Search Results for author: François Bachoc

Found 10 papers, 4 papers with code

The sample complexity of level set approximation

no code implementations26 Oct 2020 François Bachoc, Tommaso Cesari, Sébastien Gerchinovitz

We study the problem of approximating the level set of an unknown function by sequentially querying its values.

Rate of convergence for geometric inference based on the empirical Christoffel function

no code implementations31 Oct 2019 Mai Trang Vu, François Bachoc, Edouard Pauwels

We consider the problem of estimating the support of a measure from a finite, independent, sample.

Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC

no code implementations15 Jan 2019 Andrés F. López-Lopera, François Bachoc, Nicolas Durrande, Jérémy Rohmer, Déborah Idier, Olivier Roustant

Finally, on 2D and 5D coastal flooding applications, we show that more flexible and realistic GP implementations can be obtained by considering noise effects and by enforcing the (linear) inequality constraints.

Gaussian Processes

Explaining Machine Learning Models using Entropic Variable Projection

2 code implementations18 Oct 2018 François Bachoc, Fabrice Gamboa, Max Halford, Jean-Michel Loubes, Laurent Risser

In order to emphasize the impact of each input variable, this formalism uses an information theory framework that quantifies the influence of all input-output observations based on entropic projections.

Maximum likelihood estimation for Gaussian processes under inequality constraints

1 code implementation10 Apr 2018 François Bachoc, Agnès Lagnoux, Andrés F. López-Lopera

We first show that the (unconstrained) maximum likelihood estimator has the same asymptotic distribution, unconditionally and conditionally, to the fact that the Gaussian process satisfies the inequality constraints.

Statistics Theory Probability Statistics Theory

Gaussian Processes indexed on the symmetric group: prediction and learning

no code implementations16 Mar 2018 François Bachoc, Baptiste Broto, Fabrice Gamboa, Jean-Michel Loubes

In the framework of the supervised learning of a real function defined on a space X , the so called Kriging method stands on a real Gaussian field defined on X.

Gaussian Processes

Finite-dimensional Gaussian approximation with linear inequality constraints

1 code implementation20 Oct 2017 Andrés F. López-Lopera, François Bachoc, Nicolas Durrande, Olivier Roustant

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems.

A Gaussian Process Regression Model for Distribution Inputs

no code implementations31 Jan 2017 François Bachoc, Fabrice Gamboa, Jean-Michel Loubes, Nil Venet

We prove that the Gaussian processes indexed by distributions corresponding to these kernels can be efficiently forecast, opening new perspectives in Gaussian process modeling.

Gaussian Processes

A supermartingale approach to Gaussian process based sequential design of experiments

no code implementations3 Aug 2016 Julien Bect, François Bachoc, David Ginsbourger

Thisobservation enables us to establish generic consistency results for abroad class of SUR strategies.

Global Optimization

Nested Kriging predictions for datasets with large number of observations

1 code implementation19 Jul 2016 Didier Rullière, Nicolas Durrande, François Bachoc, Clément Chevalier

This work falls within the context of predicting the value of a real function at some input locations given a limited number of observations of this function.

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