If a polyhedral distance is used, the problem can be formulated as that of minimizing a piecewise-linear concave function on a polyhedral set which is shown to be equivalent to a bilinear program: minimizing a bilinear function on a polyhedral set.A fast finite k-Median Algorithm consisting of solving few linear programs in closed form leads to a stationary point of the bilinear program. Computational testing on a number of realworld databaseswas carried out. On the Wisconsin Diagnostic Breast Cancer (WDBC) database, k-Median training set correctness wascomparable to that of the k-Mean Algorithm, however its testing set correctness was better. Additionally, on the Wisconsin Prognostic Breast Cancer (WPBC) database, distinct and clinically importantsurvival curves were extracted by the k-Median Algorithm, whereas the k-Mean Algorithm failed to obtain such distinct survival curves for the same database.

A Bayesian formulation of the problem leads to a clear concept of a solution whose computation, however, appears to entail an examination of an intractably-large number of hyperstates. This paper hassuggested extending the Gittins index approach (which applies with great power and elegance to the special class of multi-armed bandit processes) to general adaptive MDP's. The hope has been that if certain salient features of the value of information could be captured, even approximately, then one could be led to a reasonable method for avoiding certain defects of certainty-equivalence approaches (problems with identifiability, "metastability"). Obviously, positive evidence, in the form of empirical results from simulation experiments, would lend support to these ideas-work along these lines is underway. Local bandit approximation is but one approximate computational approach for problems of optimal learning and dual control. Most prominent in the literature of control theory is the "wide-sense" approach of [Bar-Shalom & Tse, 1976], which utilizes localquadratic approximations about nominal state/control trajectories. For certain problems, this method has demonstrated superior performance compared to a certainty-equivalence approach, but it is computationally very intensive and unwieldy, particularly for problems with controller dimension greater than one. One could revert to the view of the bandit problem, or general adaptive MDP, as simply a very large MDP defined over hyperstates, and then consider a some- Local Bandit Approximationfor Optimal Learning Problems 1025 what direct approach in which one performs approximate dynamic programming with function approximation over this domain-details of function-approximation, feature-selection, and "training" all become important design issues.

Binocular rivalry is the alternating percept that can result when the two eyes see different scenes. Recent psychophysical evidence supports an account for one component of binocular rivalry similar to that for other bistable percepts. Recent neurophysiological evidence showsthat some binocular neurons are modulated with the changing percept; others are not, even if they are selective between thestimuli presented to the eyes. We extend our model to a hierarchy to address these effects. 1 Introduction Although binocular rivalry leads to distinct perceptual distress, it is revealing about the mechanisms of visual information processing. Various experiments have suggested that simple input competition cannot be the whole story. This work was supported by the NIH.

Many popular learning rules are formulated in terms of continuous, analoginputs and outputs. Biological systems, however, use action potentials, which are digital-amplitude events that encode analog information in the inter-event interval. Action-potential representations are now being used to advantage in neuromorphic VLSI systems as well. We report on a simple learning rule, based on the Riccati equation described by Kohonen [1], modified for action-potential neuronal outputs. We demonstrate this learning rule in an analog VLSI chip that uses volatile capacitive storage for synaptic weights. We show that our time-dependent learning rule is sufficient to achieve approximate weight normalization and can detect temporal correlations in spike trains.

Probability models can be used to predict outcomes and compensate for missing data, but even a perfect model cannot be used to make decisions unless the utility of the outcomes, or preferences between them, are also provided. This arises in many real-world problems, such as medical diagnosis, wherethe cost of the test as well as the expected improvement in the outcome must be considered. Relatively little work has been done on learning the utilities of outcomes for optimal decision making. In this paper, we show how temporal-difference reinforcement learning (TO(A» can be used to determine decision theoretic utilities within the context of a mixture model and apply this new approach to a problem in medical diagnosis. TO(A) learning of utilities reduces the number of tests that have to be done to achieve the same level of performance compared with the probability model alone, which results in significant cost savings and increased efficiency.

