• Julien MARTINELLI (Inserm Bordeaux Population Health), Post-doctorant
  Multi-Fidelity Bayesian Optimization with Unreliable Information Sources
  Bayesian optimization (BO) is a powerful framework for optimizing black-box, expensive-to-evaluate functions. Over the past decade, many algorithms have been proposed to integrate cheaper, lower-fidelity approximations of the objective function into the optimization process, with the goal of converging towards the global optimum at a reduced cost. This task is generally referred to as multi-fidelity Bayesian optimization (MFBO). However, MFBO algorithms can lead to higher optimization costs than their vanilla BO counterparts, especially when the low-fidelity sources are poor approximations of the objective function, therefore defeating their purpose. To address this issue, we propose rMFBO (robust MFBO), a methodology to make any GP-based MFBO scheme robust to the addition of unreliable information sources. rMFBO comes with a theoretical guarantee that its performance can be bound to its vanilla BO analog, with high controllable probability. We demonstrate the effectiveness of the proposed methodology on a number of numerical benchmarks, outperforming earlier MFBO methods on unreliable sources. We expect rMFBO to be particularly useful to reliably include human experts with varying knowledge within BO processes.

• Dimitrios TZIVRAILLIS (CEA List, CNRS LPTMS), Post-doctorant
  Uncertainty in AI Driven Physical Simulation
  AI has significantly impacted scientific research, particularly in physics and chemistry. A major challenge in these fields is efficiently sampling physical configurations in complex systems to compute observable quantities. The primary bottleneck in such numerical simulations is often the costly computation of energies and forces for these samples, with interatomic potentials being a well-known example. Deep learning models have been employed to accelerate these simulations by learning to predict these computationally expensive quantities. In this work, we examine the reliability of this approach through the lens of AI uncertainty. Specifically, we show that despite strong training performance, AI models introduce epistemic uncertainty into physical simulations, leading to biases in the computation of physical observables. To address this issue, we develop a technique that corrects these biases, overcoming a key limitation in the deployment of AI for numerical simulations in physics.

• Paul MANGOLD (Ecole Polytechnique), Post-doctorant
  Convergence and Linear Speed-Up In Stochastic Federated Learning
  In federated learning, multiple users collaboratively train a machine learning model without sharing local data. To reduce communication, users perform multiple local stochastic gradient steps that are then aggregated by a central server. However, due to data heterogeneity, local training introduces bias. In this talk, I will present a novel interpretation of the Federated Averaging algorithm, establishing its convergence to a stationary distribution. By analyzing this distribution, I will show that the bias consists of two components: one due to heterogeneity and another due to gradient stochasticity. I will then extend this analysis to the Scaffold algorithm, demonstrating that it effectively mitigates heterogeneity bias but not stochasticity bias. Finally, I will show that both algorithms achieve linear speed-up in the number of agents, a key property in federated stochastic optimization.

• Ragansu CHAKKAPPAI (IJCLab, Université Paris-Saclay), Doctorant
  An implementation of neural simulation-based inference for parameter estimation in ATLAS
  Neural simulation-based inference (NSBI) is a powerful class of machine-learning-based methods for statistical inference that naturally handles high-dimensional parameter estimation without the need to bin data into low-dimensional summary histograms. Such methods are promising for a range of measurements, including at the Large Hadron Collider, where no single observable may be optimal to scan over the entire theoretical phase space under consideration, or where binning data into histograms could result in a loss of sensitivity. This work develops a neural simulation-based inference framework for statistical inference, using neural networks to estimate probability density ratios, which enables the application to a full-scale analysis. It incorporates a large number of systemic uncertainties, quantifies the uncertainty due to the finite number of events in training samples, develops a method to construct confidence intervals, and demonstrates a series of intermediate diagnostic checks that can be performed to validate the robustness of the method. As an example, the power and feasibility of the method are assessed on simulated data for a simplified version of an off-shell Higgs boson couplings measurement in the four-lepton final states at the Large Hadron Collider.
  This talk will cover https://arxiv.org/abs/2412.01600, which itself details the NSBI technique developped for https://arxiv.org/abs/2412.01548 which is the first use of NSBI at the LHC. 

