Bayesian methods have been successfully applied to regression and classification problems in multi-layer perceptrons. We present a novel application of Bayesian techniques to Radial Basis Function networks by developing a Gaussian approximation to the posterior distribution which, for fixed basis function widths, is analytic in the parameters. The setting of regularization constants by crossvalidation is wasteful as only a single optimal parameter estimate is retained. We treat this issue by assigning prior distributions to these constants, which are then adapted in light of the data under a simple re-estimation formula. 1 Introduction Radial Basis Function networks are popular regression and classification tools[lO]. For fixed basis function centers, RBFs are linear in their parameters and can therefore be trained with simple one shot linear algebra techniques[lO]. The use of unsupervised techniques to fix the basis function centers is, however, not generally optimal since setting the basis function centers using density estimation on the input data alone takes no account of the target values associated with that data. Ideally, therefore, we should include the target values in the training procedure[7, 3, 9]. Unfortunately, allowing centers to adapt to the training targets leads to the RBF being a nonlinear function of its parameters, and training becomes more problematic. Most methods that perform supervised training of RBF parameters minimize the ·Present address: SNN, University of Nijmegen, Geert Grooteplein 21, Nijmegen, The Netherlands.

Our aim in this paper is to develop a Bayesian framework for matching hierarchicalrelational models. The goal is to make discrete label assignments so as to optimise a global cost function that draws information concerning the consistency of match from different levels ofthe hierarchy.

Peter M Williams School of Cognitive and Computing Sciences University of Sussex Falmer, Brighton BN1 9QH, UK. email: peterw@cogs.susx.ac.uk Abstract This paper presents a new approach to the problem of modelling daily rainfall using neural networks. We first model the conditional distributions ofrainfall amounts, in such a way that the model itself determines the order of the process, and the time-dependent shape and scale of the conditional distributions. After integrating over particular weather patterns, weare able to extract seasonal variations and long-term trends. 1 Introduction Analysis of rainfall data is important for many agricultural, ecological and engineering activities. Design of irrigation and drainage systems, for instance, needs to take account not only of mean expected rainfall, but also of rainfall volatility. Estimates of crop yields also depend on the distribution of rainfall during the growing season, as well as on the overall amount.

Department of Cognitive Science University of California, San Diego La Jolla, CA 92092-0515 Abstract We discuss the problem of catastrophic fusion in multimodal recognition systems.This problem arises in systems that need to fuse different channels in non-stationary environments. Practice shows that when recognition modules within each modality are tested in contexts inconsistent with their assumptions, their influence on the fused product tends to increase, with catastrophic results. We explore aprincipled solution to this problem based upon Bayesian ideas of competitive models and inference robustification: each sensory channel is provided with simple white-noise context models, andthe perceptual hypothesis and context are jointly estimated. Consequently,context deviations are interpreted as changes in white noise contamination strength, automatically adjusting the influence of the module. The approach is tested on a fixed lexicon automatic audiovisual speech recognition problem with very good results. 1 Introduction In this paper we address the problem of catastrophic fusion in automatic multimodal recognition systems.

In contrast to the maximum likelihood approach which finds only a single estimate for the regression parameters, the Bayesian approach yields a distribution of weight parameters, p(wID), conditional on the training data D, and predictions are ex- ·Present address: SNN, University of Nijmegen, Geert Grooteplein 21, Nijmegen, The Netherlands.

Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112 Abstract We propose diffusion networks, a type of recurrent neural network with probabilistic dynamics, as models for learning natural signals that are continuous in time and space. We give a formula for the gradient of the log-likelihood of a path with respect to the drift parameters for a diffusion network. This gradient can be used to optimize diffusion networks in the nonequilibrium regime for a wide variety of problems paralleling techniques which have succeeded in engineering fields such as system identification, state estimation and signal filtering. An aspect of this work which is of particular interestto computational neuroscience and hardware design is that with a suitable choice of activation function, e.g., quasi-linear sigmoidal, the gradient formula is local in space and time. 1 Introduction Many natural signals, like pixel gray-levels, line orientations, object position, velocity andshape parameters, are well described as continuous-time continuous-valued stochastic processes; however, the neural network literature has seldom explored the continuous stochastic case. Since the solutions to many decision theoretic problems of interest are naturally formulated using probability distributions, it is desirable to have a flexible framework for approximating probability distributions on continuous pathspaces.

Department of Physics, Cavendish Laboratory Cambridge University Abstract Until recently, artificial intelligence researchers have frowned upon the application of probability propagation in Bayesian belief networks thathave cycles. The probability propagation algorithm is only exact in networks that are cycle-free. However, it has recently been discovered that the two best error-correcting decoding algorithms areactually performing probability propagation in belief networks with cycles. 1 Communicating over a noisy channel Our increasingly wired world demands efficient methods for communicating bits of information over physical channels that introduce errors. Examples of real-world channels include twisted-pair telephone wires, shielded cable-TV wire, fiberoptic cable, deep-space radio, terrestrial radio, and indoor radio. Engineers attempt to correct the errors introduced by the noise in these channels through the use of channel coding which adds protection to the information source, so that some channel errors can be corrected.

We consider the general problem of learning multi-category classification fromlabeled examples. We present experimental results for a nearest neighbor algorithm which actively selects samples from different pattern classes according to a querying rule instead of the a priori class probabilities. The amount of improvement of this query-based approach over the passive batch approach depends on the complexity of the Bayes rule. The principle on which this algorithm isbased is general enough to be used in any learning algorithm which permits a model-selection criterion and for which the error rate of the classifier is calculable in terms of the complexity of the model. 1 INTRODUCTION We consider the general problem of learning multi-category classification from labeled examples.In many practical learning settings the time or sample size available for training are limited. This may have adverse effects on the accuracy of the resulting classifier.For instance, in learning to recognize handwritten characters typical time limitation confines the training sample size to be of the order of a few hundred examples. It is important to make learning more efficient by obtaining only training data which contains significant information about the separability of the pattern classes thereby letting the learning algorithm participate actively in the sampling process. Querying for the class labels of specificly selected examples in the input space may lead to significant improvements in the generalization error (cf.

This paper describes a new approach to extracting 3D perspective structure from 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying pointcorrespondence matches.Unification is realised by constructing a mixture model over the bipartite graph representing the correspondence matchand by effecting optimisation using the EM algorithm. According to our EM framework the probabilities of structural correspondence gatecontributions to the expected likelihood function used to estimate maximum likelihood perspective pose parameters. This provides a means of rejecting structural outliers.

Prioritized sweeping is a model-based reinforcement learning method that attempts to focus an agent's limited computational resources to achieve a good estimate of the value of environment states. To choose effectively whereto spend a costly planning step, classic prioritized sweeping uses a simple heuristic to focus computation on the states that are likely to have the largest errors. In this paper, we introduce generalized prioritized sweeping, a principled method for generating such estimates in a representation-specific manner. This allows us to extend prioritized sweeping beyond an explicit, state-based representation to deal with compact representationsthat are necessary for dealing with large state spaces. We apply this method for generalized model approximators (such as Bayesian networks), and describe preliminary experiments that compare our approach with classical prioritized sweeping.