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Probabilistic Numerics - a snapshot of an emerging community

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If you have a question about this talk, please contact Dr Jes Frellsen .

Numerical methods for tasks like quadrature, optimization, linear algebra and the solution of differential equations estimate latent quantities from the observed result of tractable computations. In this sense, they are learning machines, and accessible to the framework of probabilistic inference.

What started as an entertaining observation has, over the past few years, given rise to a small community of researchers studying probabilistic numerical methods that has begun to produce nontrivial findings. I will give a brief (and biased) overview of recent developments, emphasizing a string of results identifying classic numerical methods—Gaussian quadrature, conjugate gradients, BFGS , Runge-Kutta—with maximum a posteriori estimators.

Stirring potential applications, coupled with a stack of fundamental questions up for grabs, make probabilistic numerics an exciting area at the boundary between mathematics and computer science. Machine learning is ideally positioned to both contribute and benefit from these developments.

This talk is part of the Machine Learning @ CUED series.

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