ABSTRACT We present a Bayesian framework for inferring the parameters of a mixture of experts model based on ensemble learning by variational free energy minimisation. The Bayesian approach avoids the over-fitting and noise level underestimation problems of traditional maximum likelihood inference. We demonstrate these methods on artificial problems and sunspot time series prediction. INTRODUCTION The task of estimating the parameters of adaptive models such as artificial neural networks using Maximum Likelihood (ML) is well documented ego Geman, Bienenstock & Doursat (1992). ML estimates typically lead to models with high variance, a process known as "over-fitting".

Recently, however, there have been some successful applications of neural networks in a totally different context - that of sequential decision making under uncertainty (stochastic control). Stochastic control problems have been studied extensively in the operations research and control theory literature for a long time, using the methodology of dynamic programming [Bertsekas, 1995]. In dynamic programming, the most important object is the cost-to-go (or value) junction, which evaluates the expected future 1046 B. V. ROY, 1. N. TSITSIKLIS

The additive clustering (ADCL US) model (Shepard & Arabie, 1979) treats the similarity of two stimuli as a weighted additive measure of their common features. Inspired by recent work in unsupervised learning with multiple cause models, we propose anew, statistically well-motivated algorithm for discovering the structure of natural stimulus classes using the ADCLUS model, which promises substantial gains in conceptual simplicity, practical efficiency, and solution quality over earlier efforts.

The center-surround opponent receptive field (CSRF) mechanism represents one such example. Here, analogous CSRFs are shown to be formed in an artificial neural network which learns to localize contours (edges) of the luminance difference. Furthermore, when the input pattern is corrupted by a background noise, the CSRFs of the hidden units becomes shallower and broader with decrease of the signal-to-noise ratio (SNR). The same kind of SNR-dependent plasticity is present in the CSRF of real visual neurons; in bipolar cells of the carp retina as is shown here experimentally, as well as in large monopolar cells of the fly compound eye as was described by others. Also, analogous SNRdependent plasticity is shown to be present in the biphasic flash responses (BPFR) of these artificial and biological visual systems. Thus, the spatial (CSRF) and temporal (BPFR) filtering properties with which a wide variety of creatures see the world appear to be optimized for detectability of changes in space and time. 1 INTRODUCTION A number of learning algorithms have been developed to make synthetic neural machines be trainable to function in certain optimal ways. If the brain and nervous systems that we see in nature are best answers of the evolutionary process, then one might be able to find some common'softwares' in real and artificial neural systems. This possibility is examined in this paper, with respect to a basic visual 160 S. Y ASUI, T. FURUKAWA, M. YAMADA, T. SAITO

Intermediate and higher vision processes require selection of a subset of the available sensory information before further processing. Usually, this selection is implemented in the form of a spatially circumscribed region of the visual field, the so-called "focus of attention" which scans the visual scene dependent on the input and on the attentional state of the subject. We here present a model for the control of the focus of attention in primates, based on a saliency map. This mechanism is not only expected to model the functionality of biological vision but also to be essential for the understanding of complex scenes in machine vision.

This paper describes a neural network based controller for allocating capacity in a telecommunications network. This system was proposed in order to overcome a "real time" response constraint. Two basic architectures are evaluated: 1) a feedforward network-heuristic and; 2) a feedforward network-recurrent network. These architectures are compared against a linear programming (LP) optimiser as a benchmark. This LP optimiser was also used as a teacher to label the data samples for the feedforward neural network training algorithm. It is found that the systems are able to provide a traffic throughput of 99% and 95%, respectively, of the throughput obtained by the linear programming solution. Once trained, the neural network based solutions are found in a fraction of the time required by the LP optimiser.

A theory of early stopping as applied to linear models is presented. The backpropagation learning algorithm is modeled as gradient descent in continuous time. Given a training set and a validation set, all weight vectors found by early stopping must lie on a certain quadric surface, usually an ellipsoid. Given a training set and a candidate early stopping weight vector, all validation sets have least-squares weights lying on a certain plane. This latter fact can be exploited to estimate the probability of stopping at any given point along the trajectory from the initial weight vector to the leastsquares weights derived from the training set, and to estimate the probability that training goes on indefinitely. The prospects for extending this theory to nonlinear models are discussed.

Matching feature point sets lies at the core of many approaches to object recognition. We present a framework for nonrigid matching that begins with a skeleton module, affine point matching, and then integrates multiple features to improve correspondence and develops an object representation based on spatial regions to model local transformations.

Therefore, we want c to be less than 0.5. In order to get a 2:1 margin, we choose c 0.25. The classifier is trained only on individual partial characters instead of all possible combinations of partial characters. Therefore, we can specify the classifier using only 1523 constraints, instead of creating a training set of approximately 128,000 possible combinations of partial characters. Applying these constraints is therefore much faster than back-propagation on the entire data set.

Backpropagation learning algorithms typically collapse the network's structure into a single vector of weight parameters to be optimized. We suggest that their performance may be improved by utilizing the structural information instead of discarding it, and introduce a framework for ''tempering'' each weight accordingly. In the tempering model, activation and error signals are treated as approximately independent random variables. The characteristic scale of weight changes is then matched to that ofthe residuals, allowing structural properties such as a node's fan-in and fan-out to affect the local learning rate and backpropagated error. The model also permits calculation of an upper bound on the global learning rate for batch updates, which in turn leads to different update rules for bias vs. non-bias weights. This approach yields hitherto unparalleled performance on the family relations benchmark, a deep multi-layer network: for both batch learning with momentum and the delta-bar-delta algorithm, convergence at the optimal learning rate is sped up by more than an order of magnitude.