This paper describes how the early visual process of contour organisation canbe realised using the EM algorithm. The underlying computational representation is based on fine spline coverings. According toour EM approach the adjustment of spline parameters draws on an iterative weighted least-squares fitting process. The expectation step of our EM procedure computes the likelihood of the data using a mixture model defined over the set of spline coverings. Thesesplines are limited in their spatial extent using Gaussian windowing functions.

Local disparity information is often sparse and noisy, which creates two conflicting demands when estimating disparity in an image region: theneed to spatially average to get an accurate estimate, and the problem of not averaging over discontinuities. We have developed anetwork model of disparity estimation based on disparityselective neurons,such as those found in the early stages of processing in visual cortex. The model can accurately estimate multiple disparities in a region, which may be caused by transparency or occlusion, inreal images and random-dot stereograms. The use of a selection mechanism to selectively integrate reliable local disparity estimates results in superior performance compared to standard back-propagation and cross-correlation approaches. In addition, the representations learned with this selection mechanism are consistent withrecent neurophysiological results of von der Heydt, Zhou, Friedman, and Poggio [8] for cells in cortical visual area V2. Combining multi-scale biologically-plausible image processing with the power of the mixture-of-experts learning algorithm represents a promising approach that yields both high performance and new insights into visual system function.

An adaptive online algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gradient flowinformation it can be applied to learning continuous functions or distributions, even when no explicit loss function is given andthe Hessian is not available. Its efficiency is demonstrated for a non-stationary blind separation task of acoustic signals. 1 Introduction Neural networks provide powerful tools to capture the structure in data by learning. Often the batch learning paradigm is assumed, where the learner is given all training examplessimultaneously and allowed to use them as often as desired. In large practical applications batch learning is often experienced to be rather infeasible and instead online learning is employed.

When triangulating a belief network we aim to obtain a junction tree of minimum state space. According to (Rose, 1970), searching for the optimal triangulation can be cast as a search over all the permutations of the graph's vertices. Our approach is to embed the discrete set of permutations in a convex continuous domain D. By suitably extending the cost function over D and solving the continous nonlinear optimization task we hope to obtain a good triangulation with respect to the aformentioned cost. This paper presents two ways of embedding the triangulation problem into continuous domain and shows that they perform well compared to the best known heuristic.

Department of Brain and Cognitive Sciences Massachusetts Institute of Technology Cambridge, MA 02139 Abstract We develop a recursive node-elimination formalism for efficiently approximating large probabilistic networks. No constraints are set on the network topologies. Yet the formalism can be straightforwardly integratedwith exact methods whenever they are/become applicable. The approximations we use are controlled: they maintain consistentlyupper and lower bounds on the desired quantities at all times. We show that Boltzmann machines, sigmoid belief networks, or any combination (i.e., chain graphs) can be handled within the same framework.

I describe a querying criterion that attempts to minimize the error of a learner by minimizing its estimated squared bias. I describe experiments with locally-weighted regression on two simple problems, andobserve that this "bias-only" approach outperforms the more common "variance-only" exploration approach, even in the presence of noise.

A modification is described to the use of mean field approximations inthe E step of EM algorithms for analysing data from latent structure models, as described by Ghahramani (1995), among others. Themodification involves second-order Taylor approximations to expectations computed in the E step. The potential benefits of the method are illustrated using very simple latent profile models. 1 Introduction Ghahramani (1995) advocated the use of mean field methods as a means to avoid the heavy computation involved in the E step of the EM algorithm used for estimating parameters within a certain latent structure model, and Ghahramani & Jordan (1995) used the same ideas in a more complex situation. Dunmur & Titterington (1996a) identified Ghahramani's model as a so-called latent profile model, they observed that Zhang (1992,1993) had used mean field methods for a similar purpose, and they showed, in a simulation study based on very simple examples, that the mean field version of the EM algorithm often performed very respectably. By this it is meant that, when data were generated from the model under analysis, the estimators of the underlying parameters were efficient, judging by empirical results, especially in comparison with estimators obtained by employing the'correct' EM algorithm: the examples therefore had to be simple enough that the correct EM algorithm is numerically feasible, although any success reported for the mean field 432 A. P. Dunmur and D. M. Titterington version is, one hopes, an indication that the method will also be adequate in more complex situations in which the correct EM algorithm is not implementable because of computational complexity. In spite of the above positive remarks, there were circumstances in which there was a perceptible, if not dramatic, lack of efficiency in the simple (naive) mean field estimators, and the objective of this contribution is to propose and investigate ways of refining the method so as to improve performance without detracting from the appealing, and frequently essential, simplicity of the approach. The procedure used here is based on a second order correction to the naive mean field well known in statistical physics and sometimes called the cavity or TAP method (Mezard, Parisi & Virasoro, 1987). It has been applied recently in cluster analysis (Hofmann & Buhmann, 1996). In Section 2 we introduce the structure of our model, Section 3 explains the refined mean field approach, Section 4 provides numerical results, and Section 5 contains a statement of our conclusions.

By now it is widely accepted that learning a task from scratch, i.e., without any prior knowledge, is a daunting undertaking.

Constructing amulti-layered neural network with fixed architecture which implements orientation selectivity, we define output elements corresponding todifferent orientations, which allow us to make a selection decision. The algorithm takes into account the granularity of the lattice as well as the presence of noise and inefficiencies. The method is applied to a sample of data collected with the ZEUS detector at HERA in order to identify cosmic muons that leave a linear pattern of signals in the segmented calorimeter. A two dimensional representation of the relevant part of the detector is used. The algorithm performs very well. Given its architecture, this system becomes a good candidate for fast pattern recognition in parallel processing devices.

This paper describes a new technique for object recognition based on learning appearance models. The image is decomposed into local regions which are described by a new texture representation called "Generalized Second Moments" thatare derived from the output of multiscale, multiorientation filter banks. Class-characteristic local texture features and their global composition is learned by a hierarchical mixture of experts architecture (Jordan & Jacobs). The technique is applied to a vehicle database consisting of 5 general car categories (Sedan, Van with backdoors, Van without backdoors, old Sedan, and Volkswagen Bug). This is a difficult problem with considerable in-class variation. The new technique has a 6.5% misclassification rate, compared to eigen-images which give 17.4% misclassification rate, and nearest neighbors which give 15 .7%