Publications

2024

• Optimal control methods for systemic risk
  
  • Bassou Leila
  , 2024. This thesis is dedicated to the study of cross-holding game's Nash equilibria in various frameworks. The related model, which was introduced by M-F. Djete & N. Touzi in 2020, aims to capture the interdependence between differenteconomic agents by taking into account, on the one hand, the mutual holding of sharesbetween the entities, and on the other hand, their incomes that can be correlated.- The first part is devoted to the finite population game within the framework of the exponential utility criterion. In the static and dynamic settings under gaussian Bachelier type dynamic, we completely characterize the Nash equilibria and their existence conditions.- The second part is dedicated to the one-period mean field game with common noise (the revenues are correlated), by considering the mean-variance criterion. The formulation of the problem reveals a No-arbitrage condition. In this framework, we characterized explicitly this condition, as well as the mean field equilibria.- In the third part, we extended the study of the mean-field game, with common noise, to the continuous time setting. Here, the problem reveals a weak notion of No-arbitrage condition. The characterization of this condition reduces the analysis of the mean field equilibria to the classical problem of optimal portfolio with random endowment.
• Enhanced wave transmission in random media with mirror symmetry
  
  • Borcea Liliana
  • Garnier Josselin
  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2024, 480 (2292). We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation, and we consider two setups, where the wave propagation is along a preferred direction: in a randomly layered medium and in a randomly perturbed waveguide. We use the asymptotic stochastic theory of wave propagation in random media to characterize the statistical moments of the frequency-dependent random transmission and reflection coefficients, which are scalar-valued in layered media and matrix-valued in waveguides. With these moments, we can quantify explicitly the enhancement of the net mean transmitted intensity, induced by wave interference near the barrier. (10.1098/rspa.2024.0073)
  DOI : 10.1098/rspa.2024.0073
• Mathematical Models for Personalized Interventional Radiology : Application to Cancer Treatment
  
  • Boeken Tom
  , 2024. The integration of computer vision into Image-Guided interventions has the potential to change our medical practice. This work lays some bricks for the future of autonomous interventions in our specific field regarding cancer patients, addressing key components necessary for its realization.We first explore the transformative impact of AI on the physical abilities of interventional radiologists. We emphasize the need to navigate technical and ethical challenges. Interdisciplinary collaboration and robust evaluation processes are highlighted as essential for the safe integration of AI into clinical practiceWe then propose an organ agnostic method for detecting focal anomalies on volumetric cross-sectional imaging. Leveraging the Large Diffeomorphic Deformation Metric Mapping (LDDMM) framework, this approach showcases enhanced object reconstruction and precise lesion localization. In the same framework, we propose a classifier, where patient selection presents unique challenges due to the complex benefice/risk ratios.To go beyond images, clinical data from tumor DNA analysis is integrated into a prospective study specifically conducted for this work. Generative Adversarial Networks (GAN) and Modelling Atlases Using the Markov Chain Monte Carlo - Stochastic Approximation Expectation-Maximization (MCMC-SAEM) Algorithms are used to predict patient trajectories. This approach enables the exploration of new trajectories, enhancing our understanding of disease progression and treatment response in relationship of circulating tumor DNA.Lastly, we explore advanced visualization techniques for in vivo and ex vivo 3D vasculature. We propose a planar representation of undescribed anatomy, offering a promising avenue for further exploration and understanding.Together, these sections offer solutions to parts of the realization of autonomous interventions in our field.
• Simulation of the impact of a high-velocity jet at high-temperature on a liquid surface with a two-temperature diffuse interface model
  
  • Haegeman Ward
  • Massot Marc
  • Le Touze Clément
  • Dupays Joël
  , 2024.
• Quantification post-hoc de l'incertitude prédictive : méthodes avec applications à la prévision des prix de l'électricité
  
