Exact inference in densely connected Bayesian networks is computationally intractable,and so there is considerable interest in developing effective approximation schemes. One approach which has been adopted is to bound the log likelihood using a mean-field approximating distribution. While this leads to a tractable algorithm, the mean field distribution is assumed tobe factorial and hence unimodal.

Human subjects are known to adapt their motor behavior to a shift of the visual field brought about by wearing prism glasses over their eyes. We have studied the analog of this effect in speech. U sing a device that can feed back transformed speech signals in real time, we exposed subjects to alterations of their own speech feedback. We found that speakers learn to adjust their production of a vowel to compensate for feedback alterations that change the vowel's perceived phonetic identity; moreover, the effect generalizes across consonant contexts and to different vowels. 1 INTRODUCTION For more than a century, it has been know that humans will adapt their reaches to altered visual feedback [8]. One of the most studied examples of this adaptation is prism adaptation, which is seen when a subject reaches to targets while wearing image-shifting prism glasses [2].

The learning and inferencing algorithms presented here speak an extended form of the classical figured bass representation common in Bach's time. Paired with a melody, figured bass provides a sufficient amount of information to reconstruct the harmonic content of a piece of music. Figured bass has several characteristics which make it well-disposed to learning rules. It is a symbolic format which uses a relatively small alphabet of symbols. It is also hierarchical - it specifies first the chord function that is to be played at the current note/timestep, then the scale step to be played by the bass voice, then additional information as needed to specify the alto and tenor scale steps. This allows our algorithm to fire sets of rules sequentially, to first determine the chord function which should be associated with a new melody note, and then to use that chord function as an input attribute to subsequent rulebases which determine the bass, alto, and tenor scale steps. In this way we can build up the final chord from simpler pieces, each governed by a specialized rulebase.

The observed distribution of natural images is far from uniform. On the contrary, real images have complex and important structure thatcan be exploited for image processing, recognition and analysis. There have been many proposed approaches to the principled statisticalmodeling of images, but each has been limited in either the complexity of the models or the complexity of the images. Wepresent a nonparametric multi-scale statistical model for images that can be used for recognition, image de-noising, and in a "generative mode" to synthesize high quality textures.

Scale invariance is a fundamental property of ensembles of natural images[1]. Their non Gaussian properties [15, 16] are less well understood, but they indicate the existence of a rich statistical structure.In this work we present a detailed study of the marginal statistics of a variable related to the edges in the images. A numerical analysis shows that it exhibits extended self-similarity [3, 4, 5]. This is a scaling property stronger than self-similarity: all its moments can be expressed as a power of any given moment. More interesting, all the exponents can be predicted in terms of a multiplicative log-Poisson process. This is the very same model that was used very recently to predict the correct exponents of the structure functions of turbulent flows [6]. These results allow us to study the underlying multifractal singularities. In particular we find that the most singular structures are one-dimensional: the most singular manifold consists of sharp edges.

In contrast to the maximum likelihood approach which finds only a single estimate for the regression parameters, the Bayesian approach yields a distribution of weight parameters, p(wID), conditional on the training data D, and predictions are ex- ·Present address: SNN, University of Nijmegen, Geert Grooteplein 21, Nijmegen, The Netherlands.

Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112 Abstract We propose diffusion networks, a type of recurrent neural network with probabilistic dynamics, as models for learning natural signals that are continuous in time and space. We give a formula for the gradient of the log-likelihood of a path with respect to the drift parameters for a diffusion network. This gradient can be used to optimize diffusion networks in the nonequilibrium regime for a wide variety of problems paralleling techniques which have succeeded in engineering fields such as system identification, state estimation and signal filtering. An aspect of this work which is of particular interestto computational neuroscience and hardware design is that with a suitable choice of activation function, e.g., quasi-linear sigmoidal, the gradient formula is local in space and time. 1 Introduction Many natural signals, like pixel gray-levels, line orientations, object position, velocity andshape parameters, are well described as continuous-time continuous-valued stochastic processes; however, the neural network literature has seldom explored the continuous stochastic case. Since the solutions to many decision theoretic problems of interest are naturally formulated using probability distributions, it is desirable to have a flexible framework for approximating probability distributions on continuous pathspaces.

We have a developed an analog VLSI system that models the coordination ofneurobiological segmental oscillators. We have implemented and tested a system that consists of a chain of eleven pattern generating circuits thatare synaptically coupled to their nearest neighbors. Each pattern generating circuit is implemented with two silicon Morris-Lecar neurons that are connected in a reciprocally inhibitory network. We discuss themechanisms of oscillations in the two-cell network and explore system behavior based on isotropic and anisotropic coupling, and frequency gradientsalong the chain of oscillators.

Weconsider a deterministic system with continuous state and time with infinite horizon discounted cost functional.

Department of Physics, Cavendish Laboratory Cambridge University Abstract Until recently, artificial intelligence researchers have frowned upon the application of probability propagation in Bayesian belief networks thathave cycles. The probability propagation algorithm is only exact in networks that are cycle-free. Examples of real-world channels include twisted-pair telephone wires, shielded cable-TV wire, fiberoptic cable, deep-space radio, terrestrial radio, and indoor radio. Engineers attempt to correct the errors introduced by the noise in these channels through the use of channel coding which adds protection to the information source, so that some channel errors can be corrected. A popular model of a physical channel is shown in Figure 1.