB, Belgium). In the dimension reduction framework, there is a large international community in Europe, America or Asia working on SIR and related methods. However, to our knowledge, the ASTRAL team was the first to introduce importance of variables and recursive methods in SIR, and the first to adapt the SIR approach to data stream.

Project-team positioning:

In the last three decades, the use of Feynman-Kac type particle models has been developed in variety of scientific disciplines, including in molecular chemistry, risk analysis, biology, signal processing, Bayesian inference and data assimilation.

The design and the mathematical analysis of Feynman-Kac particle methodologies has been one of the main research topics of P. Del Moral since the late 1990's  53, 50, 48, see also the books  52, 47, 51, 54 and references therein. These mean field particle sampling techniques encapsulate particle filters, sequential Monte Carlo methods, spatial branching and evolutionary algorithms, Fleming-Viot genetic type particles methods arising in the computation of quasi-invariant measures and simulation of non absorbed processes, as well as diffusion Monte Carlo methods arising in numerical physics and molecular chemistry. The term "particle filters" was first coined in the article  53 published in 1996 in reference to branching and mean field interacting particle methods used in fluid mechanics since the beginning of the 1960s. This article presents the first rigorous analysis of these mean field type particle algorithms.

The INRIA project teams applying the particle methodology developed by ASTRAL include the INRIA project team SIMSMART (rare event simulation as well as particle filters) and the INRIA project team Matherials (applications in molecular chemistry). The project team ASTRAL also has several collaborative research projects with these, teams as well as with researchers from international universities working in this subject, including Oxford, Cambridge, New South Wales Sydney, UTS, Bath, Warwick and Singapore Universities.

Discrete-time models.

In this framework, the basic model can be described by a state space where the system evolves, an action space, a stochastic kernel governing the dynamic and, depending on the state and action variables, a one-step cost (reward) function. The distribution of the controlled stochastic process is defined through the control policy which is then selected in order to optimize the objective function. This is a very general model for dynamic optimization in discrete-time, which also goes by the name of stochastic dynamic programming. For references, the interested reader may consult the following books 41, 43, 56, 57, 59, 60, 61, 62, 66, 65, 68 and the references therein (this list of references is, of course, not exhaustive).

Continuous-time models.

Most of the continuous-time stochastic processes consist of a combination of the following three different ingredients: stochastic jumps, diffusion and deterministic motions. In this project, we will focus on non-diffusive models, in other words, stochastic models for which the randomness appears only at fixed or random times, i.e. those combining deterministic motions and random jumps. These stochastic processes are the so-called piecewise deterministic Markov processes (PDMPs) 42, 44, 45, 58, 63, 64, 67. This family of models plays a central role in applied probability because it forms the bulk of models in many research fields such as, e.g. operational research, management science and economy and covers an enormous variety of applications.

These models can be framed in several different forms of generality, depending on their mathematical properties such as the type of performance criterion, full or incomplete state information, with or without constraints, adaptative or not, but more importantly, the nature of the boundary of the state space, the type of dynamic between two jumps and on the number of decision-makers. These last three characteristics make the analysis of the controlled process much more involved.

Part of this project will cover both theoretical and numerical aspects of stochastic optimal control. It is clear that stochastic problems and control games have been extensively studied in the literature. Nevertheless, important challenges remain to be addressed. From the theoretical side, there are still many technical issues that are, for the moment, still unanswered or at most have received partial answers. This is precisely what makes them difficult and requires either the creative transposition of pre-existing methodologies or the development of new approaches. It is interesting to note that one of the feature of these theoretical problems is that they are closely related to practical issues. Solving such problems not only gives rise to challenging mathematical questions, but also allow a better insight into the structure and properties of real practical problems. Theory for applications will be for us the thrust that will guide us in this project. From the numerical perspective, solving a stochastic decision model remains a critical issue. Indeed, except for very few specific models, the determination of an optimal policy and the associated value function is an extremely difficult problem to tackle. The development of computational and numerical methods to get quasi-optimal solutions is, therefore, of crucial importance to demonstrate the practical interest of stochastic decision model as a powerful modeling tool. During the International Conference on Dynamic Programming and Its Applications held at the University of British Columbia, Canada in April 1977, Karl Hinderer, a pioneer in the field of stochastic dynamic programming emphasized that "whether or not our field will have a lasting impact on science beyond academic circles depends heavily on the success of implemented applications". We believe that this statement is still in force some forty years later.

The objective of this project is to address these important challenges. They are mainly related to models with general state/action spaces and with continuous time variables covering a large field of applications. Here is a list of topics we would like to study: games, constrained control problems, non additive types of criteria, numerical and computational challenges, analysis of partially observed/known stochastic decision processes. This list is not necessarily exhaustive and may of course evolve over time.

Our research agenda on optimal stochastic control is developed around the applied mathematical axis as well as the numerical perspective, including concrete industrial transfers with a special focus on Naval Group. Our mid-term objectives will focus on the following themes described above: properties of control policies in continuous-time control problems, non additive types of criteria, numerical and computational challenges. Our long-term objectives will focus on the analysis of partially observed/known stochastic control problems, constrained control problems and games.

