We extend radial basis function (RBF) networks to the scenario in which multiple correlated tasks are learned simultaneously, and present the corresponding learningalgorithms. We develop the algorithms for learning the network structure, in either a supervised or unsupervised manner. Training data may also be actively selected to improve the network's generalization totest data. Experimental results based on real data demonstrate the advantage of the proposed algorithms and support our conclusions.

When trying to understand the brain, it is of fundamental importance to analyse (e.g. from EEG/MEG measurements) what parts of the cortex interact with each other in order to infer more accurate models of brain activity. Common techniques like Blind Source Separation (BSS) can estimate brainsources and single out artifacts by using the underlying assumption ofsource signal independence. However, physiologically interesting brain sources typically interact, so BSS will--by construction-- fail to characterize them properly. Noting that there are truly interacting sources and signals that only seemingly interact due to effects of volume conduction, this work aims to contribute by distinguishing these effects. For this a new BSS technique is proposed that uses anti-symmetrized cross-correlation matrices and subsequent diagonalization. The resulting decomposition consists of the truly interacting brain sources and suppresses anyspurious interaction stemming from volume conduction. Our new concept of interacting source analysis (ISA) is successfully demonstrated onMEG data.

MCMC offers no obvious way of approximating this wildly intractable sum [5, 8].

We present a new kernel method for extracting semantic relations between entitiesin natural language text, based on a generalization of subsequence kernels.This kernel uses three types of subsequence patterns that are typically employed in natural language to assert relationships between two entities. Experiments on extracting protein interactions from biomedical corpora and top-level relations from newspaper corpora demonstrate the advantages of this approach.

The problem of resource allocation in sparse graphs with real variables is studied using methods of statistical physics. An efficient distributed algorithm is devised on the basis of insight gained from the analysis and is examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

Gaussian processes are attractive models for probabilistic classification but unfortunately exact inference is analytically intractable. We compare Laplace's method and Expectation Propagation (EP) focusing on marginal likelihood estimates and predictive performance. We explain theoretically and corroborate empirically that EP is superior to Laplace. We also compare to a sophisticated MCMC scheme and show that EP is surprisingly accurate. In recent years models based on Gaussian process (GP) priors have attracted much attention in the machine learning community. Whereas inference in the GP regression model with Gaussian noise can be done analytically, probabilistic classification using GPs is analytically intractable. Several approaches to approximate Bayesian inference have been suggested, including Laplace's approximation, Expectation Propagation (EP), variational approximations and Markov chain Monte Carlo (MCMC) sampling, some of these in conjunction with generalisation bounds, online learning schemes and sparse approximations. Despite the abundance of recent work on probabilistic GP classifiers, most experimental studies provide only anecdotal evidence, and no clear picture has yet emerged, as to when and why which algorithm should be preferred.

There have been many graph-based approaches for semi-supervised classification. Oneproblem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, transformation ofthe graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semisupervised classification.Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an inference problemover the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification. The hyperparameters are learned using EM for evidence maximization. We also show that the posterior mean can be written in terms of the kernel matrix, providing a Bayesian classifier to classify new points. Tests on synthetic and real datasets show cases where there are significant improvements in performance over the existing approaches.

We consider the case in which the true distribution is contained in the learner model.

This paper describes a highly successful application of MRFs to the problem ofgenerating high-resolution range images. A new generation of range sensors combines the capture of low-resolution range images with the acquisition of registered high-resolution camera images. The MRF in this paper exploits the fact that discontinuities in range and coloring tend to co-align. This enables it to generate high-resolution, low-noise range images by integrating regular camera images into the range data. We show that by using such an MRF, we can substantially improve over existing range imaging technology.

This paper addresses the issue of numerical computation in machine learning domains based on similarity metrics, such as kernel methods, spectral techniques and Gaussian processes. It presents a general solution strategybased on Krylov subspace iteration and fast N-body learning methods. The experiments show significant gains in computation and storage on datasets arising in image segmentation, object detection and dimensionality reduction. The paper also presents theoretical bounds on the stability of these methods.