We develop a principled strategy to sample a function optimally for function approximation tasks within a Bayesian framework. Using ideas from optimal experiment design, we introduce an objective function (incorporating both bias and variance) to measure the degree of approximation, and the potential utility of the data points towards optimizing this objective. We show how the general strategy can be used to derive precise algorithms to select data for two cases: learning unit step functions and polynomial functions. In particular, we investigate whether such active algorithms can learn the target with fewer examples. We obtain theoretical and empirical results to suggest that this is the case. 1 INTRODUCTION AND MOTIVATION Learning from examples is a common supervised learning paradigm that hypothesizes a target concept given a stream of training examples that describes the concept. In function approximation, example-based learning can be formulated as synthesizing 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 are concerned in this paper with the application of multiple models, specifically the Hierarchical Mixtures of Experts, to time series prediction, specifically the problem of predicting acoustic vectors for use in speech coding. There have been a number of applications of multiple models in time series prediction. A classic example is the Threshold Autoregressive model (TAR) which was used by Tong & 836 S. R. Waterhouse, A. J. Robinson Lim (1980) to predict sunspot activity. More recently, Lewis, Kay and Stevens (in Weigend & Gershenfeld (1994)) describe the use of Multivariate and Regression Splines (MARS) to the prediction of future values of currency exchange rates. Finally, in speech prediction, Cuperman & Gersho (1985) describe the Switched Inter-frame Vector Prediction (SIVP) method which switches between separate linear predictors trained on different statistical classes of speech.

We first rederive the known results for the'thermodynamic limit' of infinite perceptron size N and show explicitly that 9

The spatial distribution and time course of electrical signals in neurons have important theoretical and practical consequences. Because it is difficult to infer how neuronal form affects electrical signaling, we have developed a quantitative yet intuitive approach to the analysis of electrotonus. This approach transforms the architecture of the cell from anatomical to electrotonic space, using the logarithm of voltage attenuation as the distance metric. We describe the theory behind this approach and illustrate its use. 1 INTRODUCTION The fields of computational neuroscience and artificial neural nets have enjoyed a mutually beneficial exchange of ideas. This has been most evident at the network level, where concepts such as massive parallelism, lateral inhibition, and recurrent excitation have inspired both the analysis of brain circuits and the design of artificial neural net architectures. Less attention has been given to how properties of the individual neurons or processing elements contribute to network function. Biological neurons and brain circuits have 70 Nicholas Carnevale, Kenneth Y. Tsai, Brenda J. Claiborne, Thomas H. Brown

An novel class of locally excitatory, globally inhibitory oscillator networks is proposed.

If data collection is costly, there is much to be gained by actively selecting particularly informative data points in a sequential way. In a Bayesian decision-theoretic framework we develop a query selection criterion which explicitly takes into account the intended use of the model predictions. By Markov Chain Monte Carlo methods the necessary quantities can be approximated to a desired precision. As the number of data points grows, the model complexity is modified by a Bayesian model selection strategy. The properties of two versions of the criterion ate demonstrated in numerical experiments.

With the exception of (Becker 1992), there has been little attempt to use non-linearity in networks to achieve something a linear network could not. Nonlinear networks, however, are capable of computing more general statistics than those second-order ones involved in decorrelation, and as a consequence they are capable of dealing with signals (and noises) which have detailed higher-order structure. The success of the'H-J' networks at blind separation (Jutten & Herault 1991) suggests that it should be possible to separate statistically independent components, by using learning rules which make use of moments of all orders. This paper takes a principled approach to this problem, by starting with the question of how to maximise the information passed on in nonlinear feed-forward network. Starting with an analysis of a single unit, the approach is extended to a network mapping N inputs to N outputs. In the process, it will be shown that, under certain fairly weak conditions, the N ---. N network forms a minimally redundant encoding ofthe inputs, and that it therefore performs Independent Component Analysis (ICA). 2 Information maximisation The information that output Y contains about input X is defined as: I(Y, X) H(Y) - H(YIX) (1) where H(Y) is the entropy (information) in the output, while H(YIX) is whatever information the output has which didn't come from the input. In the case that we have no noise (or rather, we don't know what is noise and what is signal in the input), the mapping between X and Y is deterministic and H(YIX) has its lowest possible value of

An impedence controlled manipulandum for human movement studies.

Increasing attention has been paid to reinforcement learning algorithms in recent years, partly due to successes in the theoretical analysis of their behavior in Markov environments. If the Markov assumption is removed, however, neither generally the algorithms nor the analyses continue to be usable. We propose and analyze a new learning algorithm to solve a certain class of non-Markov decision problems. Our algorithm applies to problems in which the environment is Markov, but the learner has restricted access to state information. The algorithm involves a Monte-Carlo policy evaluation combined with a policy improvement method that is similar to that of Markov decision problems and is guaranteed to converge to a local maximum. The algorithm operates in the space of stochastic policies, a space which can yield a policy that performs considerably better than any deterministic policy. Although the space of stochastic policies is continuous-even for a discrete action space-our algorithm is computationally tractable.

This paper outlines a dynamic theory of development and adaptation in neural networks with feedback connections. Given input ensemble, the connections change in strength according to an associative learning rule and approach a stable state where the neuronal outputs are decorrelated. We apply this theory to primary visual cortex and examine the implications of the dynamical decorrelation of the activities of orientation selective cells by the intracortical connections. The theory gives a unified and quantitative explanation of the psychophysical experiments on orientation contrast and orientation adaptation. Using only one parameter, we achieve good agreements between the theoretical predictions and the experimental data.