The 2-class transduction problem, as formulated by Vapnik [1], involves finding a separating hyperplane for a labelled data set that is also maximally distant from a given set of unlabelled test points. In this form, the problem has exponential computational complexity in the size of the working set. So far it has been attacked by means of integer programming techniques [2] that do not scale to reasonable problem sizes, or by local search procedures [3]. In this paper we present a relaxation of this task based on semidefinite programming (SDP), resulting in a convex optimization problem that has polynomial complexity in the size of the data set. The results are very encouraging for mid sized data sets, however the cost is still too high for large scale problems, due to the high dimensional search space. To this end, we restrict the feasible region by introducing an approximation based on solving an eigenproblem. With this approximation, the computational cost of the algorithm is such that problems with more than 1000 points can be treated.

This allows for non-Gaussian processes and non-Gaussian noise. The learning algorithm chooses a nonlinear transformation such that transformed data is well-modelled by a GP. This can be seen as including a preprocessing transformation as an integral part of the probabilistic modelling problem, rather than as an ad-hoc step. We demonstrate on several real regression problems that learning the transformation can lead to significantly better performance than using a regular GP, or a GP with a fixed transformation.

We consider situations where training data is abundant and computing resources are comparatively scarce. We argue that suitably designed online learning algorithms asymptotically outperform any batch learning algorithm. Both theoretical and experimental evidences are presented.

In this paper we introduce a new underlying probabilistic model for principal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior's covariance function constrains the mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance functions which allow nonlinear mappings. This more general Gaussian process latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our nonlinear algorithm can be further kernelised leading to'twin kernel PCA' in which a mapping between feature spaces occurs.

In this article, we present a novel approach to solving the localization problem in cellular networks. The goal is to estimate a mobile user's position, based on measurements of the signal strengths received from network base stations. Our solution works by building Gaussian process models for the distribution of signal strengths, as obtained in a series of calibration measurements. In the localization stage, the user's position can be estimated by maximizing the likelihood of received signal strengths with respect to the position. We investigate the accuracy of the proposed approach on data obtained within a large indoor cellular network.

There exist many different generalization error bounds for classification. Each of these bounds contains an improvement over the others for certain situations. Our goal is to combine these different improvements into a single bound. In particular we combine the PAC-Bayes approach introduced by McAllester [1], which is interesting for averaging classifiers, with the optimal union bound provided by the generic chaining technique developed by Fernique and Talagrand [2]. This combination is quite natural since the generic chaining is based on the notion of majorizing measures, which can be considered as priors on the set of classifiers, and such priors also arise in the PACbayesian setting.

Is there a way for an algorithm linked to an unknown body to infer by itself information about this body and the world it is in? Taking the case of space for example, is there a way for this algorithm to realize that its body is in a three dimensional world? Is it possible for this algorithm to discover how to move in a straight line? And more basically: do these questions make any sense at all given that the algorithm only has access to the very high-dimensional data consisting of its sensory inputs and motor outputs? We demonstrate in this article how these questions can be given a positive answer. We show that it is possible to make an algorithm that, by analyzing the law that links its motor outputs to its sensory inputs, discovers information about the structure of the world regardless of the devices constituting the body it is linked to. We present results from simulations demonstrating a way to issue motor orders resulting in "fundamental" movements of the body as regards the structure of the physical world.

A common way of image denoising is to project a noisy image to the subspace of admissible images made for instance by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion.

Super-resolution aims to produce a high-resolution image from a set of one or more low-resolution images by recovering or inventing plausible high-frequency image content. Typical approaches try to reconstruct a high-resolution image using the sub-pixel displacements of several lowresolution images, usually regularized by a generic smoothness prior over the high-resolution image space. Other methods use training data to learn low-to-high-resolution matches, and have been highly successful even in the single-input-image case. Here we present a domain-specific image prior in the form of a p.d.f.

We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.