  • Zaffran Margaux
  , 2024. The surge of more and more powerful statistical learning algorithms offers promising prospects for electricity prices forecasting. However, these methods provide ad hoc forecasts, with no indication of the degree of confidence to be placed in them. To ensure the safe deployment of these predictive models, it is crucial to quantify their predictive uncertainty. This PhD thesis focuses on developing predictive intervals for any underlying algorithm. While motivated by the electrical sector, the methods developed, based on Split Conformal Prediction (SCP), are generic: they can be applied in many sensitive fields.First, this thesis studies post-hoc predictive uncertainty quantification for time series. The first bottleneck to apply SCP in order to obtain guaranteed probabilistic electricity price forecasting in a post-hoc fashion is the highly non-stationary temporal aspect of electricity prices, breaking the exchangeability assumption. The first contribution proposes a parameter-free algorithm tailored for time series, which is based on theoretically analysing the efficiency of the existing Adaptive Conformal Inference method. The second contribution conducts an extensive application study on novel data set of recent turbulent French spot prices in 2020 and 2021.Another challenge are missing values (NAs). In a second part, this thesis analyzes the interplay between NAs and predictive uncertainty quantification. The third contribution highlights that NAs induce heteroskedasticity, leading to uneven coverage depending on which features are observed. Two algorithms recovering equalized coverage for any NAs under distributional assumptions on the missigness mechanism are designed. The forth contribution pushes forwards the theoretical analysis to understand precisely which distributional assumptions are unavoidable for theoretical informativeness. It also unifies the previously proposed algorithms into a general framework that demontrastes empirical robustness to violations of the supposed missingness distribution.
• Interpretable seasonal multisite hidden Markov model for stochastic rain generation in France
  
  • Gobet Emmanuel
  • Métivier David
  • Parey Sylvie
  Advances in Statistical Climatology, Meteorology and Oceanography, Copernicus Publications, 2024, 11 (2), pp.159–201. We present a lightweight stochastic weather generator (SWG) based on a multisite hidden Markov model (HMM) trained on a large area with French weather station data. Our model captures spatiotemporal precipitation patterns with a strong emphasis on seasonality and the accurate reproduction of dry and wet spell distributions. The hidden states serve as interpretable large-scale weather regimes, learned directly from the data without requiring exogenous inputs. Compared to existing approaches, it offers a robust balance between interpretability and performance, particularly for extremes. The model architecture enables seamless integration of additional weather variables. Finally, we demonstrate its application to future climate scenarios, highlighting how parameter evolution and extreme event distributions can be analyzed in a changing climate. (10.5194/ascmo-11-159-2025)
  DOI : 10.5194/ascmo-11-159-2025
• Feller's test for explosions of stochastic Volterra equations
  
  • Bondi Alessandro
  • Pulido Sergio
  , 2024. This paper provides a Feller’s test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of the processes and introduce memory features through a path- dependent drift. In contrast to the classical path-independent case, the sufficient condition derived in this study for a Volterra process to remain in the interior of an interval is generally more restrictive than the necessary condition. The results are illustrated with three specifications of the dynamics: the Volterra square-root diffusion, the Volterra Jacobi process and the Volterra power-type diffusion. For the Volterra square-root diffusion, also known as the Volterra CIR process, the paper presents a detailed discussion on the approximation of the singular fractional kernel with a sum of exponentials, a method commonly employed in the mathematical finance literature.
• Bridging Rayleigh-Jeans and Bose-Einstein condensation of a guided fluid of light with positive and negative temperatures
  
