We consider the problem of prediction of stationary time series, using the architecture known as mixtures of experts (MEM). Here we suggest a mixture which blends several autoregressive models. This study focuses on some theoretical foundations of the prediction problem in this context. More precisely, it is demonstrated that this model is a universal approximator, with respect to learning the unknown prediction function. This statement is strengthened as upper bounds on the mean squared error are established. Based on these results it is possible to compare the MEM to other families of models (e.g., neural networks and state dependent models). It is shown that a degenerate version of the MEM is in fact equivalent to a neural network, and the number of experts in the architecture plays a similar role to the number of hidden units in the latter model.

Automatic processing of visual scenes often begins by detecting regions of an image with common values of simple local features, such as texture, and mapping the pattern offeature activation into a predicted region label. We develop a self-organizing neural architecture, called the ARTEX algorithm, for automatically extracting a novel and effective array of such features and mapping them to output region labels. ARTEX is made up of biologically motivated networks, the Boundary Contour System and Feature Contour System (BCS/FCS) networks for visual feature extraction (Cohen & Grossberg, 1984; Grossberg & Mingolla, 1985a, 1985b; Grossberg & Todorovic, 1988; Grossberg, Mingolla, & Williamson, 1995), and the Gaussian ARTMAP (GAM) network for classification (Williamson, 1996). ARTEX is first evaluated on a difficult real-world task, classifying regions of synthetic aperture radar (SAR) images, where it reliably achieves high resolution (single 874 S. Grossberg and 1. R. Williamson pixel) classification results, and creates accurate probability maps for its class predictions. ARTEX is then evaluated on classification of natural textures, where it outperforms the texture classification system in Greenspan, Goodman, Chellappa, & Anderson (1994) using comparable preprocessing and training conditions. 2 FEATURE EXTRACTION NETWORKS

We have been conducting research on bottom-up classification techniques ba;ed on trainable artificial neural networks (ANNs), in combination with comprehensive but weakly-applied language models. To focus our work on a subproblem that is tractable enough to le.:'ld to usable products in a reasonable time, we have restricted the domain to hand-printing, so that strokes are clearly delineated by pen lifts. In the process of optimizing overall performance of the recognizer, we have discovered some useful techniques for architecting and training ANNs that must participate in a larger recognition process. Some of these techniques-especially the normalization of output error, frequency balanCing, and error emphal;is-suggest a common theme of significant value derived by reducing the effect of a priori biases in training data to better represent low frequency, low probability smnples, including second and third choice probabilities. There is mnple prior work in combining low-level classifiers with various search strategies to provide integrated segmentation and recognition for writing (Tappert et al 1990) and speech (Renals et aI1992). And there is a rich background in the use of ANNs a-; classifiers, including their use as a low-level, character classifier in a higher-level word recognition system (Bengio et aI1995).

We have investigated the possibility that rapid processing in the visual system could be achieved by using the order of firing in different neurones as a code, rather than more conventional firing rate schemes. Using SPIKENET, a neural net simulator based on integrate-and-fire neurones and in which neurones in the input layer function as analogto-delay converters, we have modeled the initial stages of visual processing. Initial results are extremely promising. Even with activity in retinal output cells limited to one spike per neuron per image (effectively ruling out any form of rate coding), sophisticated processing based on asynchronous activation was nonetheless possible.

The Neurothermostat is an adaptive controller that regulates indoor air temperature in a residence by switching a furnace on or off. The task is framed as an optimal control problem in which both comfort and energy costs are considered as part of the control objective. Because the consequences of control decisions are delayed in time, the N eurothermostat must anticipate heating demands with predictive models of occupancy patterns and the thermal response of the house and furnace. Occupancy pattern prediction is achieved by a hybrid neural net / lookup table. The Neurothermostat searches, at each discrete time step, for a decision sequence that minimizes the expected cost over a fixed planning horizon.

Two dimensional image motion detection neural networks have been implemented using a general purpose analog neural computer. The neural circuits perform spatiotemporal feature extraction based on the cortical motion detection model of Adelson and Bergen. The neural computer provides the neurons, synapses and synaptic time-constants required to realize the model in VLSI hardware. Results show that visual motion estimation can be implemented with simple sum-andthreshold neural hardware with temporal computational capabilities. The neural circuits compute general 20 visual motion in real-time.

We present a connectionist method for representing images that explicitly addresses their hierarchical nature.

We introduce a model for noise-robust analog computations with discrete time that is flexible enough to cover the most important concrete cases, such as computations in noisy analog neural nets and networks of noisy spiking neurons. We show that the presence of arbitrarily small amounts of analog noise reduces the power of analog computational models to that of finite automata, and we also prove a new type of upper bound for the VC-dimension of computational models with analog noise. 1 Introduction Analog noise is a serious issue in practical analog computation. However there exists no formal model for reliable computations by noisy analog systems which allows us to address this issue in an adequate manner. The investigation of noise-tolerant digital computations in the presence of stochastic failures of gates or wires had been initiated by [von Neumann, 1956]. We refer to [Cowan, 1966] and [Pippenger, 1989] for a small sample of the nllmerous results that have been achieved in this direction. The same framework (with stochastic failures of gates or wires) hac; been applied to analog neural nets in [Siegelmann, 1994].

Further im- 528 F. Leisch and K. Hornik provements should be possible based on a better understanding of the theoretical properties of resample and combine techniques. These issues are currently being investigated.

We have calculated analytical expressions for how the bias and variance of the estimators provided by various temporal difference value estimation algorithms change with offline updates over trials in absorbing Markov chains using lookup table representations. We illustrate classes of learning curve behavior in various chains, and show the manner in which TD is sensitive to the choice of its stepsize and eligibility trace parameters. 1 INTRODUCTION A reassuring theory of asymptotic convergence is available for many reinforcement learning (RL) algorithms. What is not available, however, is a theory that explains the finite-term learning curve behavior of RL algorithms, e.g., what are the different kinds of learning curves, what are their key determinants, and how do different problem parameters effect rate of convergence. Answering these questions is crucial not only for making useful comparisons between algorithms, but also for developing hybrid and new RL methods. In this paper we provide preliminary answers to some of the above questions for the case of absorbing Markov chains, where mean square error between the estimated and true predictions is used as the quantity of interest in learning curves.