Julien Bect
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View article: Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification
Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification Open
Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probability that the output belongs to a specific region remains bel…
View article: Bayesian Sequential Design of Computer Experiments for Quantile Set Inversion
Bayesian Sequential Design of Computer Experiments for Quantile Set Inversion Open
International audience
View article: Rational kernel-based interpolation for complex-valued frequency response functions (matlab code, stk-kriging/contrib-cork)
Rational kernel-based interpolation for complex-valued frequency response functions (matlab code, stk-kriging/contrib-cork) Open
Complex rational kernel-based interpolation This software package contains some code & data associated with the paper:Julien Bect (‡), Niklas Georg (§), Ulrich Römer (†), Sebastian Schöps (§),Rational kernel-based interpolation for complex…
View article: Quantitative risk assessment of Haemolytic and Uremic Syndrome (HUS) from consumption of raw milk soft cheese
Quantitative risk assessment of Haemolytic and Uremic Syndrome (HUS) from consumption of raw milk soft cheese Open
The aim of this quantitative risk assessment model is to estimate the risk of Haemolytic Uremic Syndrome (HUS) caused by Shiga-toxin producing Escherichia coli (STEC) in raw milk soft cheese and explore intervention strategies to minimise …
View article: Parameter Selection in Gaussian Process Interpolation: An Empirical Study of Selection Criteria
Parameter Selection in Gaussian Process Interpolation: An Empirical Study of Selection Criteria Open
International audience
View article: Bayesian sequential design of computer experiments for quantile set inversion
Bayesian sequential design of computer experiments for quantile set inversion Open
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose …
View article: Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method
Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method Open
This article focuses on the multi-objective optimization of stochastic simulators with high output variance, where the input space is finite and the objective functions are expensive to evaluate. We rely on Bayesian optimization algorithms…
View article: Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization
Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization Open
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive distribut…
View article: Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization
Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization Open
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive distribut…
View article: Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods
Integration of bounded monotone functions: Revisiting the nonsequential case, with a focus on unbiased Monte Carlo (randomized) methods Open
In this article we revisit the problem of numerical integration for monotone bounded functions, with a focus on the class of nonsequential Monte Carlo methods. We first provide new a lower bound on the maximal $L^p$ error of nonsequential …
View article: A BAYESIAN APPROACH FOR THE OPTIMAL INTEGRATION OF RENEWABLE ENERGY SOURCES IN DISTRIBUTION NETWORKS OVER MULTI-YEAR HORIZONS
A BAYESIAN APPROACH FOR THE OPTIMAL INTEGRATION OF RENEWABLE ENERGY SOURCES IN DISTRIBUTION NETWORKS OVER MULTI-YEAR HORIZONS Open
International audience
View article: Parameter selection in Gaussian process interpolation: an empirical study of selection criteria
Parameter selection in Gaussian process interpolation: an empirical study of selection criteria Open
This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of Bayes…
View article: Parameter selection in Gaussian process interpolation: an empirical\n study of selection criteria
Parameter selection in Gaussian process interpolation: an empirical\n study of selection criteria Open
This article revisits the fundamental problem of parameter selection for\nGaussian process interpolation. By choosing the mean and the covariance\nfunctions of a Gaussian process within parametric families, the user obtains a\nfamily of Ba…
View article: Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction
Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction Open
This article deals with the sequential design of experiments for\n(deterministic or stochastic) multi-fidelity numerical simulators, that is,\nsimulators that offer control over the accuracy of simulation of the physical\nphenomenon or sys…
View article: Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation
Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation Open
This article investigates the origin of numerical issues in maximum likelihood parameter estimation for Gaussian process (GP) interpolation and investigates simple but effective strategies for improving commonly used open-source software i…
View article: On the Quantification of Discretization Uncertainty: Comparison of Two Paradigms
On the Quantification of Discretization Uncertainty: Comparison of Two Paradigms Open
Numerical models based on partial differential equations (PDE), or\nintegro-differential equations, are ubiquitous in engineering and science,\nmaking it possible to understand or design systems for which physical\nexperiments would be exp…
View article: Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction
Sequential Design of Multi-Fidelity Computer Experiments: Maximizing the Rate of Stepwise Uncertainty Reduction Open
This article deals with the sequential design of experiments for (deterministic or stochastic) multi-fidelity numerical simulators, that is, simulators that offer control over the accuracy of simulation of the physical phenomenon or system…
View article: Sequential design of multi-fidelity computer experiments: maximizing the rate of stepwise uncertainty reduction
Sequential design of multi-fidelity computer experiments: maximizing the rate of stepwise uncertainty reduction Open
This article deals with the sequential design of experiments for (deterministic or stochastic) multi-fidelity numerical simulators, that is, simulators that offer control over the accuracy of simulation of the physical phenomenon or system…
View article: Towards new cross-validation-based estimators for Gaussian process regression: efficient adjoint computation of gradients
Towards new cross-validation-based estimators for Gaussian process regression: efficient adjoint computation of gradients Open
We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an effi…
View article: A supermartingale approach to Gaussian process based sequential design of experiments
A supermartingale approach to Gaussian process based sequential design of experiments Open
Gaussian process (GP) models have become a well-established frameworkfor the adaptive design of costly experiments, and notably of computerexperiments. GP-based sequential designs have been found practicallyefficient for various objectives…
View article: Bayesian Multi-objective Optimization with Noisy Evaluations using the Knowledge Gradient
Bayesian Multi-objective Optimization with Noisy Evaluations using the Knowledge Gradient Open
Slides presented at the PGMO Days 2019, held the 3rd and 4th December 2019 at EDF Lab Paris-Saclay. Abstract: We consider the problem of multi-objective optimization in the case where each objective is a stochastic black box that provides …
View article: A supermartingale approach to Gaussian process based sequential design of experiments
A supermartingale approach to Gaussian process based sequential design of experiments Open
Gaussian process (GP) models have become a well-established frameworkfor the\nadaptive design of costly experiments, and notably of computerexperiments.\nGP-based sequential designs have been found practicallyefficient for various\nobjecti…
View article: Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure
Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure Open
A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a …
View article: User preferences in Bayesian multi-objective optimization: the expected weighted hypervolume improvement criterion
User preferences in Bayesian multi-objective optimization: the expected weighted hypervolume improvement criterion Open
In this article, we present a framework for taking into account user preferences in multi-objective Bayesian optimization in the case where the objectives are expensive-to-evaluate black-box functions. A novel expected improvement criterio…
View article: Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure
Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure Open
A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a …
View article: Sequential design of experiments to estimate a probability of exceeding a threshold in a multi-fidelity stochastic simulator
Sequential design of experiments to estimate a probability of exceeding a threshold in a multi-fidelity stochastic simulator Open
In this article, we consider a stochastic numerical simulator to assess the impact of some factors on a phenomenon. The simulator is seen as a black box with inputs and outputs. The quality of a simulation, hereafter referred to as fidelit…