  • Zanaglia Lucas
  • Garnier Josselin
  • Rica Sergio
  • Kaiser Robin
  • Wabnitz Stefano
  • Michel Claire
  • Doya Valerie
  • Picozzi Antonio
  , 2024. We consider the free propagation geometry of a light beam (or fluid of light) in a multimode waveguide. As a result of the effective photon-photon interactions, the photon fluid thermalizes to an equilibrium state during its conservative propagation. In this configuration, Rayleigh-Jeans (RJ) thermalization and condensation of classical light waves have been recently observed experimentally in graded index multimode optical fibers characterized by a 2D parabolic trapping potential. As well-known, the properties of RJ condensation differ substantially from those of Bose-Einstein (BE) condensation: The condensate fraction decreases quadratically with the temperature for BE condensation, while it decreases linearly for RJ condensation. Furthermore, for quantum particles the heat capacity tends to zero at small temperatures, and it takes a constant value in the classical particle limit at high temperatures. This is in contrast with classical RJ waves, where the specific heat takes a constant value at small temperatures, and tends to vanish above the condensation transition in the normal (uncondensed) state. Here, we reconcile the thermodynamic properties of BE and RJ condensation: By introducing a frequency cut-off inherent to light propagation in a waveguide, we derive generalized expressions of the thermodynamic properties that include the RJ and BE limits as particular cases. We extend the approach to encompass negative temperatures. In contrast to positive temperatures, the specific heat does not display a singular behavior at negative temperatures, reflecting the non-critical nature of the transition to a macroscopic population of the highest energy level. Our work contributes to understanding the quantum-to-classical crossover in the equilibrium properties of light, within a versatile experimental platform based on nonlinear optical propagation in multimode waveguides.
• Boundary Hölder regularity for the fractional Laplacian over Reifenberg flat domains via ABP maximum principle
  
  • Prade Adriano
  , 2025. For $0
• Polygonal Faber-Krahn inequality: Local minimality via validated computing
  
  • Bogosel Beniamin
  • Bucur Dorin
  , 2024. The main result of the paper shows that the regular $n$-gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among $n$-gons having fixed area for $n \in \{5,6\}$. The eigenvalue is seen as a function of the coordinates of the vertices in $\Bbb R^{2n}$. Relying on fine regularity results of the first eigenfunction in a convex polygon, an explicit a priori estimate is given for the eigenvalues of the Hessian matrix associated to the discrete problem, whose coefficients involve the solutions of some Poisson equations with singular right hand sides. The a priori estimates, in conjunction with certified finite element approximations of these singular PDEs imply the local minimality for $n \in \{5,6\}$. All computations, including the finite element computations, are realized using interval arithmetic.
• Holistic characterization of an under-expanded high-enthalpy jet under uncertainty
  
  • Capriati Michele
  • Turchi Alessandro
  • Congedo Pietro Marco
  • Magin Thierry E.
  Physics of Fluids, American Institute of Physics, 2024, 36 (6). Elaborate methodologies have been developed to study the thermo-chemical response of materials in high-enthalpy flows. To reach the high magnitudes of heat flux encountered in some hypersonic applications, one can resort to supersonic jets. They involve several physical effects, such as detached shocks ahead of probes. Because of these features, characterizing supersonic flows is a challenging task, especially when one accounts for experimental and modeling uncertainties. Building on the development of stochastic approaches, we propose a holistic methodology to determine the quantities of interest in an optimal manner for an under-expanded high-enthalpy jet, using both experimental measurements and high-fidelity flow simulations. Given the high computational cost of the high-fidelity simulations needed to describe the flow, we built an adaptive/multi-fidelity surrogate model to replace the estimation of the costly computer solver. A Bayesian inference method then allowed for characterizing an experiment carried out in the von Karman Institute's Plasmatron facility, for which no robust methodology currently exists. We show that the reservoir pressure and temperature and the nitrogen catalytic recombination coefficient of the copper probes can be accurately determined from the available measurements. Contrarily, the test conditions do not allow us to estimate the oxygen catalytic recombination coefficient. Finally, the characterized uncertainties are propagated through the numerical solver, yielding an uncertainty-based high-fidelity representation of the hypersonic flow's structure variability. (10.1063/5.0203490)
  DOI : 10.1063/5.0203490
• Diffusion posterior sampling for simulation-based inference in tall data settings
  
