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Poster
Riemannian Score-Based Generative Modelling
Valentin De Bortoli · Emile Mathieu · Michael Hutchinson · James Thornton · Yee Whye Teh · Arnaud Doucet

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #908
in Poster Session 4 »

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance.Score-based generative modelling (SGM) consists of a noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails adenoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here \emph{Riemannian Score-based Generative Models} (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of compact manifolds, and in particular with earth and climate science spherical data.

Keywords: generative modeling · Riemannian Manifolds · diffusion models · score matching

Author Information

Valentin De Bortoli (ENS Ulm, CNRS)
Emile Mathieu (University of Cambridge)
Michael Hutchinson (University of Oxford)

Hi I'm Michael, a first year DPhil student at Oxford under the supervision of Yee Whye Teh and Max Welling. I'm interested in Probabalistic Machine Leanring in general, with a specific interests in distributed learning, generative modelling and uncertianty at a functional level.

James Thornton (None)
Yee Whye Teh (University of Oxford, DeepMind)

I am a Professor of Statistical Machine Learning at the Department of Statistics, University of Oxford and a Research Scientist at DeepMind. I am also an Alan Turing Institute Fellow and a European Research Council Consolidator Fellow. I obtained my Ph.D. at the University of Toronto (working with Geoffrey Hinton), and did postdoctoral work at the University of California at Berkeley (with Michael Jordan) and National University of Singapore (as Lee Kuan Yew Postdoctoral Fellow). I was a Lecturer then a Reader at the Gatsby Computational Neuroscience Unit, UCL, and a tutorial fellow at University College Oxford, prior to my current appointment. I am interested in the statistical and computational foundations of intelligence, and works on scalable machine learning, probabilistic models, Bayesian nonparametrics and deep learning. I was programme co-chair of ICML 2017 and AISTATS 2010.

Arnaud Doucet (Oxford)

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