We compare two regularization methods which can be used to improve thegeneralization capabilities of Gaussian mixture density estimates. The first method uses a Bayesian prior on the parameter space.We derive EM (Expectation Maximization) update rules which maximize the a posterior parameter probability. In the second approachwe apply ensemble averaging to density estimation. This includes Breiman's "bagging", which recently has been found to produce impressive results for classification networks.

A technique for segmenting sounds using processing based on mammalian earlyauditory processing is presented. The technique is based on features in sound which neuron spike recording suggests are detected in the cochlear nucleus. The sound signal is bandpassed andeach signal processed to enhance onsets and offsets. The onset and offset signals are compressed, then clustered both in time and across frequency channels using a network of integrateand-fire neurons.Onsets and offsets are signalled by spikes, and the timing of these spikes used to segment the sound. 1 Background Traditional speech interpretation techniques based on Fourier transforms, spectrum recoding, and a hidden Markov model or neural network interpretation stage have limitations both in continuous speech and in interpreting speech in the presence of noise, and this has led to interest in front ends modelling biological auditory systems for speech interpretation systems (Ainsworth and Meyer 92; Cosi 93; Cole et al 95). Auditory modelling systems use similar early auditory processing to that used in biological systems.

A hybrid and contextual radial basis function networklhidden Markov model off-line handwritten word recognition system is presented. The task assigned to the radial basis function networks is the estimation of emission probabilities associated to Markov states. The model is contextual becausethe estimation of emission probabilities takes into account the left context of the current image segment as represented by its predecessor inthe sequence. The new system does not outperform the previous system without context but acts differently.

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

The wake-sleep algorithm (Hinton, Dayan, Frey and Neal 1995) is a relatively efficientmethod of fitting a multilayer stochastic generative model to high-dimensional data. In addition to the top-down connections inthe generative model, it makes use of bottom-up connections for approximating the probability distribution over the hidden units given the data, and it trains these bottom-up connections using a simple delta rule. We use a variety of synthetic and real data sets to compare the performance ofthe wake-sleep algorithm with Monte Carlo and mean field methods for fitting the same generative model and also compare it with other models that are less powerful but easier to fit. 1 INTRODUCTION Neural networks are often used as bottom-up recognition devices that transform input vectors intorepresentations of those vectors in one or more hidden layers. But multilayer networks ofstochastic neurons can also be used as top-down generative models that produce patterns with complicated correlational structure in the bottom visible layer. In this paper we consider generative models composed of layers of stochastic binary logistic units. Given a generative model parameterized by top-down weights, there is an obvious way to perform unsupervised learning. The generative weights are adjusted to maximize the probability thatthe visible vectors generated by the model would match the observed data.

A Bayesian-Kullback learning scheme, called Ying-Yang Machine, is proposed based on the two complement but equivalent Bayesian representations for joint density and their Kullback divergence. Not only the scheme unifies existing major supervised and unsupervised learnings,including the classical maximum likelihood or least square learning, the maximum information preservation, the EM & em algorithm and information geometry, the recent popular Helmholtz machine, as well as other learning methods with new variants and new results; but also the scheme provides a number of new learning models. 1 INTRODUCTION Many different learning models have been developed in the literature. We may come to an age of searching a unified scheme for them. With a unified scheme, we may understand deeply the existing models and their relationships, which may cause cross-fertilization on them to obtain new results and variants; We may also be guided to develop new learning models, after we get better understanding on which cases we have already studied or missed, which deserve to be further explored. Recently, a Baysian-Kullback scheme, called the YING-YANG Machine, has been proposed as such an effort(Xu, 1995a). It bases on the Kullback divergence and two complement but equivalent Baysian representations for the joint distribution of the input space and the representation space, instead of merely using Kullback divergence formatching un-structuralized joint densities in information geometry type learnings (Amari, 1995a&b; Byrne, 1992; Csiszar, 1975).

Therefore, we want c to be less than 0.5. In order to get a 2:1 margin, we choose c 0.25. The classifier is trained only on individual partial characters instead of all possible combinations of partial characters. Therefore, we can specify the classifier using only 1523 constraints, instead of creating a training set of approximately 128,000 possible combinations of partial characters. Applying these constraints is therefore much faster than back-propagation on the entire data set.

We introduce and analyze a mixture model for supervised learning of probabilistic transducers. We devise an online learning algorithm that efficiently infers the structure and estimates the parameters of each model in the mixture. Theoretical analysis and comparative simulations indicate that the learning algorithm tracks the best model from an arbitrarily large (possibly infinite) pool of models. We also present an application of the model for inducing a noun phrase recognizer.

We describe the reinforcement learning problem, motivate algorithms whichseek an approximation to the Q function, and present new convergence results for two such algorithms. 1 INTRODUCTION AND BACKGROUND Imagine an agent acting in some environment. At time t, the environment is in some state Xt chosen from a finite set of states. The agent perceives Xt, and is allowed to choose an action at from some finite set of actions. Meanwhile, the agent experiences a real-valued cost Ct, chosen from a distribution which also depends only on Xt and at and which has finite mean and variance. Such an environment is called a Markov decision process, or MDP.

Tel: [ 44] 1223 332815 ajr@eng.cam.ac.uk ABSTRACT We present a Bayesian framework for inferring the parameters of a mixture of experts model based on ensemble learning by variational freeenergy minimisation. The Bayesian approach avoids the over-fitting and noise level underestimation problems of traditional maximum likelihood inference. We demonstrate these methods on artificial problems and sunspot time series prediction. INTRODUCTION The task of estimating the parameters of adaptive models such as artificial neural networks using Maximum Likelihood (ML) is well documented ego Geman, Bienenstock & Doursat (1992). ML estimates typically lead to models with high variance, a process known as "over-fitting".