Although one can derive the Gaussian noise assumption based on a maximum entropy approach, the main reason for this assumption is practicability: underthe Gaussian noise assumption the maximum likelihood parameter estimate can simply be found by minimization of the squared error. Despite its common use it is far from clear that the Gaussian noise assumption is a good choice for many practical problems. Areasonable approach therefore would be a noise distribution which contains the Gaussian as a special case but which has a tunable parameter that allows for more flexible distributions.

In this paper we will treat input selection for a radial basis function (RBF) like classifier within a Bayesian framework. We approximate the a-posteriori distribution over both model coefficients and input subsets by samples drawn with Gibbs updates and reversible jump moves. Using some public datasets, we compare the classification accuracy of the method with a conventional ARD scheme. These datasets are also used to infer the a-posteriori probabilities of different inputsubsets.

A system emulating the functionality of a moving eye-hence the name oculomotor system-has been built and successfully tested.

Everybody "knows" that neural networks need more than a single layer ofnonlinear units to compute interesting functions. We show that this is false if one employs winner-take-all as nonlinear unit: - Any boolean function can be computed by a single k-winner-takeall unitapplied to weighted sums of the input variables.

We describe a class of probabilistic models that we call credibility networks. Using parse trees as internal representations of images, credibility networks are able to perform segmentation and recognition simultaneously,removing the need for ad hoc segmentation heuristics. Promising results in the problem of segmenting handwritten digitswere obtained.

I consider a topographic projection between two neuronal layers with different densitiesof neurons. Given the number of output neurons connected toeach input neuron (divergence or fan-out) and the number of input neurons synapsing on each output neuron (convergence or fan-in) I determine the widths of axonal and dendritic arbors which minimize the total volume ofaxons and dendrites. My analytical results can be summarized qualitativelyin the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphology andconnectivity are known. The rule may be used to infer connectivity ofneurons from their morphology.

The speech waveform can be modelled as a piecewise-stationary linear stochastic state space system, and its parameters can be estimated using an expectation-maximisation (EM) algorithm. One problem is the initialisation ofthe EM algorithm. Standard initialisation schemes can lead to poor formant trajectories. But these trajectories however are important forvowel intelligibility. The aim of this paper is to investigate the suitability of subspace identification methods to initialise EM. The paper compares the subspace state space system identification (4SID) method with the EM algorithm. The 4SID and EM methods are similar in that they both estimate a state sequence (but using Kalman filters andKalman smoothers respectively), and then estimate parameters (but using least-squares and maximum likelihood respectively).

We consider the problem of reconstructing a temporal discrete sequence of multidimensional real vectors when part of the data is missing, under the assumption that the sequence was generated by a continuous process. Aparticular case of this problem is multivariate regression, which is very difficult when the underlying mapping is one-to-many. We propose analgorithm based on a joint probability model of the variables of interest, implemented using a nonlinear latent variable model. Each point in the sequence is potentially reconstructed as any of the modes of the conditional distribution of the missing variables given the present variables (computed using an exhaustive mode search in a Gaussian mixture). Modeselection is determined by a dynamic programming search that minimises a geometric measure of the reconstructed sequence, derived fromcontinuity constraints. We illustrate the algorithm with a toy example and apply it to a real-world inverse problem, the acoustic-toarticulatory mapping.The results show that the algorithm outperforms conditional mean imputation and multilayer perceptrons. 1 Definition of the problem

A fundamental problem with the modeling of chaotic time series data is that minimizing short-term prediction errors does not guarantee a match between the reconstructed attractors of model and experiments. We introduce a modeling paradigm that simultaneously learns to short-tenn predict and to locate the outlines of the attractor by a new way of nonlinear principal component analysis. Closed-loop predictions are constrained to stay within these outlines, to prevent divergence from the attractor. Learning is exceptionally fast: parameter estimation for the 1000 sample laser data from the 1991 Santa Fe time series competition took less than a minute on a 166 MHz Pentium PC.

A very simple model of two reciprocally connected attractor neural networks isstudied analytically in situations similar to those encountered in delay match-to-sample tasks with intervening stimuli and in tasks of memory guided attention. The model qualitatively reproduces many of the experimental data on these types of tasks and provides a framework for the understanding of the experimental observations in the context of the attractor neural network scenario.