12h15 - 13h45 | Pause déjeuner

14h45 - 15h30 | Pause goûter

• Diarra FALL (Université d'Orléans, Institut Denis Poisson)
  Bayesian formulation of Regularization by Denoising. Application to Image Restoration.
  Inverse problems are ubiquitous in signal and image processing. Canonical examples include signal/image denoising (i.e, removing noise from a signal/image) and image reconstruction. As inverse problems are known to be ill-posed or at least, ill-conditioned, they require regularization by introducing additional constraints to mitigate the lack of information brought by the observations. A common difficulty is to select an appropriate regularizer, which has a decisive influence on the quality of the reconstruction. Another challenge is the confidence we may have in the reconstructed signal/image. To put it another way, it is desirable for a method to be able to quantify the uncertainty associated with the reconstructed image in order to encourage more principled decision-making. These two tasks (regularization and uncertainty quantification) can be overcome at the same time by addressing the problem within the Bayesian statistical framework. It allows to include additional information by specifying a marginal distribution for the signal/image, known as prior distribution.  The traditional approach consists in defining the prior analytically, as a hand-crafted explicit function chosen to encourage specific desired properties of the recovered signal/image. Following the up-to-date surge of deep learning, data-driven regularization using priors specified by neural networks has become ubiquitous in signal and image inverse problems. Popular approaches within this methodology are Plug & Play (PnP) [1] and regularization by denoising (RED) [2] methods. We have proposed in [3] a probabilistic approach to the RED method, defining a new probability distribution based on a RED potential, which can be chosen as the prior distribution in a Bayesian inversion task. We have also proposed a dedicated Markov chain Monte Carlo sampling algorithm that is particularly well suited to high-dimensional sampling of the resulting posterior distribution. In addition, we provide a theoretical analysis that guarantees convergence to the target distribution, and quantify the speed of convergence. The power of the proposed approach is illustrated in various restoration tasks such as image deblurring, inpainting, and super-resolution.
  [1] S. V. Venkatakrishnan et al. « Plug-and-Play priors for model based reconstruction ». In IEEE Global Conf. on Signal and Information Processing, pp 945-948, 2013.
  [2]Y. Romano, M. Elad, and P. Milanfar, « The little engine that could:
  Regularization by denoising (RED), » SIAM Journal on Imaging Sciences, 10(4):1804–1844, 2017
  [3] E. C. Faye, M. D. Fall, and N. Dobigeon. « Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling », IEEE Transactions on Image Processing,  vol 34, pages 221-234, 2024

• Antonio OCELLO (Ecole Polytechnique, CMAP), Post-doctorant
  Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean Field Games
  In this talk, we introduce Mean Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean Field Games (MFGs) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting, we extend its methodology to the MFG framework, leveraging its stability and robustness in policy optimization. Under standard assumptions in the MFG literature, we provide a rigorous analysis of MF-TRPO, establishing theoretical guarantees on its convergence. Our results cover both the exact formulation of the algorithm and its sample-based counterpart, where we derive high-probability guarantees and finite sample complexity.