Project-team positioning:

There exists a large national/international community working on PDMPs and MDPs both on the theoretical, numerical and practical aspects. One may cite A. Almudevar (University of Rochester, USA), E. Altman (INRIA Team NEO, France), K. Avrachenkov (INRIA Team NEO, France), N. Bauerle (Karlsruhe University, Germany), D. Bertsekas (Massachusetts Institute of Technology, USA), O. Costa (Sao Paulo University, Brazil), M. Davis (Imperial College London, England), E. Feinberg (Stony Brook University, USA), D. Goreac (Université Paris-Est Marne-la-Vallée, France), X. Guo (Zhongshan University, China), O. Hernandez-Lerma (National Polytechnic Institute, Mexico), S. Marcus (University of Maryland, USA), T. Prieto-Rumeau (Facultad de Ciencias, UNED, Spain), A. Piunovskiy (University of Liverpool, England), U. Rieder (Universität Ulm, Germany), J. Tsitsiklis (Massachusetts Institute of Technology, USA), B. Van Roy (Stanford University, USA), O. Vega-Amaya (Universidad de Sonora, Mexico), Y. Zhang (University of Liverpool, England) to name just a few. Many of the colleagues cited above are at the head of research groups which have not been described in detail due to space limitation and so, this list is far from being exhaustive.

To some extent, our team is in competition wit the colleagues and teams mentioned above. We emphasize that there exists a long standing collaboration between our group and O. Costa (Sao Paulo University, Brazil) since 1998. In the last 10 years, we have established very fruitful collaborations with T. Prieto-Rumeau (Facultad de Ciencias, UNED, Spain) and A. Piunovskiy (University of Liverpool, England).

Inside INRIA, the team NEO and in particular E. Altman and K. Avrachenkov work on discrete-time MDPs but they are mainly focused on the case of countable (finite) state/action spaces MDPs. From this point of view, our results on this theme may appear complementary to theirs.

6.1.1 Multivariate Analysis of Mixed Data: The R Package PCAmixdata

Mixed data type arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends standard multivariate analysis methods to incorporate this type of data. The key techniques included in the package are PCAmix (PCA of a mixture of numerical and categorical variables), PCArot (rotation in PCAmix) and MFAmix (multiple factor analysis with mixed data within a dataset). In this paper 11 a synthetic presentation of the three algorithms will be provided and the three main procedures will be illustrated on real data composed of four datasets caracterizing conditions of life of cities of Gironde, a south-west region of France.

Participants: Marie Chavent (ASTRAL), Vanessa Kuentz-Simonet, Amaury Labenne, Jérôme Saracco (ASTRAL).

6.1.2 Advanced topics in Sliced Inverse Regression

Since its introduction in the early 90’s, the Sliced Inverse Regression (SIR) methodology has evolved adapting to increasingly complex data sets in contexts combining linear dimension reduction with non linear regression. The assumption of dependence of the response variable with respect to only a few linear combinations of the covariates makes it appealing for many computational and real data application aspects. This work 16 proposes an overview of the most active research directions in SIR modeling from multivariate regression models to regularization and variable selection.

Participants: Stéphane Girard, Hadrien Lorenzo (ASTRAL), Jérôme Saracco (ASTRAL).

6.2.1 On the equivalence of the integral and differential Bellman equations in impulse control problems

When solving optimal impulse control problems, one can use the dynamic programming approach in two different ways: at each time moment, one can make the decision whether to apply a particular type of impulse, leading to the instantaneous change of the state, or apply no impulses at all; or, otherwise, one can plan an impulse after a certain interval, so that the length of that interval is to be optimised along with the type of that impulse. The first method leads to the differential Bellman equation, while the second method leads to the integral Bellman equation. In this paper 13 we prove the equivalence of those Bellman equations in many specific models. Those include abstract dynamical systems, controlled ordinary differential equations, piece-wise deterministic Markov processes and continuous-time Markov decision processes.

Participants: François Dufour (ASTRAL), Alexei Piunovskiy, Alexander Plakhov.

6.2.2 Maximizing the probability of visiting a set infinitely often for a countable state space Markov decision process

In 14, we consider a Markov decision process with countable state space and Borel action space. We are interested in maximizing the probability that the controlled Markov chain visits some subset of the state space infinitely often. We provide sufficient conditions, based on continuity and compactness requirements, together with a stability condition on a parametrized family of auxiliary control models, which imply the existence of an optimal policy that is deterministic and stationary. We compare our hypotheses with those existing in the literature.

Participants: François Dufour (ASTRAL), Tomas Prieto-Rumeau.

6.2.3 Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games

In 14, we consider a nonzero-sum Markov game on an abstract measurable state space with compact metric action spaces. The goal of each player is to maximize his respective discounted payoff function under the condition that some constraints on a discounted payoff are satisfied. We are interested in the existence of a Nash or noncooperative equilibrium. Under suitable conditions, which include absolute continuity of the transitions with respect to some reference probability measure, additivity of the payoffs and the transition probabilities (ARAT condition), and continuity in action of the payoff functions and the density function of the transitions of the system, we establish the existence of a constrained stationary Markov Nash equilibrium, that is, the existence of stationary Markov strategies for each of the players yielding an optimal profile within the class of all history-dependent profiles.

