We wish to exploit the linear autoregressive technique in a manner that will enable a substantial increase in modeling power, in a framework which is nonlinear and yet mathematically tractable. The novel model, whose main building blocks are linear AR models, deviates from linearity in the integration process, that is, the way these blocks are combined. This model was first formulated in the context of a regression problem, and an extension to a hierarchical structure was also given [2]. It was termed the mixture of experts model (MEM). Variants of this model have recently been used in prediction problems both in economics and engineering.

Large dots indicate SVs .

In this paper we apply the method of complexity regularization to derive estimationbounds for nonlinear function estimation using a single hidden layer radial basis function network.

A new regression technique based on Vapnik's concept of support vectors is introduced. We compare support vector regression (SVR) with a committee regression technique (bagging) based on regression trees and ridge regression done in feature space. On the basis of these experiments, it is expected that SVR will have advantages in high dimensionality space because SVR optimization does not depend on the dimensionality of the input space.

Shun-ichi Amari RIKEN Frontier Research Program, RIKEN, Hirosawa 2-1, Wako-shi 351-01, Japan amari@zoo.riken.go.jp Abstract The parameter space of neural networks has a Riemannian metric structure.The natural Riemannian gradient should be used instead of the conventional gradient, since the former denotes the true steepest descent direction of a loss function in the Riemannian space. The behavior of the stochastic gradient learning algorithm is much more effective if the natural gradient is used. The present paper studies the information-geometrical structure of perceptrons and other networks, and prove that the online learning method based on the natural gradient is asymptotically as efficient as the optimal batch algorithm. Adaptive modification of the learning constant is proposed and analyzed in terms of the Riemannian measure andis shown to be efficient. The natural gradient is finally applied to blind separation of mixtured independent signal sources. 1 Introd uction Neural learning takes place in the parameter space of modifiable synaptic weights of a neural network.

The weakly electric fish, Eigenmannia, generates a quasi sinusoidal, dipole-like electric fieldat individually fixed frequencies (250 - 600 Hz) by discharging an electric organ located in its tail (see Bullock and Heilgenberg, 1986 for reviews).

Recognition of specific objects, such as recognition of a particular face, can be based on representations that are object centered, such as 3D structural models. Alternatively, a 3D object may be represented for the purpose of recognition in terms of a set of views. This latter class of models is biologically attractive because model acquisition - the learning phase - is simpler and more natural. A simple model for this strategy of object recognition was proposed by Poggio and Edelman (Poggio and Edelman, 1990). They showed that, with few views of an object usedas training examples, a classification network, such as a Gaussian radial basis function network, can learn to recognize novel views of that object, in partic- 42 E.Bricolo, T. Poggio and N. Logothetis (a) (b) View angle Figure 1: (a) Schematic representation of the architecture of the Poggio-Edelman model. The shaded circles correspond to the view-tuned units, each tuned to a view of the object, while the open circle correspond to the view-invariant, object specific output unit.

Machine-learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (1) the improvement of classification accuracy by learning ensembles of classifiers, (2) methods for scaling up supervised learning algorithms, (3) reinforcement learning, and (4) the learning of complex stochastic models.

We study numerically the properties of the bayesian perceptron through a gradient descent on the optimal cost function. The theoretical distribution of stabilities is deduced. It predicts that the optimal generalizer lies close to the boundary of the space of (error-free) solutions. The numerical simulations are in good agreement with the theoretical distribution. The extrapolation of the generalization error to infinite input space size agrees with the theoretical results. Finite size corrections are negative and exhibit two different scaling regimes, depending on the training set size. The variance of the generalization error vanishes for $N \rightarrow \infty$ confirming the property of self-averaging.

The National Aeronautics and Space Administration (NASA) is being challenged to perform more frequent and intensive space-exploration missions at greatly reduced cost. Nowhere is this challenge more acute than among robotic planetary exploration missions that the Jet Propulsion Laboratory (JPL) conducts for NASA. This article describes recent and ongoing work on spacecraft autonomy and ground systems that builds on a legacy of existing success at JPL applying AI techniques to challenging computational problems in planning and scheduling, real-time monitoring and control, scientific data analysis, and design automation.