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Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received growing attention in the machine learning community over the past decade. The book provides a long-needed, systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is(More)
Two features distinguish the Bayesian approach to learning models from data. First, beliefs derived from background knowledge are used to select a prior probability distribution for the model parameters. Second, predictions of future observations are made by integrating the model's predictions with respect to the posterior parameter distribution obtained by(More)
In a Bayesian mixture model it is not necessary a priori to limit the number of components to be finite. In this paper an infinite Gaussian mixture model is presented which neatly sidesteps the difficult problem of finding the " right " number of mixture components. Inference in the model is done using an efficient parameter-free Markov Chain that relies(More)
We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the methods are using. This allows new insights to be gained, and highlights the relationship between existing methods. It also allows for a clear theoretically(More)
This thesis develops two Bayesian learning methods relying on Gaussian processes and a rigorous statistical approach for evaluating such methods. In these experimental designs the sources of uncertainty in the estimated generalisation performances due to both variation in training and test sets are accounted for. The framework allows for estimation of(More)
In this paper, we introduce pilco, a practical , data-efficient model-based policy search method. Pilco reduces model bias, one of the key problems of model-based reinforcement learning, in a principled way. By learning a probabilistic dynamics model and explicitly incorporating model uncertainty into long-term planning, pilco can cope with very little data(More)
Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques have been proposed. In this work we review and compare Laplace's method and Expectation Propagation for approximate Bayesian inference in the binary Gaussian(More)
We present a new sparse Gaussian Process (GP) model for regression. The key novel idea is to sparsify the spectral representation of the GP. This leads to a simple, practical algorithm for regression tasks. We compare the achievable trade-offs between predictive accuracy and computational requirements, and show that these are typically superior to existing(More)