Participants: François Dufour (ASTRAL), Tomas Prieto-Rumeau.

6.2.4 Optimal Control of Piecewise Deterministic Markov Processes

In this Book's chapter 33 we study the infinite-horizon continuous-time optimal control problem of piece- wise deterministic Markov processes (PDMPs) with the control acting continuously on the jump intensity λ and on the transition measure Q of the process. Two optimality criteria are considered, the discounted cost case and the long run average cost case. We provide conditions for the existence of a solution to an integro-differential optimality equality, the so called Hamilton-Jacobi-Bellman (HJB) equation, for the discounted cost case, and a solution to an HJB inequality for the long run average cost case, as well as conditions for the existence of a deterministic stationary optimal policy. From the results for the discounted cost case and under some continuity and compactness hypothesis on the parameters and non-explosive assumptions for the process, we derive the conditions for the long run average cost case by employing the so-called vanishing discount approach.

Participants: Oswaldo Do Valle Costa, François Dufour (ASTRAL).

6.3.1 Log-normalization constant estimation using the ensemble Kalman–Bucy filter with application to high-dimensional models

In this article 12, we consider the estimation of the log-normalization constant associated to a class of continuous-time filtering models. In particular, we consider ensemble Kalman-Bucy filter based estimates based upon several nonlinear Kalman-Bucy diffusions. Based upon new conditional bias results for the mean of the afore-mentioned methods, we analyze the empirical log-scale normalization constants in terms of their Ln-errors and conditional bias. Finally, we use these results for online static parameter estimation for above filtering models and implement the methodology for both linear and nonlinear models.

Participants: Dan Crisan, Pierre del Moral (ASTRAL), Ajay Jasra, Hamza Ruzayqat.

6.3.2 Asymptotic moments of spatial branching processes

In this paper 17, it is assumed that $X=(X_t,t\ge 0)$ is either a superprocess or a branching Markov process on a general space E, with non-local branching mechanism and probabilities $P_{{\delta }_x}$ , when issued from a unit mass at $x\in E$. For a general setting in which the first moment semigroup of $X$ displays a Perron-Frobenius type behaviour, we show that for $k\ge 2$ and any positive bounded measurable function $f$ on $E$, ${lim}_{t\to \infty }g\left(t\right)E_{{\delta }_x}\left[{(f,X_t)}^k\right]=C_k(x,f)$ where the constant $C_k(x,f)$ can be identified in terms of the principal right eigenfunction and left eigen-measure and $g\left(t\right)$ is an appropriate determinisitic normalisation, which can be identified explicitly as either polynomial in $t$ or exponential in $t$, depending on whether $X$ is a critical, supercritical or subcritical process. The method we employ is extremely robust and we are able to extract similarly precise results that additionally give us the moment growth with time of ${\int }_0^t(g,X_t)ds$, for bounded measurable $g$ on $E$.

Authors: Isaac Gonzalez, Emma Horton (ASTRAL), Andreas E Kyprianou

6.3.3 Yaglom limit for critical nonlocal branching markov processes

In 19, we consider the classical Yaglom limit theorem for the Neutron Branching Process (NBP) in the setting that the mean semigroup is critical, i.e. its leading eigenvalue is zero. We show that the law of the process conditioned on survival is asymptotically equivalent to an exponential distribution. As part of the proof, we also show that the probability of survival decays inversely proportionally to time. Although Yaglom limit theorems have recently been handled in the setting of spatial branching processes and superprocesses, as well as in the setting of isotropic homogeneous Neutron Branching Processes, our approach and the main novelty of this work is based around a precise result for the scaled asymptotics for the k-th martingale moments of the NBP (rather than the Yaglom limit itself). Our proof of the asymptotic martingale moments turns out to offer a general approach to asymptotic martingale moments of critical branching Markov processes with a non-local branching mechanism. Indeed this is the context in which we give both our moment proofs and the Yaglom limit.

Authors: Simon C Harris, Emma Horton (ASTRAL), Andreas E Kyprianou, Minmin Wang.

6.3.4 Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes

Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article 20 , we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.

Participants: Emma Horton (ASTRAL), A. R. Watson.

6.3.5 A note on Riccati matrix difference equations

Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article 21 we provide a self-contained study of discrete time Riccati matrix difference equations. In particular, we provide a novel Riccati semigroup duality formula and a new Floquet-type representation for these equations. Due to the aperiodicity of the underlying flow of the solution matrix, conventional Floquet theory does not apply in this setting and thus further analysis is required. We illustrate the impact of these formulae with an explicit description of the solution of time-varying Riccati difference equations and its fundamental-type solution in terms of the fixed point of the equation and an invertible linear matrix map, as well as uniform upper and lower bounds on the Riccati maps. These are the first results of this type for time varying Riccati matrix difference equations.

Participants: Pierre Del Moral (ASTRAL), Emma Horton (ASTRAL).

