arXiv subjects

Loïc Giraldi

Publications and source records attributed to Loïc Giraldi.

7 recordsLinked to original sources

arXiv2026

Bounding Box Anomaly Scoring for simple and efficient Out-of-Distribution detection

Out-of-distribution (OOD) detection aims to identify inputs that differ from the training distribution in order to reduce unreliable predictions by deep neural networks. Among post-hoc feature-space approaches, OOD detection is commonly performed by approximating the in-distribution support in the representation space of a pretrained network. Existing methods often reflect a trade-off between compact parametric models, such as Mahalanobis-based scores, and more flexible but reference-based methods, such as k-nearest neighbors. Bounding-box abstraction provides an attractive intermediate perspective by representing in-distribution support through compact axis-aligned summaries of hidden activations. In this paper, we introduce Bounding Box Anomaly Scoring (BBAS), a post-hoc OOD detection method that leverages bounding-box abstraction. BBAS combines graded anomaly scores based on interval exceedances, monitoring variables adapted to convolutional layers, and decoupled clustering and box construction for richer and multi-layer representations. Experiments on image-classification benchmarks show that BBAS provides robust separation between in-distribution and out-of-distribution samples while preserving the simplicity, compactness, and updateability of the bounding-box approach.

cs.LG↗

arXiv2026

A Gaussian process and linear-based framework for computing cut distributions in modular Bayesian calibration of two chained computer models

Computer models are widely used in science and engineering to simulate complex systems. However, these models are affected by several sources of uncertainty, which may limit their use for decision making in risk management. We present a Bayesian approach for quantifying parameter uncertainty in a chain of two computer models motivated by multiphysics simulations in the nuclear field. Part of the inputs of a downstream model parametrized by $θ\in \mathbb{R}^p$ come from the outputs of an upstream model parametrized by $λ\in \mathbb{R}^q$. Usually, the joint posterior distribution of $(θ, λ)$ would be obtained by applying Bayes' theorem using the experimental observations of both models. However, when the observations of the downstream model are too indirect to provide informative inference on $λ$, it may be preferable to compute a modular posterior distribution of $(θ, λ)$, referred to as the \emph{cut distribution}. Assuming that the posterior distribution of $λ$ has been previously estimated from observations of the upstream model only, we aim to compute the posterior distribution of $θ$ conditional on $λ$ using observations from the downstream model. To this end, we propose a Gaussian-process and linear-based framework to estimate the functional dependence between $θ$ and $λ$, denoted by $θ(λ)$, where each component is modeled as a realization of a Gaussian process. As the downstream model is approximated by a linear function of $θ(λ)$, Bayesian conjugacy allows us to derive a Gaussian posterior predictive distribution of $θ(λ)$ for any realization of $λ$. The effectiveness of the method is illustrated through several synthetic examples, and we highlight how variations in $λ$ impact the predictive distribution of the chained simulation.

stat.CO↗

arXiv2024

Ensemble Data Assimilation for Particle-based Methods

This study presents a novel approach to applying data assimilation techniques for particle-based simulations using the Ensemble Kalman Filter. While data assimilation methods have been effectively applied to Eulerian simulations, their application in Lagrangian solution discretizations has not been properly explored. We introduce two specific methodologies to address this gap. The first methodology employs an intermediary Eulerian transformation that combines a projection with a remeshing process. The second is a purely Lagrangian scheme designed for situations where remeshing is not appropriate. The second is a purely Lagrangian scheme that is applicable when remeshing is not adapted. These methods are evaluated using a one-dimensional advection-diffusion model with periodic boundaries. Performance benchmarks for the one-dimensional scenario are conducted against a grid-based assimilation filter Subsequently, assimilation schemes are applied to a non-linear two-dimensional incompressible flow problem, solved via the Vortex-In-Cell method. The results demonstrate the feasibility of applying these methods in more complex scenarios, highlighting their effectiveness in both the one-dimensional and two-dimensional contexts.

math.NA↗

arXiv2020

Conditional Latent Block Model: a Multivariate Time Series Clustering Approach for Autonomous Driving Validation

Autonomous driving systems validation remains one of the biggest challenges car manufacturers must tackle in order to provide safe driverless cars. The high complexity stems from several factors: the multiplicity of vehicles, embedded systems, use cases, and the very high required level of reliability for the driving system to be at least as safe as a human driver. In order to circumvent these issues, large scale simulations reproducing this huge variety of physical conditions are intensively used to test driverless cars. Therefore, the validation step produces a massive amount of data, including many time-indexed ones, to be processed. In this context, building a structure in the feature space is mandatory to interpret the various scenarios. In this work, we propose a new co-clustering approach adapted to high-dimensional time series analysis, that extends the standard model-based co-clustering. The FunCLBM model extends the recently proposed Functional Latent Block Model and allows to create a dependency structure between row and column clusters. This structured partition acts as a feature selection method, that provides several clustering views of a dataset, while discriminating irrelevant features. In this workflow, times series are projected onto a common interpolated low-dimensional frequency space, which allows to optimize the projection basis. In addition, FunCLBM refines the definition of each latent block by performing block-wise dimension reduction and feature selection. We propose a SEM-Gibbs algorithm to infer this model, as well as a dedicated criterion to select the optimal nested partition. Experiments on both simulated and real-case Renault datasets shows the effectiveness of the proposed tools and the adequacy to our use case.

cs.LG↗

arXiv2018

Optimal projection of observations in a Bayesian setting

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback-Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.

math.ST↗

arXiv2014

To be or not to be intrusive? The solution of parametric and stochastic equations --- Proper Generalized Decomposition

A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlinear problems are associated with the minimization of a parameterized differentiable convex functional. We first introduce a bilinear parameterization of fixed-rank tensors and employ an alternating minimization scheme for computing the low-rank approximation. In keeping with the idea of non-intrusiveness, at each step of the algorithm the minimizations are carried out with a quasi-Newton method to avoid the computation of the Hessian. The algorithm is made non-intrusive through the use of numerical integration. It only requires the evaluation of residuals at specific parameter values. The algorithm is then applied to two numerical examples.

math.NA↗

arXiv2013

To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case

In parametric equations - stochastic equations are a special case - one may want to approximate the solution such that it is easy to evaluate its dependence of the parameters. Interpolation in the parameters is an obvious possibility, in this context often labeled as a collocation method. In the frequent situation where one has a "solver" for the equation for a given parameter value - this may be a software component or a program - it is evident that this can independently solve for the parameter values to be interpolated. Such uncoupled methods which allow the use of the original solver are classed as "non-intrusive". By extension, all other methods which produce some kind of coupled system are often - in our view prematurely - classed as "intrusive". We show for simple Galerkin formulations of the parametric problem - which generally produce coupled systems - how one may compute the approximation in a non-intusive way.

math.NA↗