Seminar 19th November 2012 2 p.m. 13/5019
Some new classes of kernels for Gaussian Process modelling
David Ginsbourger
University of Bern
- Web page
- http://www.imsv.unibe.ch/content/staff/dr_david_ginsbourger/index_eng.html
- Categories
- Complex Systems, Optimisation
- Submitter
- Luke Goater
Gaussian Process modeling has become commonplace in the design and analysis of computer experiments. Thanks to convenient properties of the conditional distributions (Gaussianity, interpolation in the case of deterministic responses, etc.), GP emulators not only allow predicting simulator responses for untried input configurations, but can also be used as a basis for evaluation strategies dedicated to optimization, inversion, uncertainty quantification, probability of failure estimation, and more.
Two functional parameters, the mean function and the covariance kernel, can be tuned in order for GP models to stick as much as possible to the anticipated and/or observed properties of the function of interest. In a majority of applications, a constant trend and a stationary kernel from some parametric family (e.g., anisotropic Matérn) are assumed. In some cases, the trend is upgraded to a linear combination of basis functions and/or a more sophisticated non-stationary covariance kernel is used. Here we will mostly focus on the design of admissible covariance kernels respecting different kinds of prior knowledge on the objective function. This includes algebraic invariances, additivity, as well as other mathematical features, and also applied questions related to the use of proxy simulations to complement and speed up analyses based on time-consuming high-fidelity simulations.
Following a few recent results on the characterization of additivity or group invariance of GP paths through related properties of the underlying kernel, we will discuss about some promising options for designing admissible kernels tailored to specific needs. To conclude with, we will present a proxy-based covariance kernel that was recently introduced in hydrogeology to perform sequential Kriging-based inversion using a computer experiment where the inputs are maps and the outputs are curves.