6.3.6 A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters

Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type particle filters (a.k.a. sequential Monte Carlo), this ensemble-type methodology can also be interpreted as mean-field particle approximations of the Kalman-Bucy filtering equation. In contrast with conventional mean-field type interacting particle methods equipped with a globally Lipschitz interacting drift-type function, Ensemble Kalman filters depend on a nonlinear and quadratic-type interaction function defined in terms of the sample covariance of the particles. Most of the literature in applied mathematics and computer science on these sophisticated interacting particle methods amounts to designing different classes of useable observer-type particle methods. These methods are based on a variety of inconsistent but judicious ensemble auxiliary transformations or include additional inflation/localisationtype algorithmic innovations, in order to avoid the inherent time-degeneracy of an insufficient particle ensemble size when solving a filtering problem with an unstable signal. To the best of our knowledge, the first and the only rigorous mathematical analysis of these sophisticated discrete generation particle filters is developed in the pioneering articles by Le Gland-Monbet-Tran and by Mandel-Cobb-Beezley, which were published in the early 2010s. Nevertheless, besides the fact that these studies prove the asymptotic consistency of the Ensemble Kalman filter, they provide exceedingly pessimistic meanerror estimates that grow exponentially fast with respect to the time horizon, even for linear Gaussian filtering problems with stable one dimensional signals. In the present article 22 we develop a novel self-contained and complete stochastic perturbation analysis of the fluctuations, the stability, and the long-time performance of these discrete generation ensemble Kalman particle filters, including time-uniform and non-asymptotic mean-error estimates that apply to possibly unstable signals. To the best of our knowledge, these are the first results of this type in the literature on discrete generation particle filters, including the class of genetic-type particle filters and discrete generation ensemble Kalman filters. The stochastic Riccati difference equations considered in this work are also of interest in their own right, as a prototype of a new class of stochastic rational difference equation.

Participants: Pierre Del Moral (ASTRAL), Emma Horton (ASTRAL).

6.3.7 On the Stability of Positive Semigroups

In 23, the stability and contraction properties of positive integral semigroups on locally compact Polish spaces are investigated. We provide a novel analysis based on an extension of V-norm, Dobrushin-type, contraction techniques on functionally weighted Banach spaces for Markov operators. These are applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. Under mild regularity conditions, the Lipschitz-type contraction analysis presented in this article simplifies and extends several exponential estimates developed in the literature. The spectraltype theorems that we develop can also be seen as an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to time-varying positive semigroups. We review and illustrate in detail the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and advanced signal processing.

Participants: Pierre Del Moral (ASTRAL), Emma Horton (ASTRAL), Ajay Jasra.

6.3.8 A Review of Neural Network-Based Emulation of Guitar Amplifiers

In 24, Review of Neural Network-Based Emulation of Guitar Amplifiers is proposed. Vacuum tube amplifiers present sonic characteristics frequently coveted by musicians, that are often due to the distinct nonlinearities of their circuits, and accurately modelling such effects can be a challenging task. A recent rise in machine learning methods has lead to the ubiquity of neural networks in all fields of study including virtual analog modelling. This has lead to the appearance of a variety of architectures tailored to this task. This work aims to provide an overview of the current state of the research in neural emulation of analog distortion circuits by first presenting preceding methods in the field and then focusing on a complete review of the deep learning landscape that has appeared in recent years, detailing each subclass of available architectures. This is done in order to bring to light future possible avenues of work in this field.

Participants: Tara Vanhatalo (ASTRAL), Pierrick Legrand (ASTRAL), Myriam Desainte-Catherine, Pierre Hanna, Antoine Brusco, Guillaume Pille, Yann Bayle.

Naval Group

Participants: Pierre Del Moral, François Dufour, Alexandre Genadot, Emma Horton, Dann Laneuville, Olivier Marceau, Adrien Nègre, Raymond Zhang.

Thales AVS

Participants: Bastien Berthelot, Pierrick Legrand.

The collaboration is centered around some contributions to the estimation of the Hurst coefficient and his application on biosignals in the domain of crew monitoring.

Case Law Analytics

Participants: Pierrick Legrand.

Pierrick Legrand is a consultant for the startup Case Law Analytics. The object of the consulting is confidential.

Sartorius

Participants: Hadrien Lorenzo, Jérôme Saracco.

The team is currently initiating a 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 and Services. The current work concerns the development of a PLS (Partial Least Squares) inspired method in the context of multiblock of covariates (corresponding to different technologies and/or different sampling, statistical natures...) and high dimensional datasets (with the sample size n much smaller than the number of variables in the different blocks). The proposed method, called ddsPLS for data-driven sparse PLS, allows variable selection in the X and in the Y parts thanks to interpretable parameters associate with the soft-thresolding of the empirical correlation matrices (between the X's blocks and the Y block) decomposed in SVD (Singular Values Decomposition) ways. In addition a methodology to handle specific missing values (i.e. missing samples in some covariate blocks) is also under investigation.

Safran Aircraft Engines

Participants: Marie Chavent, Jérôme Lacaille, Alex Mourer, Madalina Olteanou.

