In ECAI-92, pp. 689–693.

For a detailed rationale the reader is referred to the work of Rissanen (1984) or Wallace and Freeman (1987) and the references therein. Note that the Minimum Description Length (MDL) technique (as Rissanen's approach has become known) is implicitly related to Maximum A Posteriori (MAP) Bayesian estimation techniques if cast in the appropriate framework.

Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

The Neural Prediction Model is the speech recognition model based on pattern prediction by multilayer perceptrons. Its effectiveness was confirmed by the speaker-independent digit recognition experiments. This paper presents an improvement in the model and its application to large vocabulary speech recognition, based on subword units. The improvement involves an introduction of "backward prediction," which further improves the prediction accuracy of the original model with only "forward prediction". In application of the model to speaker-dependent large vocabulary speech recognition, the demi-syllable unit is used as a subword recognition unit.

A Boltzmann machine ([AHS], [HS], [AK]) is a neural network model in which the units update their states according to a stochastic decision rule. It consists of a set U of units, a set C of unordered pairs of elements of U, and an assignment of connection strengths S: C -- R. A configuration of a Boltzmann machine is a map k: U -- {O, I}.

M2/n' for sufficiently large values of M. Here, Poo(error) denotes the probability of error in the infinite sample limit, and is at most twice the error of a Bayes classifier. Although the value of the coefficient a depends upon the underlying probability distributions, the exponent of M is largely distribution free. We thus obtain a concise relation between a classifier's ability to generalize from a finite reference sample and the dimensionality of the feature space, as well as an analytic validation of Bellman's well known "curse of dimensionality." 1 INTRODUCTION One of the primary tasks assigned to neural networks is pattern classification. Common applications include recognition problems dealing with speech, handwritten characters, DNA sequences, military targets, and (in this conference) sexual identity. Two fundamental concepts associated with pattern classification are generalization (how well does a classifier respond to input data it has never encountered before?) and scalability (how are a classifier's processing and training requirements affected by increasing the number of features that describe the input patterns?).

Previous work has shown the ability of Multilayer Perceptrons (MLPs) to estimate emission probabilities for Hidden Markov Models The advantages of a speech recognition system incorporating(HMMs).

A Boltzmann machine ([AHS], [HS], [AK]) is a neural network model in which the units update their states according to a stochastic decision rule. It consists of a set U of units, a set C of unordered pairs of elements of U, and an assignment of connection strengths S: C -- R. A configuration of a Boltzmann machine is a map k: U -- {O, I}.

John S. Denker and Yann leCun AT&T Bell Laboratories Holmdel, NJ 07733 Abstract (1) The outputs of a typical multi-output classification network do not satisfy the axioms of probability; probabilities should be positive and sum to one. This problem can be solved by treating the trained network as a preprocessor that produces a feature vector that can be further processed, for instance by classical statistical estimation techniques. It is particularly useful to combine these two ideas: we implement the ideas of section 1 using Parzen windows, where the shape and relative size of each window is computed using the ideas of section 2. This allows us to make contact between important theoretical ideas (e.g. the ensemble formalism) and practical techniques (e.g. Our results also shed new light on and generalize the well-known "softmax" scheme. 1 Distribution of Categories in Output Space In many neural-net applications, it is crucial to produce a set of C numbers that serve as estimates of the probability of C mutually exclusive outcomes. For example, inspeech recognition, these numbers represent the probability of C different phonemes; the probabilities of successive segments can be combined using a Hidden Markov Model.

Padhraic Smyth Communications Systems Research Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 Abstract Given some training data how should we choose a particular network classifier froma family of networks of different complexities? In this paper we discuss how the application of stochastic complexity theory to classifier design problems can provide some insights into this problem. In particular we introduce the notion of admissible models whereby the complexity of models under consideration is affected by (among other factors) the class entropy, the amount of training data, and our prior belief. In particular we discuss the implications of these results with respect to neural architectures anddemonstrate the approach on real data from a medical diagnosis task. 1 Introduction and Motivation In this paper we examine in a general sense the application of Minimum Description Length (MDL) techniques to the problem of selecting a good classifier from a large set of candidate models or hypotheses. Pattern recognition algorithms differ from more conventional statistical modeling techniques in the sense that they typically choose from a very large number of candidate models to describe the available data.