Christopher K. I. Williams

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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)
The Pascal Visual Object Classes (VOC) challenge is a benchmark in visual object category recognition and detection, providing the vision and machine learning communities with a standard dataset of images and annotation, and standard evaluation procedures. Organised annually from 2005 to present, the challenge and its associated dataset has become accepted(More)
Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis, which is based on a linear transformation between the latent space and the data space. In this article, we introduce a form of nonlinear latent variable model(More)
The Pascal Visual Object Classes (VOC) challenge consists of two components: (i) a publicly available dataset of images together with ground truth annotation and standardised evaluation software; and (ii) an annual competition and workshop. There are five challenges: classification, detection, segmentation, action classification, and person layout. In this(More)
In this paper we investigate multi-task learning in the context of Gaussian Processes (GP). We propose a model that learns a shared covariance function on input-dependent features and a “free-form” covariance matrix over tasks. This allows for good flexibility when modelling inter-task dependencies while avoiding the need for large amounts of data for(More)
We consider the problem of assigning an input vector to one of m classes by predicting P(c|x) for c = 1, o, m. For a twoclass problem, the probability of class one given x is estimated by s(y(x)), where s(y) = 1/(1 + ey ). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points. We provide a(More)
The main aim of this paper is to provide a tutorial on regression with Gaussian processes We start from Bayesian linear regression and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions rather than on priors over parameters This leads in to a more general discussion of Gaussian processes(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 to(More)