By these internal representations, networks can solve multiple problems.

Given such a classification task in most cases it is not too difficult to devise a network architecture that is capable of learning the input-output relation as represented by a number of training examples.

Increasing attention has recently been paid to algorithms based on dynamic programming (DP) due to the suitability of DP for learning problemsinvolving control. In stochastic environments where the system being controlled is only incompletely known, however, a unifying theoretical account of these methods has been missing. In this paper we relate DPbased learning algorithms to the powerful techniquesof stochastic approximation via a new convergence theorem, enabling us to establish a class of convergent algorithms to which both TD("\) and Q-Iearning belong. 1 INTRODUCTION Learning to predict the future and to find an optimal way of controlling it are the basic goals of learning systems that interact with their environment. A variety of algorithms are currently being studied for the purposes of prediction and control in incompletely specified, stochastic environments. Here we consider learning algorithms definedin Markov environments. There are actions or controls (u) available for the learner that affect both the state transition probabilities, and the probability distributionfor the immediate, state dependent costs (Ci( u)) incurred by the learner.

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The model consists of a two-dimensional sheet of leaky integrateand-fire neuronswith feedback connectivity consisting of local excitation andsurround inhibition. Each neuron is independently driven by homogeneous external noise. Spontaneous symmetry breaking occurs, resulting in the formation of "hotspots" of activity inthe network. These localized patterns of excitation appear as clusters that coalesce, disintegrate, or fluctuate in size while simultaneously movingin a random walk constrained by the interaction with other clusters. The emergent cross-correlation functions have a dual structure, with a sharp peak around zero on top of a much broader hill.

An approach is presented to learning high dimensional functions in the case where the learning algorithm can affect the generation of new data. A local modeling algorithm, locally weighted regression, is used to represent the learned function. Architectural parameters of the approach, such as distance metrics, are also localized and become a function of the query point instead of being global. Statistical tests are given for when a local model is good enough and sampling should be moved to a new area. Our methods explicitly deal with the case where prediction accuracy requirements exist during exploration: By gradually shifting a "center of exploration" and controlling the speed of the shift with local prediction accuracy,a goal-directed exploration of state space takes place along the fringes of the current data support until the task goal is achieved.

We show how randomly scrambling the output classes of various fractions of the training data may be used to improve predictive accuracy of a classification algorithm. We present a method for calculating the "noise sensitivity signature" of a learning algorithm which is based on scrambling the output classes. This signature can be used to indicate a good match between the complexity of the classifier and the complexity of the data. Use of noise sensitivity signatures is distinctly different from other schemes to avoid overtraining, suchas cross-validation, which uses only part of the training data, or various penalty functions, which are not data-adaptive. Noise sensitivity signature methods use all of the training data and are manifestly data-adaptive and nonparametric.

In this procedure one transforms variables to a basis in which the covariance isdiagonal and then projects out the low variance directions. While application of PCA to remove input variables is useful in some cases (Leen et al., 1990), there is no guarantee that low variance variables have little effect on error. We propose a saliency measure, based on PCA, that identifies those variables that have the least effect on error. Our proposed Principal Components Pruning algorithm applies this measure to obtain a simple and cheap pruning technique in the context of supervised learning. Fast Pruning Using Principal Components 37 Special Case: PCP in Linear Regression In unbiased linear models, one can bound the bias introduced from pruning the principal degrees of freedom in the model.

Hayit Greenspan Department of Electrical Engineering California Institute of Technology, 116-81 Pasadena, CA 91125 There is an increasing interest in the area of Learning in Computer Vision and Image Understanding, both from researchers in the learning community and from researchers involved with the computer vision world. The field is characterized by a shift away from the classical, purely model-based, computer vision techniques, towards data-driven learning paradigms for solving real-world vision problems. Using learning in segmentation or recognition tasks has several advantages over classical model-based techniques. These include adaptivity to noise and changing environments, as well as in many cases, a simplified system generation procedure. Yet, learning from examples introduces a new challenge - getting a representative data set of examples from which to learn.

We extend Optimal Brain Surgeon (OBS) - a second-order method for pruning networks - to allow for general error measures, and explore a reduced computational and storage implementation via a dominant eigenspace decomposition. Simulations on nonlinear, noisy pattern classification problems reveal that OBS does lead to improved generalization, and performs favorably in comparison with Optimal Brain Damage (OBD). We find that the required retraining steps in OBD may lead to inferior generalization, that can be interpreted as due to injecting noise backa result the system. A common technique is to stop training of a largeinto at the minimum validation error. We found that the testnetwork error could be reduced even further by means of OBS (but not OBD) pruning.