Gaussian processes and related topics

Liste des Contributions

1. Introduction

François Bachoc (Institut de Mathématiques de Toulouse)

07/07/2025 14:00

2. Mini-course 1: lecture “Introduction to Gaussian processes” (Chair: Pierre Neuvial)

François Bachoc (Institut de Mathématiques de Toulouse)

07/07/2025 14:10

3. Long talk: Modeling and simulating spatio-temporal, multivariate and nonstationary Gaussian Random Fields: a Gaussian mixtures perspective (Chair: Pierre Neuvial))

Denis Allard (INRAE, Avignon)

07/07/2025 15:10

Gaussian Random Fields (GRFs) play a critical role in modeling and simulating environmental and climate-driven processes. The simulation of GRFs enables the representation of the variability of the process under study through the generation of multiple equally plausible realizations. Gaussian vectors corresponding to a sample of moderate size of a GRF can easily be simulated using the Cholesky...

4. Short talk: On the equivalence and orthogonality of zero-mean Gaussian measures (Chair: Pierre Neuvial)

Michael Hediger (University of Zurich)

07/07/2025 16:25

We discuss some key considerations that are helpful in identifying orthogonal measures, including both established and novel approaches.

5. Poster session

07/07/2025 16:45

6. Mini-course 1: lecture “Constrained Gaussian processes” (Chair: Agnès Lagnoux)

M. Andrés LOPEZ-LOPERA (UPHF), Mathis Deronzier (IMT)

08/07/2025 09:00

7. Mini-course 1: lab session “Gaussian processes and constrained Gaussian processes”

M. Andrés LOPEZ-LOPERA (UPHF), Mathis Deronzier (IMT)

08/07/2025 10:35

20. Poster session

08/07/2025 13:15

8. Mini-course 2: lecture “Gaussian processes in nonparametric statistics” (Chair: Agnès Lagnoux)

Elie Odin (Institut de Mathématiques de Toulouse), Ismaël Castillo (Sorbonne Université)

08/07/2025 13:45

9. Short talk: On L^2 posterior contraction rates in Bayesian nonparametric regression models (Chair Olivier Roustant))

Paul Rosa (University of Cambridge)

08/07/2025 15:15

The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating distribution (assuming a true frequentist model) and a semi-metric d(.,.) on the space of regression functions that satisfy the so called testing condition,...

10. Long talk: Bayesian optimization applied to constrained black box problems for aeronautical applications (Chair: Olivier Roustant)

Nathalie Bartoli (ONERA Toulouse)

08/07/2025 16:05

11. Short talk: Convergence rates of deep Gaussian processes (Chair: Olivier Roustant)

Conor Osborne (University of Edinburgh)

08/07/2025 16:50

Gaussian processes have proven to be powerful and flexible tools for various statistical inference and machine learning tasks. However, they can be limited when the underlying datasets exhibit non-stationary or anisotropic properties. Deep Gaussian processes extend the capabilities of standard Gaussian processes by introducing a hierarchical structure, where the outputs of one Gaussian process...

12. Poster session

08/07/2025 17:10

13. Mini-course 2: lecture “Gaussian processes in nonparametric statistics” (Chair François Bachoc)

Elie Odin (Institut de Mathématiques de Toulouse), Ismaël Castillo (Sorbonne Université)

09/07/2025 08:30

14. Long talk: Vecchia gaussian processes: Probabilistic properties, minimax rates and methodological developments (Chair François Bachoc)

Botond Szabo (Bocconi University)

09/07/2025 10:30

Gaussian Processes (GPs) are widely used to model dependency in spatial statistics and machine learning, yet the exact computation suffers an intractable time complexity of O(n^3). Vecchia approximation allows scalable Bayesian inference of GPs in O(n) time by introducing sparsity in the spatial dependency structure that is characterized by a directed acyclic graph (DAG). Despite the...

15. Long talk: To BayesOpt and Beyond (Remote speaker) (Chair François Bachoc)

Henry Moss (Lancaster University)

09/07/2025 11:15

Bayesian optimisation (BO) pairs Gaussian-process surrogates with exploration-aware acquisition rules to locate the optimum of costly, black-box functions in just a handful of trials. In this introductory talk we unpack how GPs supply calibrated uncertainty that powers the explore-exploit trade-off, walk through the classical BO loop and its staple acquisition functions, and outline practical...

16. Long talk: Kernel based sensitivity analysis for set-valued models (Chair Andrés Felipe Lopez Lopera))

Christophette Blanchet-Scalliet (École Centrale de Lyon)

09/07/2025 13:30

The goal of this work is to use goal-directed sensitivity analysis in order to
reduce the cost of solving a robust optimization problem. Specifically, we focus on
quantifying the impact of uncertain inputs on feasible sets, which are subsets of the
design domain. While most sensitivity analysis methods deal with scalar outputs,
we introduce a novel approach for performing sensitivity...

17. Long talk: Physics-informed Gaussian process priors (Chair Andrés Felipe Lopez Lopera)

Iain Henderson (ISAE-SUPAERO)

09/07/2025 14:15

18. Long talk: Asymptotics for constrained Gaussian processes (Chair Andrés Felipe Lopez Lopera)

Agnès LAGNOUX

09/07/2025 15:25

19. Short talk: Variational Gaussian processes for linear inverse problems (Chair Andrés Felipe Lopez Lopera)

Thibault Randrianarisoa (University of Toronto)

09/07/2025 16:10

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further corrupted with noise. Bayes offers a natural way to regularize these problems via the prior distribution and provides a probabilistic solution, quantifying...