Uncertainty quantification using Gaussian Process with squared exponential kernel - VVSOR - VVSOR

Netherlands Society for Statistics and Operations Research | Dutch
04 May 2018

Uncertainty quantification using Gaussian Process with squared exponential kernel

We cordially invite you to the next Bayes club meeting, taking place on Friday, the 4th of May, in Leiden (MI, Nils Bohrweg 1)

Speaker: Amine Hadji (Leiden University)
Title: Uncertainty quantification using Gaussian Process with squared exponential kernel
Time: 15:00-16:00 on the 4th of May, 2018
Location: room 401, Leiden University, Nils Bohrweg 1.

Gaussian processes are widely used as nonparametrical priors in various fields of applications, including finance, machine learning, genomics, and epidemiology. Arguably, one of the most frequently used covariance kernel is the squared exponential kernel. As sample paths from the corresponding process are too smooth, it is common to rescale the kernel. The optimal rescaling factor depends however on the true parameter, which leads in practice to the use of empirical or hierarchical Bayes methods. The current results focus mainly on the recovery of the underlying functional parameter in different contexts and derive (nearly) optimal posterior contraction rates. However less is known about the reliability of uncertainty quantification using this type of process.  In our work, we investigate the coverage properties of the corresponding credible sets in context of the Gaussian white noise model. We show that the resulting posterior distribution is not suitable for uncertainty quantification as the credible sets will have coverage tending to zero for typical signals. The derived theoretical findings are demonstrated on a thorough simulation study, where amongst others we obtain that Gaussian processes with squared exponential kernel have substantially worse coverage properties than other Gaussian processes. On the other hand, blowing the radius of our credible set by a log n factor allows it to encompass the truth.
This is an ongoing joint work with Botond Szabo and Aad van der Vaart.

For the list of upcoming talks and further information about the seminar please visit the (relocated) seminar website: http://pub.math. leidenuniv.nl/~szabobt/bayes_ club.html