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

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

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.

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.

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

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.

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

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

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

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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