The collaboration is centered around an applied mathematics thesis defining a formalism and a methodology for processing and interpretation by the importance of variables (from measurements and calculated indicators) in the case of unsupervised problems. This methodology is accompanied by code programming and a demonstration on an example data set from Safran Aircraft Engines.

Orosys

Participants: Tara Vanhatalo, Pierrick Legrand.

Within the framework of Tara Vanhatalo’s Cifre PhD thesis on the stochastic modelingof guitar amplifiers, a strong collaboration was established between the company Orosys and the ASTRAL team.

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

8.2.1 Visits of international scientists

8.2.2 Visits to international teams

8.3.1 Other european programs/initiatives

PHC Alliance 2022/23 E. Horton and Dr. Ellen Powell (University of Durham) obtained funding for bilateral mobility to work on applications of branching processes to the nuclear industry.

PHC FASIC Chercheur 2022 E. Horton and Dr. Sophie Hautphenne (University of Melbourne) obtained funding to work on parameter estimation of subcritical branching processes that arise in ecology.

Project PID2021-122442NB-I00 F. Dufour. "Analysis and control of deterministic, stochastic, and game theoretical dynamical systems" from 01/09/2022 to 31/08/2025. Ministry of Science and Innovation, Spain.

Naval Group

Astral is a joint INRIA team project with Naval Group. The topic of this collaboration is described in section 4.1.

QuAMProcs of the program Project Blanc of the ANR

The mathematical analysis of metastable processes started 75 years ago with the seminal works of Kramers on Fokker-Planck equation. Although the original motivation of Kramers was to « elucidate some points in the theory of the velocity of chemical reactions », it turns out that Kramers’ law is observed to hold in many scientific fields: molecular biology (molecular dynamics), economics (modelization of financial bubbles), climate modeling, etc. Moreover, several widely used efficient numerical methods are justified by the mathematical description of this phenomenon.

Recently, the theory has witnessed some spectacular progress thanks to the insight of new tools coming from Spectral and Partial Differential Equations theory.

Semiclassical methods together with spectral analysis of Witten Laplacian gave very precise results on reversible processes. From a theoretical point of view, the semiclassical approach allowed to prove a complete asymptotic expansion of the small eigen values of Witten Laplacian in various situations (global problems, boundary problems, degenerate diffusions, etc.). The interest in the analysis of boundary problems was rejuvenated by recent works establishing links between the Dirichlet problem on a bounded domain and the analysis of exit event of the domain. These results open numerous perspectives of applications. Recent progress also occurred on the analysis of irreversible processes (e.g. on overdamped Langevin equation in irreversible context or full (inertial) Langevin equation).

The above progresses pave the way for several research tracks motivating our project: overdamped Langevin equations in degenerate situations, general boundary problems in reversible and irreversible case, non-local problems, etc.

Mission pour les initiatives transverses et interdisciplinaires, Défi Modélisation du Vivant, projet MISGIVING

The aim of MISGIVING (MathematIcal Secrets penGuins dIVING) is to use mathematical models to understand the complexity of the multiscale decision process conditioning not only the optimal duration of a dive but also the diving behaviour of a penguin inside a bout. A bout is a sequence of succesive dives where the penguin is chasing prey. The interplay between the chasing period (dives) and the resting period due to the physiological cost of a dive (the time spent at the surface) requires some kind of optimization.

9.1.1 Scientific events: organisation

9.1.2 Scientific events: selection

9.1.3 Journal

9.1.4 Invited talks

Emma Horton

• Probability seminar, KTH, Sweden, March 2022.
• Workshop: Pólya urns, stochastic approximation and quasi-stationary distributions: new developments, University of Bath, UK, April 2022.
• Workshop: Branching systems, reaction-diffusion equations and population models, Université de Montréal, Canada, May 2022.
• Probability seminar, University of Durham, UK, September 2022.
• Auckland Probability Workshop on Branching Processes, University of Auckland, New Zealand, November 2022.
• Asia-Pacific Seminar in Probability and Statistics, online seminar, November 2022.

9.1.5 Leadership within the scientific community

Pierrick Legrand is the president of the association Evolution Artificielle.

9.1.6 Scientific expertise

E. Horton is secretary of the RSS Applied Probability section committee.

J. Saracco is regularly an expert for the HCERES (expertise of French mathematics laboratories) and for the ANRT (expertise of CIFRE thesis applications).

P. Legrand is regularly an expert for the ANR program.

9.1.7 Research administration

$•$National responsibilities

J. Saracco is treasurer of the French Statistical Society (SFdS) and an elected member of its board.

J. Saracco is an elected member of the national council of universities in applied mathematics (CNU 26).

$•$Universities and schools

F. Dufour is an invited member of the scientific council of the Institute of Mathematics of Bordeaux.

F. Dufour is member of the council of ENSEIRB MATMECA - Bordeaux INP since 2022.

J. Saracco is an elected member of the Bordeaux INP Board of Studies.

J. Saracco is an elected member of the Board of ENSC Bordeaux INP.

J. Saracco is head of the research team "OptimAl" (mathematical optimisation, random and statistical models) of the Mathematical Institute of Bordeaux (UMR 5251 CNRS).

