PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Gaussian Process Training with Input Noise
Andrew McHutchon and Carl Edward Rasmussen
In: NIPS 2011, 12-17th December 2011, Granada, Spain.

Abstract

In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d. Gaussian noise. To make computations tractable we use a local linear expansion about each input point. This allows the input noise to be recast as output noise proportional to the squared gradient of the GP posterior mean. The input noise variances are inferred from the data as extra hyperparameters. They are trained alongside other hyperparameters by the usual method of maximisation of the marginal likelihood. Training uses an iterative scheme, which alternates between optimising the hyperparameters and calculating the posterior gradient. Analytic predictive moments can then be found for Gaussian distributed test points. We compare our model to others over a range of different regression problems and show that it improves over current methods.

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EPrint Type:Conference or Workshop Item (Poster)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:8456
Deposited By:Andrew McHutchon
Deposited On:19 January 2012