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A journey through Gaussian random fields with a view towards Bayesian optimization.

Lecturer: David Ginsbourger (IDIAP / Uni Bern)

Lecture abstract and outline.

Gaussian random fields have been used as a flexible and practical family of priors in the context of Bayesian statistics when the parameter of interest is functional. In particular, these priors are now massively used in machine learning as a building block of adaptive strategies for approximating and optimizing functions based on limited evaluation budgets. We will review the basics of GRFs and give an introduction to Bayesian optimization.


* Basics of Gaussian random fields (GRFs)
* On the use of GRFs in the context of Bayesian statistics, e.g., in curve fitting
* Introduction to Bayesian optimization of deterministic functions relying on GRF priors
* Discussion on some applications of Bayesian optimization relevant to physical modelling

Conservative estimate for the excursion set of a deterministic function under a Gaussian random field model
Performing Bayesian Model Selection with Nested Sampling
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