Christopher K. I. Williams

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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)
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)
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)
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 two-class problem, the probability of class one given x is estimated by s(y(x)), where s(y) = 1/(1 + e-y). 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(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(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)