The attempt to find a single "optimal" weight vector in conven(cid:173) tional network training can lead to overfitting and poor generaliza(cid:173) tion. Bayesian methods avoid this, without the need for a valida(cid:173) tion set, by averaging the outputs of many networks with weights sampled from the posterior distribution given the training data. This sample can be obtained by simulating a stochastic dynamical system that has the posterior as its stationary distribution. I view neural networks as probabilistic models, and learning as statistical inference. Conventional network learning finds a single "optimal" set of network parameter values, corresponding to maximum likelihood or maximum penalized likelihood in(cid:173) ference.

A three-step method for function approximation with a fuzzy sys(cid:173) tem is proposed. First, the membership functions and an initial rule representation are learned; second, the rules are compressed as much as possible using information theory; and finally, a com(cid:173) putational network is constructed to compute the function value. This system is applied to two control examples: learning the truck and trailer backer-upper control system, and learning a cruise con(cid:173) trol system for a radio-controlled model car.

Real-world learning tasks may involve high-dimensional data sets with arbitrary patterns of missing data. In this paper we present a framework based on maximum likelihood density estimation for learning from such data set.s. VVe use mixture models for the den(cid:173) sity estimates and make two distinct appeals to the Expectation(cid:173) Maximization (EM) principle (Dempster et al., 1977) in deriving a learning algorithm-EM is used both for the estimation of mix(cid:173) ture components and for coping wit.h missing dat.a. The result(cid:173) ing algorithm is applicable t.o a wide range of supervised as well as unsupervised learning problems.

Signal processing and classification algorithms often have limited applicability resulting from an inaccurate model of the signal's un(cid:173) derlying structure. We present here an efficient, Bayesian algo(cid:173) rithm for modeling a signal composed of the superposition of brief, Poisson-distributed functions. This methodology is applied to the specific problem of modeling and classifying extracellular neural waveforms which are composed of a superposition of an unknown number of action potentials CAPs). Previous approaches have had limited success due largely to the problems of determining the spike shapes, deciding how many are shapes distinct, and decomposing overlapping APs. A Bayesian solution to each of these problems is obtained by inferring a probabilistic model of the waveform.

Selecting a good model of a set of input points by cross validation is a computationally intensive process, especially if the number of possible models or the number of training points is high. Tech(cid:173) niques such as gradient descent are helpful in searching through the space of models, but problems such as local minima, and more importantly, lack of a distance metric between various models re(cid:173) duce the applicability of these search methods. Hoeffding Races is a technique for finding a good model for the data by quickly dis(cid:173) carding bad models, and concentrating the computational effort at differentiating between the better ones. This paper focuses on the special case of leave-one-out cross validation applied to memory(cid:173) based learning algorithms, but we also argue that it is applicable to any class of model selection problems.

In function approximation, example-based learning can be formulated as synthesiz(cid:173) ing an approximation function for data sampled from an unknown target function (Poggio and Girosi, 1990). Active learning describes a class of example-based learning paradigms that seeks out new training examples from specific regions of the input space, instead of passively accepting examples from some data generating source.

We introduce a recurrent architecture having a modular structure and we formulate a training procedure based on the EM algorithm. The resulting model has similarities to hidden Markov models, but supports recurrent networks processing style and allows to exploit the supervised learning paradigm while using maximum likelihood estimation.

Most of the common techniques for estimating conditional prob(cid:173) ability densities are inappropriate for applications involving peri(cid:173) odic variables. In this paper we introduce three novel techniques for tackling such problems, and investigate their performance us(cid:173) ing synthetic data. We then apply these techniques to the problem of extracting the distribution of wind vector directions from radar scatterometer data gathered by a remote-sensing satellite.

We present a Bayesian framework for inferring the parameters of a mixture of experts model based on ensemble learning by varia(cid:173) tional free energy minimisation. The Bayesian approach avoids the over-fitting and noise level under-estimation problems of traditional maximum likelihood inference. We demonstrate these methods on artificial problems and sunspot time series prediction.

We present new results about the temporal-difference learning al(cid:173) gorithm, as applied to approximating the cost-to-go function of a Markov chain using linear function approximators. The algo(cid:173) rithm we analyze performs on-line updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counter-examples with regards to the Significance of on-line updating and linearly parameterized function approximators.