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- Bernhard Schölkopf, John C. Platt, John Shawe-Taylor, Alexander J. Smola, Robert C. Williamson
- Neural Computation
- 2001

Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f… (More)

- Bernhard Schölkopf, Alexander J. Smola, Robert C. Williamson, Peter L. Bartlett
- Neural Computation
- 2000

We describe a new class of Support Vector algorithms for regression and classiication. In these algorithms, a parameter lets one eectively control the number of Support Vectors. While this can be useful in its own right, the parametrization has the additional beneet of enabling us to eliminate one of the other free parameters of the algorithm: the accuracy… (More)

- Jyrki Kivinen, Alexander J. Smola, Robert C. Williamson
- IEEE Transactions on Signal Processing
- 2001

Kernel-based algorithms such as support vector machines have achieved considerable success in various problems in batch setting, where all of the training data is available in advance. Support vector machines combine the so-called kernel trick with the large margin idea. There has been little use of these methods in an online setting suitable for real-time… (More)

Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a " simple " subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified between 0 and 1. We propose a method to approach this problem by trying to estimate a function f which… (More)

- John Shawe-Taylor, Peter L. Bartlett, Robert C. Williamson, Martin Anthony
- IEEE Trans. Information Theory
- 1998

The paper introduces some generalizations of Vapnik's method of structural risk min-imisation (SRM). As well as making explicit some of the details on SRM, it provides a result that allows one to trade off errors on the training sample against improved generalization performance. It then considers the more general case when the hierarchy of classes is… (More)

- Darren B. Ward, Eric A. Lehmann, Robert C. Williamson
- IEEE Trans. Speech and Audio Processing
- 2003

—Traditional acoustic source localization algorithms attempt to find the current location of the acoustic source using data collected at an array of sensors at the current time only. In the presence of strong multipath, these traditional algorithms often erroneously locate a multipath reflection rather than the true source location. A recently proposed… (More)

- Robert C. Williamson, Tom Downs
- Int. J. Approx. Reasoning
- 1990

Probabilistic arithmetic involves the calculation of the distribution of arithmetic functions of random variables. This work on probabilistic arithmetic began as an investigation into the possibility of adapting existing numerical procedures (devel-opal for fixed numbers) to handle random variables (by replacing the basic operations of arithmetic by the… (More)

- Wee Sun Lee, Peter L. Bartlett, Robert C. Williamson
- IEEE Trans. Information Theory
- 1996

We show that the class of two layer neural networks with bounded fan-in is eeciently learn-able in a realistic extension to the Probably Approximately Correct (PAC) learning model. In this model, a joint probability distribution is assumed to exist on the observations and the learner is required to approximate the neural network which minimizes the expected… (More)

- Cheng Soon Ong, Alexander J. Smola, Robert C. Williamson
- Journal of Machine Learning Research
- 2005

This paper addresses the problem of choosing a kernel suitable for estimation with a Support Vector Machine, hence further automating machine learning. This goal is achieved by defining a Reproducing Kernel Hilbert Space on the space of kernels itself. Such a formulation leads to a statistical estimation problem very much akin to the problem of minimizing a… (More)

- Biljana D. Radlovic, Robert C. Williamson, Rodney A. Kennedy
- IEEE Trans. Speech and Audio Processing
- 2000

This paper investigates the robustness of sound equalization using a room response inverse lter with respect to changing or uncertain source or microphone positions. It is shown that due to the variations of the transfer function from point t o p o i n t i n a r o o m , e v en small changes in the source or microphone position of just a few tenths of the… (More)