Abstract

Gaussian processes (GPs) are powerful models for probabilistic machine learning, but good performance requires the selection of an appropriate covariance function. Process convolutions are framework for the construction of flexible covariances for both scalar and vector valued GPs, but still require choosing a smoothing kernel, which is non-trivial. Previous approaches have built covariance functions by using GP priors over the smoothing kernel, and by extension the covariance, as a way to bypass the need to specify it in advance. However, such models have been limited in several ways: they are restricted to single dimensional inputs, e.g. time; they only allow modeling of single outputs and they do not scale to large datasets since inference is not straightforward. In this talk I will discuss the development of sampling and inference methods for nonparametric process convolutions that resolve these limitations, and allow covariances to be inferred from data in a large variety of domains. Using these methods, I’ll discuss some extensions of process convolutions framework to the case of a nonlinear operators via the Volterra series, which result in non-Gaussian output processes, and allow for the development of powerful models for system identification. I will end by discussing the limitations of the framework, some ideas for future work.

Bio —- Magnus Ross is a third-year PhD student at the University of Manchester (and previously the University of Sheffield), working with Mauricio Álvarez and Michael Smith. His research interests center around Gaussian processes, and in particular their use for physics informed machine learning.