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Searching for authors named "Christopher Williams" – sorted by Relevance.

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  • Computing With Infinite Networks  
  • by Christopher Williams — 1996 — Advances in Neural Information Processing Systems 9
  • …For neural networks with a wide class of weight-priors, it can be shown that in the limit of an infinite number of hidden units the prior over functions tends to a Gaussian process. In this paper analytic forms are derived for the covariance function of the Gaussian processes corresponding to networ…
  • Cited by 15 (2 self) – Add To MetaCart
  • Using the Nyström Method to Speed Up Kernel Machines  
  • by Christopher Williams, Matthias Seeger — 2001 — Advances in Neural Information Processing Systems 13
  • …A major problem for kernel-based predictors (such as Support Vector Machines and Gaussian processes) is that the amount of computation required to find the solution scales as O(n ), where n is the number of training examples. We show that an approximation to the eigendecomposition of the Gram matrix…
  • Cited by 139 (6 self) – Add To MetaCart
  • The Effect of the Input Density Distribution on Kernel-based Classifiers  
  • by Christopher Williams, Matthias Seeger — 2000 — Proceedings of the 17th International Conference on Machine Learning
  • …The eigenfunction expansion of a kernel function K(x, y) as used in support vector machines or Gaussian process predictors is studied when the input data is drawn from a distribution p(x). In this case it is shown that the eigenfunctions f i g obey the equation K(x, y)p(x) i (x)dx = i i (y). This ha…
  • Cited by 34 (5 self) – Add To MetaCart
  • Staging Transformations for Multimodal Web Interaction Management  
  • by Michael Narayan, Christopher Williams, Saverio Perugini, Naren Ramakrishnan — 2004
  • …Multimodal interfaces are becoming increasingly ubiquitous with the advent of mobile devices, accessibility considerations, and novel software technologies that combine diverse interaction media. In addition to improving access and delivery capabilities, such interfaces enable flexible and personali…
  • Cited by 8 (7 self) – Add To MetaCart
  • Computation With Infinite Neural Networks  
  • by Christopher K. I. Williams — 1997
  • …For neural networks with a wide class of weight priors, it can be shown that in the limit of an infinite number of hidden units the prior over functions tends to a Gaussian process. In this paper analytic forms are derived for the covariance function of the Gaussian processes corresponding to networ…
  • Cited by 14 (1 self) – Add To MetaCart
  • Regression with Gaussian Processes  
  • by Christopher K. I. Williams — 1995 — In Learning in Graphical Models. MIT
  • …The Bayesian analysis of neural networks is difficult because the prior over functions has a complex form, leading to implementations that either make approximations or use Monte Carlo integration techniques. In this paper I investigate the use of Gaussian process priors over functions, which per…
  • Cited by 13 (0 self) – Add To MetaCart
  • Combining Neural Networks and Belief Networks for Image Segmentation  
  • by Christopher K. I. Williams, Xiaojuan Feng — 1998
  • …In this paper we are concerned with segmenting an image into a number of predefined classes. We show how to fuse together local predictions for the class labels with a prior model of segmentations using the scaled-likelihood method. The prior model is based on a tree-structured belief network. B…
  • Cited by 8 (5 self) – Add To MetaCart
  • Training Bayesian networks for image segmentation  
  • by Xiaojuan Feng, Christopher K. I. Williams — 1998 — In Proceedings of SPIE
  • …We are concerned with the problem of image segmentation in which each pixel is assigned to one of a predefined finite number of classes. In Bayesian image analysis, this requires fusing together local predictions for the class labels with a prior model of segmentations. Markov Random Fields (MRFs) h…
  • Cited by 3 (1 self) – Add To MetaCart
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