The major problem that has prevented practical application of analog neuro-LSIs has been poor accuracy due to fluctuating analog device characteristics inherent in each device as a result of manufacturing. This paper proposes a dynamic control architecture that allows analog silicon neural networks to compensate for the fluctuating device characteristics and adapt to a change in input DC level. We have applied this architecture to compensate for input offset voltages of an analog CMOS WTA (Winner-Take-AlI) chip that we have fabricated. Experimental data show the effectiveness of the architecture.

Tony Plate BC Cancer Agency 601 West 10th Ave, Epidemiology Vancouver BC Canada V5Z 1L3 tap@comp.vuw.ac.nz PierreBand BC Cancer Agency 601 West 10th Ave, Epidemiology Vancouver BC Canada V5Z 1L3 Joel Bert Dept of Chemical Engineering University of British Columbia 2216 Main Mall Vancouver BC Canada V6T 1Z4 JohnGrace Dept of Chemical Engineering University of British Columbia 2216 Main Mall Vancouver BC Canada V6T 1Z4 Abstract Epidemiological data is traditionally analyzed with very simple techniques. Flexible models, such as neural networks, have the potential to discover unanticipated features in the data. However, to be useful, flexible models must have effective control on overfitting. Thispaper reports on a comparative study of the predictive quality of neural networks and other flexible models applied to real and artificial epidemiological data.

Field (1994) has suggested that neurons with line and edge selectivities found in primary visual cortex of cats and monkeys form a sparse, distributed representationof natural scenes, and Barlow (1989) has reasoned that such responses should emerge from an unsupervised learning algorithm that attempts to find a factorial code of independent visual features. We show here that nonlinear'infomax', when applied to an ensemble of natural scenes,produces sets of visual filters that are localised and oriented. Some of these filters are Gabor-like and resemble those produced by the sparseness-maximisation network of Olshausen & Field (1996). In addition, the outputs of these filters are as independent as possible, since the infomax networkis able to perform Independent Components Analysis (ICA). We compare the resulting ICA filters and their associated basis functions, with other decorrelating filters produced by Principal Components Analysis (PCA) and zero-phase whitening filters (ZCA). The ICA filters have more sparsely distributed (kurtotic) outputs on natural scenes. They also resemble thereceptive fields of simple cells in visual cortex, which suggests that these neurons form an information-theoretic coordinate system for images. 1 Introduction. Both the classic experiments of Rubel & Wiesel [8] on neurons in visual cortex, and several decadesof theorising about feature detection in vision, have left open the question most succinctly phrased by Barlow "Why do we have edge detectors?" That is: are there any coding principles which would predict the formation of localised, oriented receptive 832 A.1.

A central theme of computational vision research has been the realization thatreliable estimation of local scene properties requires propagating measurements across the image. Many authors have therefore suggested solving vision problems using architectures of locally connected units updating their activity in parallel. Unfortunately, theconvergence of traditional relaxation methods on such architectures has proven to be excruciatingly slow and in general they do not guarantee that the stable point will be a global minimum. In this paper we show that an architecture in which Bayesian Beliefs aboutimage properties are propagated between neighboring units yields convergence times which are several orders of magnitude fasterthan traditional methods and avoids local minima. In particular our architecture is non-iterative in the sense of Marr [5]: at every time step, the local estimates at a given location are optimal giventhe information which has already been propagated to that location. We illustrate the algorithm's performance on real images and compare it to several existing methods. 1 Theory The essence of our approach is shown in figure 1. Figure 1a shows the prototypical ill-posed problem: interpolation of a function from sparse data.

The softassign quadratic assignment algorithm has recently emerged as an effective strategy for a variety of optimization problems inpattern recognition and combinatorial optimization. While the effectiveness of the algorithm was demonstrated in thousands of simulations, there was no known proof of convergence. Here, we provide a proof of convergence for the most general form of the algorithm.