  • Linhart Julia
  • Cardoso Gabriel Victorino
  • Gramfort Alexandre
  • Le Corff Sylvain
  • Coelho Rodrigues Pedro Luiz
  , 2024. Determining which parameters of a non-linear model best describe a set of experimental data is a fundamental problem in science and it has gained much traction lately with the rise of complex large-scale simulators. The likelihood of such models is typically intractable, which is why classical MCMC methods can not be used. Simulation-based inference (SBI) stands out in this context by only requiring a dataset of simulations to train deep generative models capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. The proposed method is built upon recent developments from the flourishing score-based diffusion literature and allows to estimate the tall data posterior distribution, while simply using information from a score network trained for a single context observation. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
• Artificial Neural Networks for UQ and calibration of one-dimensional arterial hemodynamics
  
  • Benmahdi Meryem
  • Le Maitre Olivier
  • Congedo Pietro Marco
  , 2024. We explore using Artificial Neural Networks (ANNs) for model parameter identification tasks in high-dimensional problems with multi-dimensional outputs. The calibration of these models involves learning hundreds of parameters from sparse and noisy observations and solving high-dimensional inverse problems. Firstly, we examine ANNs as surrogates of the forward mapping. When applied to a one-dimensional hemodynamics model of the human arterial system, ANNs are excellent surrogates of time-series outputs, with only a $3\%$ prediction error. We also discuss the trade-off between the architectures' complexity and the learning database's size. We utilize the pre-trained forward surrogates to solve the ill-posed inverse problem formulated as a likelihood maximum estimation (MLE). We also explore gradient-based and gradient-free non-linear optimization methods. Finally, we investigate ANNs as direct surrogates of the inverse mapping from observations to model parameters, with comparable parameter identification accuracy to MLE. We also emphasize the importance of restricting informative observations to form the inputs of the inverse ANN surrogate.
• On the use of bifurcation curves for system identification and model updating purposes
  
  • Mélot Adrien
  • Denimal Goy Enora
  • Renson Ludovic
  , 2024, pp.1-1. The ever-increasing demand for highly performant mechanical systems often leads them to exhibit nonlinear behaviours. Furthermore, in recent years, a significant amount of research was devoted to investigating how nonlinearities can be exploited for increased performance. In order to achieve better designs and to ensure the performance, safety and resilience of mechanical systems throughout their service life, it is of utmost importance to have access to nonlinear models with both qualitative and quantitative predictive capabilities. Due to potentially strong nonlinear effects, traditional system identification features based on linear modes often prove suboptimal. Nonlinear normal modes have emerged as a key feature for identifying and updating nonlinear models due to their capability of capturing the frequency/energy dependence of nonlinear systems. Nevertheless, several other nonlinear phenomena can be observed in practice. Amongst the salient features distinguishing nonlinear systems from their linear counterparts, bifurcations occupy a prominent position, as they act as local organizing centres for the system’s dynamics. Bifurcation curves define the limits of stability of nonlinear systems and regions of multi-stability. Consequently, they provide both quantitative and qualitative information on systems operating in strongly nonlinear regimes. In this work, we show that bifurcation curves can be utilized as features to carry out nonlinear system identification and model updating. Our methodology is based on minimizing the distance between experimental bifurcation curves evaluated through control-based continuation [1] and numerical ones computed with bifurcation tracking. A nonlinear energy harvester model is employed to demonstrate the methodology’s performance in identifying nonlinear models within strongly nonlinear regimes across a broad range of operating conditions.
• Numerical methods and relaxation techniques for diffuse interface models in high-velocity two-phase flow simulations
  
