This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors.

We present a computationally efficient algorithm for function approximation with piecewise linear sigmoidal nodes. A one hidden layer network is constructed one node at a time using the method of fitting the residual. The task of fitting individual nodes is accomplished using a new algorithm that searchs for the best fit by solving a sequence of Quadratic Programming problems. This approach offers significant advantages over derivative-based search algorithms (e.g.

Until recently, artificial intelligence researchers have frowned upon the application of probability propagation in Bayesian belief networks that have 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 are actually 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.

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.

A simple linear averaging of the outputs of several networks as e.g. in bagging [3], seems to follow naturally from a bias/variance decomposition of the sum-squared error. The sum-squared error of the average model is a quadratic function of the weighting factors assigned to the networks in the ensemble [7], suggesting a quadratic programming algorithm for finding the "optimal" weighting factors. If we interpret the output of a network as a probability statement, the sum-squared error corresponds to minus the loglikelihood or the Kullback-Leibler divergence, and linear averaging of the outputs to logarithmic averaging of the probability statements: the logarithmic opinion pool. The crux of this paper is that this whole story about model averaging, bias/variance decompositions, and quadratic programming to find the optimal weighting factors, is not specific for the sumsquared error, but applies to the combination of probability statements of any kind in a logarithmic opinion pool, as long as the Kullback-Leibler divergence plays the role of the error measure. As examples we treat model averaging for classification models under a cross-entropy error measure and models for estimating variances.

This paper presents a new approach to the problem of modelling daily rainfall using neural networks. We first model the conditional distributions of rainfall 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, we are 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.

Image intensity variations can result from several different object surface effects, including shading from 3-dimensional relief of the object, or paint on the surface itself. An essential problem in vision, which people solve naturally, is to attribute the proper physical cause, e.g.

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 match and by effecting optimisation using the EM algorithm. According to our EM framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood perspective pose parameters. This provides a means of rejecting structural outliers.

We apply information maximization / maximum likelihood blind source separation [2, 6) to complex valued signals mixed with complex valued nonstationary matrices. This case arises in radio communications with baseband signals. We incorporate known source signal distributions in the adaptation, thus making the algorithms less "blind". This results in drastic reduction of the amount of data needed for successful convergence. Adaptation to rapidly changing signal mixing conditions, such as to fading in mobile communications, becomes now feasible as demonstrated by simulations. 1 Introduction In SDMA (spatial division multiple access) the purpose is to separate radio signals of interfering users (either intentional or accidental) from each others on the basis of the spatial characteristics of the signals using smart antennas, array processing, and beamforming [5, 8).

Department of Cognitive Science Department of Cognitive Science University of California, San Diego University of California, San Diego La Jolla, CA 92092-0515 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 a principled 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, and the 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.