McHutchon, A and Rasmussen, CE (2011) *Gaussian Process training with input noise.* Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011.

## 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.

Item Type: | Article |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Computational and Biological Learning |

Depositing User: | Cron job |

Date Deposited: | 16 Jul 2015 14:10 |

Last Modified: | 31 Aug 2015 10:13 |

DOI: |