  • Haegeman Ward
  • Dupays Joël
  • Le Touze Clement
  • Massot Marc
  , 2024. Compressible multiphase flows are at the heart of a great number of engineering applications in several domains. Some examples include the aerospace industry, since many rocket propulsion systems rely on the injection of a liquid reactant into the combustion chamber and the efficiency of the combustion is directly related to the atomization process. Other applications include the civil nuclear industry safety analysis but also the naval industry for which underwater solid propulsion systems are of great interest. The design and optimization requirements of these systems lead to an increasing need for predictive numerical simulations. Diffuse interface models are widely used for these tasks as they provide a good trade-off between accuracy and robustness. We consider the class of Baer-Nunziato type of models, in which the most general one allows for full disequilibrium between the two-phases. Reduced order models are obtained by assuming some local equilibrium (velocity, pressure, temperature or chemical potential equilibrium). Among this hierarchy of models, the pressure and velocity equilibrium model of Kapila et al is of particular interest. It allows to recover the classical Wood sound velocity for two-phase mixtures while still allowing thermal disequilibrium which is paramount for many applications such as high-temperature jets impinging on liquid surfaces and for proper modelling of phase changes. Several strategies to solve this model rely on a 6-equation model endowed with stiff pressure relaxation terms. For cavitating flows, an accurate computation of the pressure equilibrium is particularly important to compute the mass transfer fluxes. The purpose of the present contribution is to study the assumptions on the thermodynamics of the two phases and its impact on the mathematical structure of the resulting system of PDEs (where potentially several relaxation processes are involved either relying on finite-rate or instantaneous relaxation source terms). We propose an analysis of the pressure relaxation process in terms of thermodynamically admissible paths and propose a robust numerical scheme, which preserves the set of admissible states of the system. The robustness and accuracy of the proposed numerical scheme involving convection and sources is then assessed on several challenging configurations including shock-interface interactions and cavitating flows, such as shock-droplet interaction or Richtmyer–Meshkov instability. (10.23967/eccomas.2024.071)
  DOI : 10.23967/eccomas.2024.071
• Sampling and Estimating the Set of Pareto Optimal Solutions in Stochastic Multi-Objective Optimization
  
  • Le Maitre Olivier
  • Congedo Pietro Marco
  • Jones Zachary
  , 2024. Including uncertainty sources in multi-objective optimization allows more robust design decisions at the cost of dealing with stochastic quantities of interest. The objectives are then classically defined as the expectations of random quantities of interest, and their estimation can be computationally expensive. Robbins-Monro-type algorithms are an attractive alternative in this context, allowing for the minimization of the objectives through noisy gradient updates. The stochastic multi-gradient algorithm (SMGDA)[1] extends the Robbins-Monro approach to the multi-objective case. However, a bias in the algorithm and the inherent noise in stochastic gradients cause the algorithm to converge to only a subset of the whole Pareto front. Our contribution builds on the stochastic multi-gradient algorithm to reliably estimate the whole Pareto front (objective space) and Pareto optimal points (design space). First, we reduce the bias of the stochastic multi-gradient calculation using an exponential smoothing technique. Second, we simultaneously remove the remaining bias and promote the exploration of the Pareto front by adding non-vanishing noise tangential to the front. We prove that this algorithm generates samples in a concentrated set containing the whole Pareto front. Finally, we estimate the set of Pareto optimal design points using only the sequence generated during optimization. We also provide bootstrapped confidence intervals using a nearest-neighbor model calibrated with a novel procedure based on the hypervolume metric. Our proposed method allows for the estimation of the whole of the Pareto front using significantly fewer evaluations of the random quantities of interest when compared to a direct sample-based estimation, which is valuable in the context of costly model evalua- tions. We illustrate the efficacy of our approach with numerical examples in increasing dimension and discuss how to apply the method to more complex problems.
• Mean adaptive mesh refinement for efficient CFD simulations with operating conditions variability
  
  • Dornier Hugo
  • Le Maitre Olivier
  • Congedo Pietro Marco
  • Bourasseau Sébastien
  • Salah El Din Itham
  • Marty Julien
  , 2024.
• Semiring systems arising from hyperrings
  
