Manifold Gaussian Processes for regression

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Calandra, R 
Peters, J 
Rasmussen, CE 
Deisenroth, MP 

Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and nondifferentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of the data by introducing a feature space. This feature space is often learned in an unsupervised way, which might lead to data representations that are not useful for the overall regression task. In this paper, we propose Manifold Gaussian Processes, a novel supervised method that jointly learns a transformation of the data into a feature space and a GP regression from the feature space to observed space. The Manifold GP is a full GP and allows to learn data representations, which are useful for the overall regression task. As a proof-of-concept, we evaluate our approach on complex non-smooth functions where standard GPs perform poorly, such as step functions and robotics tasks with contacts.

46 Information and Computing Sciences, 4611 Machine Learning, Generic health relevance
Journal Title
Proceedings of the International Joint Conference on Neural Networks
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2016 International Joint Conference on Neural Networks (IJCNN)
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Engineering and Physical Sciences Research Council (EP/J012300/1)
The research leading to these results has received funding from the European Council under grant agreement #600716 (CoDyCo - FP7/2007–2013). M. P. Deisenroth was supported by a Google Faculty Research Award.