A new learning algorithm is developed for the design of statistical classifiers minimizing the rate of misclassification. The method, which is based on ideas from information theory and analogies to statistical physics, assigns data to classes in probability. The distributions arechosen to minimize the expected classification error while simultaneously enforcing the classifier's structure and a level of "randomness" measured by Shannon's entropy. Achievement of the classifier structure is quantified by an associated cost. The constrained optimizationproblem is equivalent to the minimization of a Helmholtz free energy, and the resulting optimization method is a basic extension of the deterministic annealing algorithm that explicitly enforces structural constraints on assignments while reducing theentropy and expected cost with temperature. In the limit of low temperature, the error rate is minimized directly and a hard classifier with the requisite structure is obtained. This learning algorithmcan be used to design a variety of classifier structures. The approach is compared with standard methods for radial basis function design and is demonstrated to substantially outperform other design methods on several benchmark examples, while often retainingdesign complexity comparable to, or only moderately greater than that of strict descent-based methods.

'soft' competition based estimation schemes are developed where in

James W. Howse Chaouki T. Abdallah Gregory L. Heileman Department of Electrical and Computer Engineering University of New Mexico Albuquerque, NM 87131 Abstract The process of machine learning can be considered in two stages: model selection and parameter estimation. In this paper a technique is presented for constructing dynamical systems with desired qualitative properties. The approach is based on the fact that an n-dimensional nonlinear dynamical system can be decomposed into one gradient and (n - 1) Hamiltonian systems. Thus,the model selection stage consists of choosing the gradient and Hamiltonian portions appropriately so that a certain behavior is obtainable. To estimate the parameters, a stably convergent learning rule is presented.

Department of Electrical and Computer Engineering University of Queensland St. Lucia Qld 4072 Australia Abstract We define a Gamma multi-layer perceptron (MLP) as an MLP with the usual synaptic weights replaced by gamma filters (as proposed byde Vries and Principe (de Vries and Principe, 1992)) and associated gain terms throughout all layers. We derive gradient descent update equations and apply the model to the recognition of speech phonemes. We find that both the inclusion of gamma filters in all layers, and the inclusion of synaptic gains, improves the performance of the Gamma MLP. We compare the Gamma MLP with TDNN, Back-Tsoi FIR MLP, and Back-Tsoi I1R MLP architectures, and a local approximation scheme. We find that the Gamma MLP results in an substantial reduction in error rates. 1 INTRODUCTION 1.1 THE GAMMA FILTER Infinite Impulse Response (I1R) filters have a significant advantage over Finite Impulse Response(FIR) filters in signal processing: the length of the impulse response is uncoupled from the number of filter parameters.

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 gainsin conceptual simplicity, practical efficiency, and solution quality over earlier efforts.

There is currently considerable interest in developing general nonlinear densitymodels based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying'causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, totrain such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general nonlinear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multiphase oil pipeline.

Steven Gold Department of Computer Science Yale University New Haven, CT 06520-8285 AnandRangarajan Dept. of Diagnostic Radiology Yale University New Haven, CT 06520-8042 Abstract A new technique, termed soft assign, is applied for the first time to two classic combinatorial optimization problems, the traveling salesmanproblem and graph partitioning. Softassign, which has emerged from the recurrent neural network/statistical physics framework, enforces two-way (assignment) constraints without the use of penalty terms in the energy functions. The softassign can also be generalized from two-way winner-take-all constraints to multiple membership constraints which are required for graph partitioning. Thesoftassign technique is compared to the softmax (Potts glass). Within the statistical physics framework, softmax and a penalty term has been a widely used method for enforcing the two-way constraints common within many combinatorial optimization problems.The benchmarks present evidence that softassign has clear advantages in accuracy, speed, parallelizabilityand algorithmic simplicityover softmax and a penalty term in optimization problems with two-way constraints. 1 Introduction In a series of papers in the early to mid 1980's, Hopfield and Tank introduced techniques which allowed one to solve combinatorial optimization problems with recurrent neural networks [Hopfield and Tank, 1985].

A new approach for clustering is proposed. This method is based on an analogy to a physical model; the ferromagnetic Potts model at thermal equilibrium is used as an analog computer for this hard optimization problem. We do not assume any structure of the underlying distributionof the data. Phase space of the Potts model is divided into three regions; ferromagnetic, super-paramagnetic and paramagnetic phases. The region of interest is that corresponding to the super-paramagnetic one, where domains of aligned spins appear.

In this setting, each pattern, represented as an n-dimensional feature vector, is associated with a discrete pattern class, or state of nature (Duda and Hart, 1973). Using available information, (e.g., a statistically representative set of labeled feature vectors

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 quadricsurface, 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 weightsderived 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.