M. Chavent is a member of the council of the department Sciences de l’ingénierie et du numérique of Bordeaux University.

M. Chavent is an elected member of the scientific council of the Institute of Mathematics of Bordeaux (since 2022).

A. Génadot has been an elected member of the scientific council of the Institute of Mathematics of Bordeaux (2019-2022).

P. Legrand has been an elected member of the laboratory council of the Institute of Mathematics of Bordeaux (2019-2022).

P. Legrand is an elected member of the scientific council of the Institute of Mathematics of Bordeaux (2022-).

P. Legrand is the president of the consultative commission in section CNU 26 of the Institute of Mathematics of Bordeaux (2019-).

$•$Inria

M. Chavent is a member of the CDT (Commission for Technological Development) at Inria Bordeaux since september 2022.

M. Chavent was a member of the Inria Evaluation Committee (2015-2019).

P. Del Moral is a member of the "Bureau du Comité des Projets" of the INRIA Bordeaux-Sud Ouest Research Center, since 2018.

A. Génadot is a member of the CER of Inria Bordeaux.

P. Legrand is a member of the CUMI commission.

9.2.1 Teaching

• J. Saracco is the head of the engineering department of ENSC, Graduate School of Cognitics (applied cognitive science and technology) which is a Bordeaux INP engineering school.
• Marie Chavent is in charge of the first year of the MIASHS degree program at Université de Bordeaux.
• Alexandre Genadot is in charge of the first year of the MIASHS degree program at Université de Bordeaux.
• Pierrick Legrand is in charge of the mathematics program for the MIASHS degree at Université de Bordeaux.

• Licence : P. Legrand, Algèbre, 129h, L1, Université de Bordeaux, France.
• Licence : P. Legrand, Espaces Euclidiens, 46,5h, L2, Université de Bordeaux, France.
• Licence : P. Legrand, Informatique pour les mathématiques, 30h, L2, Université de Bordeaux, France.
• DU : P. Legrand, Evolution Artificielle, Big data, 8h, DU, Bordeaux INP, France.
• Engineer School: Signal processing, 54 hours, ENSC, Bordeaux, France.
• Master: Scientific courses, 10 hours, Université de Bordeaux, France.
• Licence : A. Genadot, Bases en Probabilités, 18h, L1, Université de Bordeaux, France.
• Licence : A. Genadot, Projet Professionnel de l'étudiant, 8h, L1, Université de Bordeaux, France.
• Licence : A. Genadot, Probabilité, 30h, L2, Université de Bordeaux, France.
• Licence : A. Genadot, Techniques d'Enquêtes, 10h, L2, Université de Bordeaux, France.
• Licence : A. Genadot, Modélisation Statistiques, 16.5h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, Préparation Stage, 15h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, TER, 5h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, Processus, 16.5h, L3, Université de Bordeaux, France.
• Licence : A. Genadot, Statistiques, 20h, L3, Bordeaux INP, France.
• Master : A. Genadot, Savoirs Mathématiques, 81h, M1, Université de Bordeaux et ESPE, France.
• Master : A. Genadot, Martingales, 29h, M1, Université de Bordeaux, France.
• Licence : F. Dufour, Probabilités et statistiques, 70h, first year of école ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Master : F. Dufour, Approche probabiliste et méthode de Monte Carlo, 24h, third year of école ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : J. Saracco, Probabilités et Statistique, 27h, first year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• Licence : J. Saracco, Statistique inférentielle et Analyse des données, 45h, first year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• Licence : J. Saracco, Statistique pour l’ingénieur, 16h, first year of Graduate Schools of Engineering ENSPIMA-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• Master : J. Saracco, Modélisation statistique, 81h, second year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.
• DU : J. Saracco, Statistique et Big data, 45h, DU BDSI (Big data et statistique pour l'ingénieur), Bordeaux INP, France.
• Licence : M. Chavent, Statistique Inférentielle, 18h, L2, Université de Bordeaux, France
• Licence : M. Chavent, Techniques d'Enquêtes, 10h, L2, Université de Bordeaux, France
• Master : M. Chavent, DataMining, 43h, M2, Université de Bordeaux
• Master : M. Chavent, Machine Learning, 58h, Université de Bordeaux,
• DU: M. Chavent, Apprentissage, 12h, DU BDSI, Bordeaux INP, France
• Licence : E. Horton, Probabilités et Statistiques, 32h, ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : E. Horton, Probabilités, 22h, ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : E. Horton, Probabilités, 24h, ENSEIRB-MATMECA, Institut Polytechnique de Bordeaux, France.
• Licence : E. Horton, 30h, Statistique inférentielle et Analyse des données, first year of Graduate Schools of Engineering ENSC-Bordeaux INP, Institut Polytechnique de Bordeaux, France.

9.2.2 Supervision

• E. Horton co-supervised a summer project with Prof. Alexander Cox (University of Bath) on sensitivity analysis of branching processes.

9.2.3 Juries

Pierrick Legrand was member of the jury of the Phd of Yann Cabanes.

