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Many applications require optimizing an unknown , noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence(More)
We present a method for the sparse greedy approximation of Bayesian Gaussian process regression, featuring a novel heuristic for very fast forward selection. Our method is essentially as fast as an equivalent one which selects the " support " patterns at random, yet it can outperform random selection on hard curve fitting tasks. More importantly, it leads(More)
In this paper, on the one hand, we aim to give a review on literature dealing with the problem of supervised learning aided by additional unla-beled data. On the other hand, being a part of the author's first year PhD report, the paper serves as a frame to bundle related work by the author as well as numerous suggestions for potential future work.(More)
We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on information-theoretic principles, previously suggested for active learning. Our goal is not only to learn d–sparse predictors (which can be evaluated in O(d) rather than O(n), d n, n the number of training points), but also to perform training(More)
The linear model with sparsity-favouring prior on the coefficients has important applications in many different domains. In machine learning, most methods to date search for maximum a posteriori sparse solutions and neglect to represent posterior uncertainties. In this paper, we address problems of Bayesian optimal design (or experiment planning), for which(More)
This is a tutorial describing the Expectation Propagation (EP) algorithm for a general exponential family. Our focus is on simplicity of exposition. Although the overhead of translating a specific model into its exponential family representation can be considerable , many apparent complications of EP can simply be sidestepped by working in this canonical(More)
—Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low norm in a reproducing kernel Hilbert space. We resolve the important open problem of deriving regret bounds for this(More)
The computation required for Gaussian process regression with n training examples is about O(n 3) during training and O(n) for each prediction. This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of(More)