  • Akian Marianne
  • Gaubert Stephane
  • Rowen Louis
  Journal of Pure and Applied Algebra, Elsevier, 2024, 228 (6), pp.107584. Hyperfields and systems are two algebraic frameworks which have been developed to provide a unified approach to classical and tropical structures. All hyperfields, and more generally hyperrings, can be represented by systems. We show that, conversely, we show that the systems arising in this way, called hypersystems, are characterized by certain elimination axioms. Systems are preserved under standard algebraic constructions; for instance matrices and polynomials over hypersystems are systems, but not hypersystems. We illustrate these results by discussing several examples of systems and hyperfields, and constructions like matroids over systems. (10.1016/j.jpaa.2023.107584)
  DOI : 10.1016/j.jpaa.2023.107584
• Evolution and spread of multiadapted pathogens in a spatially heterogeneous environment
  
  • Griette Quentin
  • Alfaro Matthieu
  • Raoul Gaël
  • Gandon Sylvain
  Evolution Letters, Wiley Open Access ; Oxford University Press, 2024, 8 (3), pp.427-436. Pathogen adaptation to multiple selective pressures challenges our ability to control their spread. Here we analyze the evolutionary dynamics of pathogens spreading in a heterogeneous host population where selection varies periodically in space. We study both the transient dynamics taking place at the front of the epidemic and the long-term evolution far behind the front. We identify five types of epidemic profiles arising for different levels of spatial heterogeneity and different costs of adaptation. In particular, we identify the conditions where a generalist pathogen carrying multiple adaptations can outrace a coalition of specialist pathogens. We also show that finite host populations promote the spread of generalist pathogens because demographic stochasticity enhances the extinction of locally maladapted pathogens. But higher mutation rates between genotypes can rescue the coalition of specialists and speed up the spread of epidemics for intermediate levels of spatial heterogeneity. Our work provides a comprehensive analysis of the interplay between migration, local selection, mutation, and genetic drift on the spread and on the evolution of pathogens in heterogeneous environments. This work extends our fundamental understanding of the outcome of the competition between two specialists and a generalist strategy (single- vs. multiadapted pathogens). These results have practical implications for the design of more durable control strategies against multiadapted pathogens in agriculture and in public health. (10.1093/evlett/qrad073)
  DOI : 10.1093/evlett/qrad073
• A stochastic model for neural progenitor dynamics in the mouse cerebral cortex
  
  • Clément Frédérique
  • Olayé Jules
  Mathematical Biosciences, Elsevier, 2024, 372, pp.109185. We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations. (10.1016/j.mbs.2024.109185)
  DOI : 10.1016/j.mbs.2024.109185
• Large population asymptotics for a multitype stochastic SIS epidemic model in randomly switched environment
  
  • Prodhomme Adrien
  • Strickler Édouard
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2024, 34 (3), pp.3125-3180. We consider an epidemic SIS model described by a multitype birth-and-death process in a randomly switched environment. That is, the infection and cure rates of the process depend on the state of a finite Markov jump process (the environment), whose transitions also depend on the number of infectives. The total size of the population is constant and equal to some K ∈ N * , and the number of infectives vanishes almost surely in finite time. We prove that, as K → ∞, the process composed of the proportions of infectives of each type X^K and the state of the environment Ξ^K , converges to a piecewise deterministic Markov process (PDMP) given by a system of randomly switched ODEs. The long term behaviour of this PDMP has been previously investigated by Benaïm and Strickler, and depends only on the sign of the top Lyapunov exponent Λ of the linearised PDMP at 0: if Λ < 0, the proportion of infectives in each group converges to zero, while if Λ > 0, the disease becomes endemic. In this paper, we show that the large population asymptotics of X^K also strongly depend on the sign of Λ: if negative, then from fixed initial proportions of infectives the disease disappears in a time of order at most log(K), while if positive, the typical extinction time grows at least as a power of K. We prove that in the situation where the origin is accessible for the linearised PDMP, the mean extinction time of X^K is logarithmically equivalent to K^p * , where p * > 0 is fully characterised. We also investigate the quasi-stationary distribution µ^K of (X^K , Ξ^K) and show that, when Λ < 0, weak limit points of (µ^K), K>0 are supported by the extinction set, while when Λ > 0, limit points belong to the (non empty) set of stationary distributions of the limiting PDMP which do not give mass to the extinction set. (10.1214/23-AAP2035)
  DOI : 10.1214/23-AAP2035
• Correlation detection in trees for planted graph alignment
  
