We consider the problem of learning a grid-based map using a robot with noisy sensors and actuators. We compare two approaches: online EM, where the map is treated as a fixed parameter, and Bayesian inference, where the map is a (matrix-valued) random variable. We show that even on a very simple example, online EM can get stuck in local minima, which causes the robot to get "lost" and the resulting map to be useless. By contrast, the Bayesian approach, by maintaining multiple hypotheses, is much more robust. We then introduce a method for approximating the Bayesian solution, called Rao-Blackwellised particle filtering. We show that this approximation, when coupled with an active learning strategy, is fast but accurate.

In the analysis of data recorded by optical imaging from intrinsic signals of changes of light reflectance from cortical tissue) the removal(measurement of noise and artifacts such as blood vessel patterns is a serious problem. Often bandpass filtering is used, but the underlying assumption that a spatial frequency exists, which separates the mapping component from other components (especially the global signal), is questionable. Here we propose alternative ways of processing optical imaging data, using blind source separation techniques based on the spatial decorre1ation of the data. We first perform benchmarks on artificial data in order to select the way of processing, which is most robust with respect to sensor noise. We then apply it to recordings of optical imaging experiments BSS technique isfrom macaque primary visual cortex. We show that our able to extract ocular dominance and orientation preference maps from single condition stacks, for data, where standard post-processing procedures fail. Artifacts, especially blood vessel patterns, can often be completely removed from the maps. In summary, our method for blind source separation using extended spatial decorrelation is a superior technique for the analysis of optical recording data.

We present a new learning architecture: the Decision Directed Acyclic Graph (DDAG), which is used to combine many two-class classifiers into a multiclass classifier. For an N -class problem, the DDAG contains N(N-1)/2 classifiers, one for each pair of classes. We present a VC analysis of the case when the node classifiers are hyperplanes; the resulting boundon the test error depends on N and on the margin achieved at the nodes, but not on the dimension of the space. This motivates an algorithm, DAGSVM, which operates in a kernel-induced feature space and uses two-class maximal margin hyperplanes at each decision-node of the DDAG. The DAGSVM is substantially faster to train and evaluate thaneither the standard algorithm or Max Wins, while maintaining comparable accuracy to both of these algorithms. 1 Introduction The problem of multiclass classificatIon, especially for systems like SVMs, doesn't present an easy solution. It is generally simpler to construct classifier theory and algorithms for two mutually-exclusive classes than for N mutually-exclusive classes.

Gaussian mixtures (or so-called radial basis function networks) for density estimation provide a natural counterpart to sigmoidal neural networksfor function fitting and approximation. In both cases, it is possible to give simple expressions for the iterative improvement ofperformance as components of the network are introduced one at a time. In particular, for mixture density estimation we show that a k-component mixture estimated by maximum likelihood (or by an iterative likelihood improvement that we introduce) achieves log-likelihood within order 1/k of the log-likelihood achievable by any convex combination. Consequences for approximation and estimation usingKullback-Leibler risk are also given. A Minimum Description Length principle selects the optimal number of components kthat minimizes the risk bound. 1 Introduction In density estimation, Gaussian mixtures provide flexible-basis representations for densities that can be used to model heterogeneous data in high dimensions.

Zoubin Ghahramani and Matthew J. Beal Gatsby Computational Neuroscience Unit University College London 17 Queen Square, London WC1N 3AR, England {zoubin,m.beal}Ggatsby.ucl.ac.uk Abstract We present an algorithm that infers the model structure of a mixture offactor analysers using an efficient and deterministic variational approximationto full Bayesian integration over model parameters. Thisprocedure can automatically determine the optimal number of components and the local dimensionality of each component (Le. the number of factors in each factor analyser). Alternatively it can be used to infer posterior distributions over number of components and dimensionalities. Since all parameters are integrated out the method is not prone to overfitting. Using a stochastic procedure for adding components it is possible to perform thevariational optimisation incrementally and to avoid local maxima.

Transduction is an inference principle that takes a training sample andaims at estimating the values of a function at given points contained in the so-called working sample as opposed to the whole of input space for induction. Transduction provides a confidence measure on single predictions rather than classifiers - a feature particularly important for risk-sensitive applications. The possibly infinite number of functions is reduced to a finite number of equivalence classeson the working sample. A rigorous Bayesian analysis reveals that for standard classification loss we cannot benefit from considering more than one test point at a time. The probability of the label of a given test point is determined as the posterior measure of the corresponding subset of hypothesis space.

Three contributions to developing an algorithm for assisting engineers indesigning analog circuits are provided in this paper. First, a method for representing highly nonlinear and noncontinuous analog circuits using Kirchoff current law potential functions within the context of a Markov field is described. Second, a relatively efficient algorithmfor optimizing the Markov field objective function is briefly described and the convergence proof is briefly sketched. And third, empirical results illustrating the strengths and limitations ofthe approach are provided within the context of a JFET transistor design problem. The proposed algorithm generated a set of circuit components for the JFET circuit model that accurately generated the desired characteristic curves. 1 Analog circuit design using Markov random fields

We propose a new Markov Chain Monte Carlo algorithm which is a generalization ofthe stochastic dynamics method. The algorithm performs exploration of the state space using its intrinsic geometric structure, facilitating efficientsampling of complex distributions. Applied to Bayesian learning in neural networks, our algorithm was found to perform at least as well as the best state-of-the-art method while consuming considerably less time. 1 Introduction

In recent years, Bayesian networks have become highly successful tool for diagnosis, analysis,and decision making in real-world domains. We present an efficient algorithm for learning Bayes networks from data.

The support vector machine (SVM) is a state-of-the-art technique for regression and classification, combining excellent generalisation properties with a sparse kernel representation. However, it does suffer from a number of disadvantages, notably the absence of probabilistic outputs,the requirement to estimate a tradeoff parameter and the need to utilise'Mercer' kernel functions. In this paper we introduce the Relevance Vector Machine (RVM), a Bayesian treatment ofa generalised linear model of identical functional form to the SVM. The RVM suffers from none of the above disadvantages, and examples demonstrate that for comparable generalisation performance, theRVM requires dramatically fewer kernel functions.