International journals

• 11 articleM.Marie Chavent, V.Vanessa Kuentz-Simonet, A.Amaury Labenne and J.Jérôme Saracco. Multivariate Analysis of Mixed Data: The R Package PCAmixdata.Electronic Journal of Applied Statistical Analysis2022
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• 12 articleD.Dan Crisan, P.Pierre del Moral, A.Ajay Jasra and H.Hamza Ruzayqat. Log-normalization constant estimation using the ensemble Kalman–Bucy filter with application to high-dimensional models.Advances in Applied Probability544December 2022, 1139-1163
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• 13 articleF.François Dufour, A.Alexey Piunovskiy and A.Alexander Plakhov. On the equivalence of the integral and differential Bellman equations in impulse control problems.International Journal of Control, Automation and Systems2022
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• 14 articleF.François Dufour and T.Tomás Prieto-Rumeau. Maximizing the probability of visiting a set infinitely often for a countable state space Markov decision process.Journal of Mathematical Analysis and Applications2022
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• 15 articleF.François Dufour and T.Tomás Prieto-Rumeau. Stationary Markov Nash equilibria for nonzero-sum constrained ARAT Markov games.SIAM Journal on Control and Optimization2022
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• 16 articleS.Stéphane Girard, H.Hadrien Lorenzo and J.Jérôme Saracco. Advanced topics in Sliced Inverse Regression.Journal of Multivariate Analysis1882022, 104852
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• 17 articleI.Isaac Gonzalez, E.Emma Horton and A. E.Andreas E Kyprianou. Asymptotic moments of spatial branching processes.Probability Theory and Related Fields184April 2022, 805-858
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• 18 articleE.Eric Grivel, J.Jeremie Soetens, G.Gaetan Colin and P.Pierrick Legrand. Combining the global trends of DFA or CDFA of different orders.Digital Signal Processing2023
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• 19 articleS. C.Simon C Harris, E.Emma Horton, A. E.Andreas E Kyprianou and M.Minmin Wang. Yaglom limit for critical nonlocal branching markov processes.Annals of Probability506November 2022, 2373–2408
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• 20 articleE.Emma Horton and A. R.Alexander R Watson. Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes.ALEA : Latin American Journal of Probability and Mathematical Statistics2022
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• 21 articleP.Pierre del Moral and E.Emma Horton. A note on Riccati matrix difference equations.SIAM Journal on Control and Optimization2022
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• 22 articleP.Pierre del Moral and E.Emma Horton. A theoretical analysis of one-dimensional discrete generation ensemble Kalman particle filters.Annals of Applied Probability2022
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• 23 articleP.Pierre del Moral, E.Emma Horton and A.Ajay Jasra. On the Stability of Positive Semigroups.Annals of Applied Probability2022
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• 24 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, 5894
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International peer-reviewed conferences

• 25 inproceedingsT.Tara Vanhatalo, P.Pierrick Legrand, M.Myriam Desainte-Catherine, P.Pierre Hanna, A.Antoine Brusco, G.Guillaume Pille and Y.Yann Bayle. Neural Network-based Virtual Analog Modelling.Artificial Evolution 2022Exeter, United KingdomOctober 2022
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Conferences without proceedings

• 26 inproceedingsM.Marie Chavent, J.Jérôme Lacaille, A.Alex Mourer and M.Madalina Olteanu. Sparse and group-sparse clustering for mixed data An illustration of the vimpclust package.JDS 2022 - 53èmes Journées de Statistique de la Société Française de Statistique (SFdS)Lyon, FranceJune 2022
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• 27 inproceedingsH.Hadrien Lorenzo, J.Jérôme Saracco and O.Olivier Cloarec. Imputation for supervised learning problems in high dimension.24th International Conference on Computational Statistics (COMPSTAT 2022), 23-26 August 2022, Bologna (Italy)Bologna, Italy2022
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• 28 inproceedingsJ.Jérôme Saracco, H.Hadrien Lorenzo and O.Olivier Cloarec. Koh-Lanta, missing data imputation in supervised context.23ème Congrès de ChimiométrieBrest, FranceJune 2022
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• 29 inproceedingsJ.Jérôme Saracco and H.Hadrien Lorenzo. Détection d’individus atypiques en régression SIR.Dataquitaine 2022 (IA, Recherche Opérationnelle & Data Science), Février 2022, Bordeaux, France.Bordeaux, FranceFebruary 2022
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• 30 inproceedingsJ.Jérôme Saracco, H.Hadrien Lorenzo and S.Stéphane Girard. Advanced topics in Sliced Inverse Regression V2.JMVA 2022 - 50th Anniversary JubileeVirtual Meeting, United StatesApril 2022
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• 31 inproceedingsJ.Jérôme Saracco and H.Hadrien Lorenzo. Sélection de variables en régression SIR par seuillage doux ou seuillage dur de la matrice d’intérêt.Journées de Statistique 2022 – Société Française de Statistique, Juin 2022, Lyon, France.Lyon, FranceJune 2022
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Scientific books

