Exact learning curves for Gaussian process regression on large random graphs

author: Matthew Urry, Department of Mathematics, King's College London
published: March 25, 2011,   recorded: December 2010,   views: 253
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Description

We study learning curves for Gaussian process regression which characterise performance in terms of the Bayes error averaged over datasets of a given size. Whilst learning curves are in general very difficult to calculate we show that for discrete input domains, where similarity between input points is characterised in terms of a graph, accurate predictions can be obtained. These should in fact become exact for large graphs drawn from a broad range of random graph ensembles with arbitrary degree distributions where each input (node) is connected only to a finite number of others. The method is based on translating the appropriate belief propagation equations to the graph ensemble. We demonstrate the accuracy of the predictions for Poisson (Erdos-Renyi) and regular random graphs, and discuss when and why previous approximations to the learning curve fail.

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Download slides icon Download slides: nips2010_urry_elc_01.pdf (761.3 KB)

Download article icon Download article: nips2010_1079.pdf (324.2 KB)


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