  • Ganassali Luca
  • Lelarge Marc
  • Massoulié Laurent
  The Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2024, 34 (3). <div><p>Motivated by alignment of correlated sparse random graphs, we introduce a hypothesis testing problem of deciding whether or not two random trees are correlated. We study the likelihood ratio test and obtain sufficient conditions under which this task is impossible or feasible. We propose MPAlign, a message-passing algorithm for graph alignment inspired by the tree correlation detection problem. We prove MPAlign to succeed in polynomial time at partial alignment whenever tree detection is feasible. As a result our analysis of tree detection reveals new ranges of parameters for which partial alignment of sparse random graphs is feasible in polynomial time. 1 </p></div> (10.1214/23-AAP2020)
  DOI : 10.1214/23-AAP2020
• Progressive state space disaggregation for infinite horizon dynamic programming
  
  • Forghieri Orso
  • Castel Hind
  • Hyon Emmanuel
  • Pennec Erwan Le
  , 2024, 34, pp.221-229. High dimensionality of model-based Reinforcement Learning and Markov Decision Processes can be reduced using abstractions of the state and action spaces. Although hierarchical learning and state abstraction methods have been explored over the past decades, explicit methods to build useful abstractions of models are rarely provided. In this work, we provide a new state abstraction method for solving infinite horizon problems in the discounted and total settings. Our approach is to progressively disaggregate abstract regions by iteratively slicing aggregations of states relatively to a value function. The distinguishing feature of our method, in contrast to previous approximations of the Bellman operator, is the disaggregation of regions during value function iterations (or policy evaluation steps). The objective is to find a more efficient aggregation that reduces the error on each piece of the partition. We provide a proof of convergence for this algorithm without making any assumptions about the structure of the problem. We also show that this process decreases the computational complexity of the Bellman operator iteration and provides useful abstractions. We then plug this state space disaggregation process in classical Dynamic Programming algorithm namely Approximate Value Iteration, Q-Value Iteration and Policy Iteration. Finally, we conduct a numerical comparison on randomly generated MDPs as well as classical MDPs. Those experiments show that our policy-based algorithm is faster than both traditional dynamic programming approach and recent aggregative methods that use a fixed number of adaptive partitions. (10.1609/icaps.v34i1.31479)
  DOI : 10.1609/icaps.v34i1.31479
• Dynamic Expectation-Maximization algorithms for Mixed-type Data
  
  • Pruilh Solange
  • Allassonnière Stéphanie
  , 2024. Modelling mixed-type data is still complex because of the heterogeneity of encountered data. With clustering as the objective, many methods are already doing well, but the inference of models and a posteriori exploitation is made difficult if not impossible. In this article we propose methodological developments of mixture models designed for mixed-type data. Component distributions of the continuous attributes can be either Gaussian, Student or Shifted Asymmetric Laplace. Categorical or discrete attributes, assumed independent conditionally on the class membership, can be distributed according to Bernoulli, Multinomial or Poisson distributions. The joint estimation of the number of classes and the parameters is carried out by EM-like algorithms that we have adapted to perform correctly. We show that our different dynamic algorithms allow us to reach the real number of classes and to correctly estimate the parameters of the discrete and continuous laws. We also highlight the benefits of introducing regularization to improve performance in situations where the sample size is insufficient for the complexity of the model. Our various models are then tested on real datasets from the literature, assessing that the objective of jointly estimating the number of components and the model parameters has been achieved.
• Shape Optimization: Theoretical, Numerical and Practical Aspects
  
  • Bogosel Beniamin
  , 2024.