W is often taken to be diagonal, but if we allow W to be a general positive definite matrix which can be tuned on the basis of training data, then an eigen-analysis of W shows that we are effectively creating hidden features, where the dimensionality of the hidden-feature space is determined by the data. We demonstrate the superiority of predictions usi ng the general matrix over those based on a diagonal matrix on two test problems.

Arguably oneabilities of the most important types of information processing is the capacity for probabilistic reasoning. The properties of undirectedproDabilistic models represented as symmetric networks ethave been studied extensively using methods from statistical mechanics (Hertz aI, 1991). Detailed analyses of these models are possible by exploiting averaging that occur in the thermodynamic limit of large networks.phenomena In this paper, we analyze the limit of large, multilayer networks for probabilistic models represented as directed acyclic graphs. These models are known as Bayesian networks (Pearl, 1988; Neal, 1992), and they have different probabilistic semantics than symmetric neural networks (such as Hopfield models or Boltzmann machines). We show that the intractability of exact inference in multilayer Bayesian networks 261 Inference in Multilayer Networks via Large Deviation Bounds does not preclude their effective use. Our work builds on earlier studies of variational methods (Jordan et aI, 1997).

A recent neural model of illusory contour formation is based on a distribution of natural shapes traced by particles moving with constant speed in directions given by Brownian motions. The input to that model consists of pairs of position and direction constraints and the output consists of the distribution of contours joining all such pairs. In general, these contours will not be closed and their distribution will not be scale-invariant. In this paper, we show how to compute a scale-invariant distribution of closed contours given position constraints alone and use this result to explain a well known illusory contour effect. 1 INTRODUCTION It has been proposed by Mumford[3] that the distribution of illusory contour shapes can be modeled by particles travelling with constant speed in directions given by Brownian motions. More recently, Williams and Jacobs[7, 8] introduced the notion of a stochastic completion field, the distribution of particle trajectories joining pairs of position and direction constraints, and showed how it could be computed in a local parallel network. They argued that the mode, magnitude and variance of the completion field are related to the observed shape, salience, and sharpness of illusory contours.

The dark curve is AdaBoost, the light curve is DOOM. DOOM sacrifices significant training error forimproved test error (horizontal markson margin 0 line)_ 1 Introduction Many learning algorithms for pattern classification minimize some cost function of the training data, with the aim of minimizing error (the probability of misclassifying an example). One example of such a cost function is simply the classifier's error on the training data.

Based on a simple convexity lemma, we develop bounds for different typesof Bayesian prediction errors for regression with Gaussian processes. The basic bounds are formulated for a fixed training set. Simpler expressions are obtained for sampling from an input distribution whichequals the weight function of the covariance kernel, yielding asymptotically tight results. The results are compared with numerical experiments.

Following recent results [9, 8] showing the importance of the fatshattering dimensionin explaining the beneficial effect of a large margin on generalization performance, the current paper investigates theimplications of these results for the case of imbalanced datasets and develops two approaches to setting the threshold. The approaches are incorporated into ThetaBoost, a boosting algorithm fordealing with unequal loss functions. The performance of ThetaBoost and the two approaches are tested experimentally.

On the other hand, in 804 P.J Phillips face recognition, there are many individuals (classes), and only a few images (samples) per person, and algorithms must recognize faces by extrapolating from the training samples. In numerous applications there can be only one training sample (image) of each person. Support vector machines (SVMs) are formulated to solve a classical two class pattern recognition problem. We adapt SVM to face recognition by modifying the interpretation of the output of a SVM classifier and devising a representation of facial images that is concordant with a two class problem. Traditional SVM returns a binary value, the class of the object.

We present a stochastic clustering algorithm based on pairwise similarity ofdatapoints. Our method extends existing deterministic methods, including agglomerative algorithms, min-cut graph algorithms, andconnected components. Thus it provides a common framework for all these methods. Our graph-based method differs from existing stochastic methods which are based on analogy to physical systems. The stochastic nature of our method makes it more robust against noise, including accidental edges and small spurious clusters. We demonstrate the superiority of our algorithm using an example with 3 spiraling bands and a lot of noise. 1 Introduction Clustering algorithms can be divided into two categories: those that require a vectorial representationof the data, and those which use only pairwise representation. In the former case, every data item must be represented as a vector in a real normed space, while in the second case only pairwise relations of similarity or dissimilarity areused.

Te-Won Lee, Michael S. Lewicki and Terrence Sejnowski Howard Hughes Medical Institute Computational Neurobiology Laboratory The Salk Institute 10010 N. Torrey Pines Road La Jolla, California 92037, USA {tewon,lewicki,terry}Osalk.edu Abstract We present an unsupervised classification algorithm based on an ICA mixture model. The ICA mixture model assumes that the observed data can be categorized into several mutually exclusive data classes in which the components in each class are generated by a linear mixture of independent sources. The algorithm finds the independent sources, the mixing matrix for each class and also computes the class membership probability for each data point. This approach extends the Gaussian mixture model so that the classes can have non-Gaussian structure. We demonstrate that this method can learn efficient codes to represent images of natural scenes and text.

We describe the first single microphone sound localization system and its inspiration from theories of human monaural sound localization. Reflectionsand diffractions caused by the external ear (pinna) allow humans to estimate sound source elevations using only one ear. Our single microphone localization model relies on a specially shaped reflecting structure that serves the role of the pinna. Specially designedanalog VLSI circuitry uses echo-time processing to localize the sound. A CMOS integrated circuit has been designed, fabricated, and successfully demonstrated on actual sounds. 1 Introduction The principal cues for human sound localization arise from time and intensity differences betweenthe signals received at the two ears. For low-frequency components of sounds (below 1500Hz for humans), the phase-derived interaural time difference (lTD) can be used to localize the sound source. For these frequencies, the sound wavelength is at least several times larger than the head and the amount of shadowing (whichdepends on the wavelength of the sound compared with the dimensions of the head) is negligible.