• 32 bookM.Marie Chavent, M.Madalina Olteanu, M.Marie Cottrell, J.Jérôme Lacaille and A.Alex Mourer. Sparse Weighted K-Means for Groups of Mixed-Type Variables.533Lecture Notes in Networks and SystemsSpringer International Publishing2022
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Scientific book chapters

• 33 inbookO.O. Costa and F.François Dufour. Optimal Control of Piecewise Deterministic Markov Processes.Stochastic Analysis, Filtering, and Stochastic OptimizationSpringer International PublishingApril 2022, 53-77
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Doctoral dissertations and habilitation theses

• 34 thesisA.Alex Mourer. Variable selection and importance in statistical learning: Applications to highly correlated aircraft engine test data.Paris 1 - Panthéon-SorbonneApril 2022
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Reports & preprints

• 35 miscA.Ashot Aleksian, P.Pierre del Moral, A.Aline Kurtzmann and J.Julian Tugaut. On the exit-problem for self-interacting diffusions V2.November 2022
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• 36 miscA. M.Alexander M.G Cox, E.E Horton and D.D Villemonais. Binary branching processes with Moran type interactions.July 2022
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• 37 miscF.François Dufour and O. L.Oswaldo Luiz Do Valle Costa. Adaptive Discounted Control for Piecewise Deterministic Markov Processes.November 2022
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• 38 miscF.François Dufour and T.Tomás Prieto-Rumeau. Maximizing the probability of visiting a set infinitely often for a Markov decision process.November 2022
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• 39 miscA.Alexandre Genadot. Averaging for slow-fast piecewise deterministic Markov processes with an attractive boundary.January 2022
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• 40 miscS. C.Simon C Harris, E.Emma Horton, A. E.Andreas E Kyprianou and E.Ellen Powell. Many-to-few for non-local branching Markov process.November 2022
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Cited publications

• 41 bookE.E. Altman. Constrained Markov decision processes.Stochastic ModelingChapman & Hall/CRC, Boca Raton, FL1999, xii+242
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• 42 bookN.Nicole Bäuerle and U.Ulrich Rieder. Markov decision processes with applications to finance.UniversitextSpringer, Heidelberg2011, xvi+388URL: https://doi.org/10.1007/978-3-642-18324-9
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• 43 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+323
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• 44 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/10.1007/978-1-4614-6983-4
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• 45 bookM. H.M. H. A. Davis. Markov models and optimization.49Monographs on Statistics and Applied ProbabilityChapman & Hall, London1993, xiv+295URL: http://dx.doi.org/10.1007/978-1-4899-4483-2
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• 46 articleP.P Del Moral, A.A Doucet and J.Jasra A. Sequential Monte Carlo samplers.6832006, 411--436
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• 47 bookP.P Del Moral. Genealogical and interacting particle systems with applications.Probability and its ApplicationsSpringer-Verlag, New York2004, 573
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• 48 articleP.P Del Moral and A.A Guionnet. On the stability of Measure Valued Processes with Applications to filtering.1999, 429--434
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• 49 articleP.P Del Moral and A.A Guionnet. On the stability of interacting processes with applications to filtering and genetic algorithms.3722001, 155-194
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• 50 articleP.P Del Moral, J.J Jacod and P.P Protter. The Monte-Carlo method for filtering with discrete-time observations.12032001, 346--368
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• 51 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/9781466504059
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• 52 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--145
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• 53 articleP.Pierre Del Moral. Non Linear Filtering: Interacting Particle Solution.241996, 555--580
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• 54 bookP.P Del Moral and S.S Penev. Stochastic Processes: From Applications to Theory.Chapman and Hall/CRC2017
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• 55 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--850
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• 56 bookE.E.B. Dynkin and A.A.A. Yushkevich. Controlled Markov processes.235Grundlehren der Mathematischen WissenschaftenBerlinSpringer-Verlag1979, xvii+289
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• 57 bookJ.J. Filar and K.K. Vrieze. Competitive Markov decision processes.New YorkSpringer-Verlag1997, xii+393
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• 58 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/10.1007/978-3-642-02547-1
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• 59 bookO.O. Hernández-Lerma. Adaptive Markov control processes.79Applied Mathematical SciencesNew YorkSpringer-Verlag1989, xiv+148
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• 60 bookO.Onésimo Hernández-Lerma and J.-B.Jean-Bernard Lasserre. Discrete-time Markov control processes: Basic optimality criteria.30Applications of MathematicsNew YorkSpringer-Verlag1996, xiv+216
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• 61 bookO.Onésimo Hernández-Lerma and J.-B.Jean-Bernard Lasserre. Further topics on discrete-time Markov control processes.42Applications of MathematicsNew YorkSpringer-Verlag1999, xiv+276
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• 62 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+160
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• 63 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.9.1.112
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• 64 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.10.1.160
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• 65 bookA. B.A. B. Piunovskiy. Examples in Markov decision processes.2Imperial College Press Optimization SeriesImperial College Press, London2013, xiv+293
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• 66 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/10.1007/978-94-011-5508-3
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• 67 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/p829
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• 68 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+649
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• 69 articleV.V.N. kolokoltsov. Nonlinear Markov Processes and Kinetic Equations.2010
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