University of Cambridge > Talks.cam > Microsoft Research Cambridge, public talks > MSR-Lecture: Gaussian Processes for Pattern Discovery, Speaker: Andrew Wilson

MSR-Lecture: Gaussian Processes for Pattern Discovery, Speaker: Andrew Wilson

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Bayesian nonparametrics has the power to capture the infinite complexity in the real world, and could be used to explain how biological intelligence is capable of making extraordinary generalisations from a small number of examples. Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. When the large nonparametric support of a Gaussian process is combined with the ability to automatically discover patterns in data and extrapolate, we are a step closer to developing truly intelligent agents, with applications in essentially any learning and prediction task.

In this talk, I derive simple closed form kernels that can be used with Gaussian processes, and other kernel machines, to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density—the Fourier transform of a kernel—with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. I demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. I also show that we can reconstruct standard covariances within the proposed framework.

This is joint work with Ryan P. Adams. A pre-print is available at http://arxiv.org/pdf/1302.4245v2, and through my website, http://mlg.eng.cam.ac.uk/andrew

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