PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Variable noise and dimensionality reduction for sparse Gaussian processes
Ed Snelson and Zoubin Ghahramani
In: UAI 2006, Boston, USA(2006).

Abstract

The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M `pseudo-inputs', thereby reducing complexity from O(N^3) to O(M^2 N). One limitation of the SPGP is that this optimization space becomes impractically big for high dimensional data sets. This paper addresses this limitation by performing automatic dimensionality reduction. A projection of the input space to a low dimensional space is learned in a supervised manner, alongside the pseudo-inputs, which now live in this reduced space. The paper also investigates the suitability of the SPGP for modeling data with input-dependent noise. A further extension of the model is made to make it even more powerful in this regard -- we learn an uncertainty parameter for each pseudo-input. The combination of sparsity, reduced dimension, and input-dependent noise makes it possible to apply GPs to much larger and more complex data sets than was previously practical. We demonstrate the benefits of these methods on several synthetic and real world problems.

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EPrint Type:Conference or Workshop Item (Spotlight)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2918
Deposited By:Ed Snelson
Deposited On:23 November 2006