If a polyhedral distance is used, the problem can be formulated as that of minimizing a piecewise-linear concave function on a polyhedral set which is shown to be equivalent to a bilinear program: minimizing a bilinear function on a polyhedral set.A fast finite k-Median Algorithm consisting of solving few linear programs in closed form leads to a stationary point of the bilinear program.

Neural one-unit learning rules for the problem of Independent Component Analysis(ICA) and blind source separation are introduced. In these new algorithms, every ICA neuron develops into a separator thatfinds one of the independent components. The learning rules use very simple constrained Hebbianjanti-Hebbian learning in which decorrelating feedback may be added. To speed up the convergence of these stochastic gradient descent rules, a novel computationally efficientfixed-point algorithm is introduced. 1 Introduction Independent Component Analysis (ICA) (Comon, 1994; Jutten and Herault, 1991) is a signal processing technique whose goal is to express a set of random variables aslinear combinations of statistically independent component variables. The main applications of ICA are in blind source separation, feature extraction, and blind deconvolution.

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.

The perturbation method which we have presented overcomes the limitations of standard approaches, which are only appropriate for models with a single layer of adjustable weights, albeit at considerable computational expense. It has the added bonus of automatically taking into account the effect of regularisation techniques such as weight decay. The experimental results illustrate the application of the technique to two simple problems. As expected the number of degrees of freedom in the models is found to be related to the amount of weight decay used during training. The equivalent kernels are found to vary significantly in different regions of input space and the functions reconstructed from the estimated smoother matrices closely match the origna!

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.

Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values between nominal attribute values, but it largely ignores continuous attributes, requiring discretization to map continuous values into nominal values. This paper proposes three new heterogeneous distance functions, called the Heterogeneous Value Difference Metric (HVDM), the Interpolated Value Difference Metric (IVDM), and the Windowed Value Difference Metric (WVDM). These new distance functions are designed to handle applications with nominal attributes, continuous attributes, or both. In experiments on 48 applications the new distance metrics achieve higher classification accuracy on average than three previous distance functions on those datasets that have both nominal and continuous attributes.

The purpose of most architecture optimization schemes is to improve generalization.

In this paper we introduce new algorithms for optimizing noisy plants in which each experiment is very expensive. The algorithms build a global nonlinear model of the expected output at the same time as using Bayesian linear regression analysis of locally weighted polynomial models. The local model answers queries about confidence, noise, gradient and Hessians, and use them to make automated decisions similar to those made by a practitioner of Response Surface Methodology. The global and local models are combined naturally as a locally weighted regression. We examine the question of whether the global model can really help optimization, and we extend it to the case of time-varying functions. We compare the new algorithms with a highly tuned higher-order stochastic optimization algorithm on randomly-generated functions and a simulated manufacturing task. We note significant improvements in total regret, time to converge, and final solution quality. 1 INTRODUCTION In a stochastic optimization problem, noisy samples are taken from a plant. A sample consists of a chosen control u (a vector ofreal numbers) and a noisy observed response y.