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Poster
Bezier Gaussian Processes for Tall and Wide Data
Martin Jørgensen · Michael A Osborne

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #811

Modern approximations to Gaussian processes are suitable for tall data'', with a cost that scales well in the number of observations, but under-performs onwide data'', scaling poorly in the number of input features. That is, as the number of input features grows, good predictive performance requires the number of summarising variables, and their associated cost, to grow rapidly. We introduce a kernel that allows the number of summarising variables to grow exponentially with the number of input features, but requires only linear cost in both number of observations and input features. This scaling is achieved through our introduction of the Bezier buttress'', which allows approximate inference without computing matrix inverses or determinants. We show that our kernel has close similarities to some of the most used kernels in Gaussian process regression, and empirically demonstrate the kernel's ability to scale to both tall and wide datasets.

#### Author Information

##### Martin Jørgensen (University of Oxford)

I am a postdoctoral researcher at the University of Oxford and a Junior Research Fellow at Linacre College. Since April 2021 I have worked with Michael Osborne’s Bayesian Exploration Lab. Before that I was a PhD student under Søren Hauberg at the Technical University of Denmark. Research Interests: Gaussian Processes, Variational Bayesian Inference, Differential Geometry for Representation Learning, Bayesian Quadrature and Optimisation, Sample-efficienct methods