Sparse Multiscale Gaussian Process Regression

author: Christian Walder, Max Planck Institute for Biological Cybernetics, Max Planck Institute
published: July 29, 2008,   recorded: July 2008,   views: 5482


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Most existing sparse Gaussian process (g.p.) models seek computational advantages by basing their computations on a set of m basis functions that are the covariance function of the g.p. with one of its two inputs fixed. We generalise this for the case of Gaussian covariance function, by basing our computations on m Gaussian basis functions with arbitrary diagonal covariance matrices (or length scales). For a fixed number of basis functions and any given criteria, this additional flexibility permits approximations no worse and typically better than was previously possible. We perform gradient based optimisation of the marginal likelihood, which costs O(m2n) time where n is the number of data points, and compare the method to various other sparse g.p. methods. Although we focus on g.p. regression, the central idea is applicable to all kernel based algorithms, and we also provide some results for the support vector machine (s.v.m.) and kernel ridge regression (k.r.r.). Our approach outperforms the other methods, particularly for the case of very few basis functions, i.e. a very high sparsity ratio.

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Reviews and comments:

Comment1 Paul Goodhew, January 15, 2010 at 12:01 a.m.:

Christian, a very interesting paper.

Comment2 Jason Emery, May 7, 2011 at 12:38 p.m.:

Good to see you're using that massive fuckin brain dude. Well done.

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