Channel equalization problem is an important problem in high-speed communications. The sequences of symbols transmitted are distorted by neighboring symbols. Traditionally, the channel equalization problem is considered as a channel-inversion operation. One problem of this approach is that there is no direct correspondence between error probability andresidual error produced by the channel inversion operation. In this paper, the optimal equalizer design is formulated as a classification problem. The optimal classifier can be constructed by Bayes decision rule. In general it is nonlinear. An efficient hybrid linear/nonlinear equalizer approach has been proposed to train the equalizer. The error probability of new linear/nonlinear equalizer has been shown to be better thana linear equalizer in an experimental channel. 1 INTRODUCTION

We present a methodological framework enabling a detailed description ofthe performance of Hopfield-like attractor neural networks (ANN) in the first two iterations. Using the Bayesian approach, wefind that performance is improved when a history-based term is included in the neuron's dynamics. A further enhancement of the network's performance is achieved by judiciously choosing the censored neurons (those which become active in a given iteration) onthe basis of the magnitude of their post-synaptic potentials. Thecontribution of biologically plausible, censored, historydependent dynamicsis especially marked in conditions of low firing activity and sparse connectivity, two important characteristics of the mammalian cortex. In such networks, the performance attained ishigher than the performance of two'independent' iterations, whichrepresents an upper bound on the performance of history-independent networks.

The Bayesian "evidence" approximation has recently been employed to determine the noise and weight-penalty terms used in back-propagation. This paper shows that for neural nets it is far easier to use the exact result than it is to use the evidence approximation. Moreover, unlike the evidence approximation,the exact result neither has to be re-calculated for every new data set, nor requires the running of computer code (the exact result is closed form). In addition, it turns out that the evidence procedure's MAPestimate for neural nets is, in toto, approximation error. Another advantage of the exact analysis is that it does not lead one to incorrect intuition, like the claim that using evidence one can "evaluate different priors in light of the data". This paper also discusses sufficiency conditions for the evidence approximation to hold, why it can sometimes give "reasonable" results, etc.

This paper presents a simple framework for Horn-clause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesian belief network can be represented in this framework. The main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning. This provides a useful representation language in its own right, providing a compromise between heuristic and epistemic adequacy. It also shows how Bayesian networks can be extended beyond a propositional language.

It is known that exact computation of conditional probabilities in belief networks is NP-hard. Many investigators in the AI community have tacitly assumed that algorithms for performing approximate inference with belief networks are of polynomial complexity. Indeed, special cases of approximate inference can be performed in time polynomial in the input size. However, we have discovered that the general problem of approximating conditional probabilities with belief networks, like exact inference, resides in the NP-hard complexity class. We develop a complexity analysis to elucidate the difficulty of approximate probabilistic inference.

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"Best-first model merging" is a general technique for dynamically choosing the structure of a neural or related architecture while avoiding overfitting. It is applicable to both leaming and recognition tasks and often generalizes significantly better than fixed structures. We demonstrate the approach applied to the tasks of choosing radial basis functions for function learning, choosing local affine models for curve and constraint surface modelling, and choosing the structure of a balltree or bumptree to maximize efficiency of access.

"Best-first model merging" is a general technique for dynamically choosing the structure of a neural or related architecture while avoiding overfitting. It is applicable to both leaming and recognition tasks and often generalizes significantly better than fixed structures. We demonstrate the approach applied to the tasks of choosing radial basis functions for function learning, choosing local affine models for curve and constraint surface modelling, and choosing the structure of a balltree or bumptree to maximize efficiency of access.

In this paper we investigate an average-case model of concept learning, and give results that place the popular statistical physics and VC dimension theories of learning curve behavior in a common framework.

The Bayesian model comparison framework is reviewed, and the Bayesian Occam's razor is explained. This framework can be applied to feedforward networks, making possible (1) objective comparisons between solutions using alternative network architectures; (2) objective choice of magnitude and type of weight decay terms; (3) quantified estimates of the error bars on network parameters and on network output. The framework also generates a measure of the effective number of parameters determined by the data. The relationship of Bayesian model comparison to recent work on prediction of generalisation ability (Guyon et al., 1992, Moody, 1992) is discussed.