• Violaine COURRIER (Inria Lille, Withings), Doctorante en thèse CIFRE
  Guided Clustering Variational Autoencoder (GCVAE) : un cadre flexible pour un clustering guidé
  Le Guided Clustering Variational Autoencoder (GCVAE) est un modèle de clustering qui intègre une "variable guide" dans un cadre d'autoencodeur variationnel (VAE) couplé à un mélange gaussien (GMM). Cette architecture permet de : préserver la structure intrinsèque des données d'entrée tout en permettant leur clustering contextuel via une variable guide, maintenir la capacité de clusterisation même en l'absence de la variable guide, améliorer l'interprétabilité des clusters grace à une variable guide, quantifier efficacement les incertitudes grâce à la nature probabiliste du VAE, qui associe chaque échantillon à une distribution latente, permettant d'estimer la probabilité d'appartenance à un cluster donné et de quantifier l'incertitude associée à cette affectation. L'efficacité du GCVAE est montrée à travers deux expériences :
  1. Images MNIST-SVHN : la variable contextuelle MNIST guide le clustering des images SVHN, illustrant la capacité du modèle à s’appliquer à des données complexes. 2. Données de sommeil Withings : sur des données réelles de sommeil de l’entreprise Withings, le modèle révèle des insights pertinents sur les facteurs de risque liés à l'apnée du sommeil. Les résultats expérimentaux montrent que le GCVAE améliore significativement la pertinence et l'interprétation des clusters, tout en offrant un cadre pour la quantification des incertitudes.

• Ulysse GAZIN (Université Paris-Cité, LPSM), Doctorant en 2ème année
  Asymptotics for Conformal Inference
  Conformal inference is a versatile tool for building prediction sets in regression or classification. We study the false coverage proportion (FCP) in a transductive setting with a calibration sample of n points and a test sample of m points. We identify the exact, distribution-free, asymptotic distribution of the FCP when both n and m tend to infinity. This shows in particular that FCP control can be achieved by using the well-known Kolmogorov distribution, and puts forward that the asymptotic variance is decreasing in the ratio n/m. We then provide a number of extensions by considering weighted conformal inference  and distribution shift between the calibration sample and the test sample, wich are regime where no finite sample guarantee are known up to our knowledge.
  In particular, our  asymptotic results allow to accurately quantify the asymptotic behavior of the errors when weighted conformal inference is used even with a non-oracle weight. These results can also be used in the novelty detection framework when the Benjamini-Hochberg procedure is used with conformal p-values. This talk is based on the following publication: https://hal.science/hal-04701683.

• Jaad BELHOUARI-DURAND (Université d'Evry, Saint-Gobain Recherche), Etudiant en M2 Data Science
  Beta-Optim : Combining Frequentist and Bayesian Approaches for Uncertainty Quantification in Multi-Output Regression Problems
  In this work, we present a novel methodology for uncertainty quantification in multi-output regression problems, leveraging the strengths of both frequentist and Bayesian approaches. Our method integrates Bayesian networks, Conformal prediction, and Monte Carlo techniques to rigorously analyze and calibrate predictive models. We employ TensorFlow Probability to implement our Bayesian framework, ensuring robust and scalable computations. A key innovation of our approach is the development of new methods for simultaneous prediction intervals when outputs are in multiple dimensions. These intervals provide comprehensive uncertainty estimations for all outputs, enhancing the reliability of predictions in complex, high-dimensional settings. We demonstrate the efficiency of our method through a concrete example involving an internal use case, showcasing its practical applicability and performance. This work contributes to the field by providing a robust framework for uncertainty quantification in multi-output regression problems, with significant implications for both academic research and practical applications. Our method uses a normalized conformity score and a new objective function to optimize, adjusting the local error rate (beta) to achieve a desired global error rate (alpha). Additionally, our research highlights the adaptability of the prediction intervals provided by our method. These intervals are shorter in width compared to other state-of-the-art methods such as CQR, demonstrating the efficiency and precision of our approach.

• Yukun LIU (Télécom Paris), Doctorant en 1ère année
  Uncertainty Quantification in Electromagnetic Field Exposure Assessment with Neural Networks
  Characterizing electromagnetic field (EMF) exposure is essential due to public concerns over potential health risks, regulatory compliance, environmental monitoring, and its influence on emerging technologies. Effectively assessing EMF exposure requires not only estimating a confidence interval but also addressing uncertainties arising from intractable inputs. Therefore, quantifying uncertainty and analyzing the influence of various inputs are critical for accurate exposure assessment. In this study, we investigate the performance and limitations of neural network-based methods for uncertainty quantification and conduct a comparative analysis with statistical surrogate models.