Statistical learning and probabilistic inference techniques are used to infer thehand position of a subject from multi-electrode recordings of neural activityin motor cortex. First, an array of electrodes provides training dataof neural firing conditioned on hand kinematics. We learn a nonparametric representationof this firing activity using a Bayesian model and rigorously compare it with previous models using cross-validation. Second, we infer a posterior probability distribution over hand motion conditioned on a sequence of neural test data using Bayesian inference. The learned firing models of multiple cells are used to define a non-Gaussian likelihood term which is combined with a prior probability for the kinematics. A particle filtering method is used to represent, update, and propagate the posterior distribution over time. The approach is compared withtraditional linear filtering methods; the results suggest that it may be appropriate for neural prosthetic applications.

The marriage of Renyi entropy with Parzen density estimation has been shown to be a viable tool in learning discriminative feature transforms. However, it suffers from computational complexity proportional to the square of the number of samples in the training data. This sets a practical limit to using large databases. We suggest immediate divorce of the two methods and remarriage of Renyi entropy with a semi-parametric density estimation method, such as a Gaussian Mixture Models (GMM). This allows allof the computation to take place in the low dimensional target space, and it reduces computational complexity proportional to square of the number of components in the mixtures. Furthermore, a convenient extensionto Hidden Markov Models as commonly used in speech recognition becomes possible.

Greedy approximation algorithms have been frequently used to obtain sparse solutions to learning problems. In this paper, we present a general greedy algorithm for solving a class of convex optimization problems. We derive a bound on the rate of approximation for this algorithm, and show that our algorithm includes a number of earlier studies as special cases.

Multisensory response enhancement (MRE) is the augmentation of the response of a neuron to sensory input of one modality by simultaneous inputfrom another modality. The maximum likelihood (ML) model presented here modifies the Bayesian model for MRE (Anastasio et al.) by incorporating a decision strategy to maximize the number of correct decisions. Thus the ML model can also deal with the important tasks of stimulus discrimination and identification inthe presence of incongruent visual and auditory cues. It accounts for the inverse effectiveness observed in neurophysiological recordingdata, and it predicts a functional relation between uni-and bimodal levels of discriminability that is testable both in neurophysiological and behavioral experiments.

When applying unsupervised learning techniques like ICA or temporal decorrelation,a key question is whether the discovered projections arereliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling methods totackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the separation error.We demonstrate that this reliability estimation can be used to choose the appropriate ICA-model, to enhance significantly theseparation performance, and, most important, to mark the components that have a actual physical meaning.

We develop a tree-based reparameterization framework that provides anew conceptual view of a large class of iterative algorithms for computing approximate marginals in graphs with cycles. It includes belief propagation (BP), which can be reformulated as a very local form of reparameterization. More generally, we consider algorithms that perform exact computations over spanning trees of the full graph. On the practical side, we find that such tree reparameterization (TRP) algorithms have convergence properties superior to BP. The reparameterization perspective also provides a number of theoretical insights into approximate inference, including anew characterization of fixed points; and an invariance intrinsic to TRP /BP. These two properties enable us to analyze and bound the error between the TRP /BP approximations and the actual marginals. While our results arise naturally from the TRP perspective, most of them apply in an algorithm-independent manner to any local minimum of the Bethe free energy.

One formulation is based on SVM regression; the second is based on the Bellman equation; and the third seeks only to ensure that good moves have an advantage over bad moves. All formulations attemptto minimize the number of support vectors while fitting the data. Experiments in a difficult, synthetic maze problem show that all three formulations give excellent performance, but the advantage formulation is much easier to train. Unlike policy gradient methods,the kernel methods described here can easily'adjust the complexity of the function approximator to fit the complexity of the value function.

Recent approaches have used uncertainty over the vocabulary of symbols in a multinomial distribution as a means of accounting for sparsity. We present a Bayesian approach that allows weak prior knowledge, in the form of a small set of approximate candidate vocabularies, to be used to dramatically improve the resulting estimates. We demonstrate these improvements in applications to text compression andestimating distributions over words in newsgroup data. 1 Introduction Sparse multinomial distributions arise in many statistical domains, including natural languageprocessing and graphical models. Consequently, a number of approaches toparameter estimation for sparse multinomial distributions have been suggested [3]. These approaches tend to be domain-independent: they make little use of prior knowledge about a specific domain. In many domains where multinomial distributionsare estimated there is often at least weak prior knowledge about' the potential structure of distributions, such as a set of hypotheses about restricted vocabularies from which the symbols might be generated. Such knowledge can be solicited from experts or obtained from unlabeled data. We present a method for Bayesian_parameter estimation in sparse discrete domains that exploits this weak form of prior knowledge to improve estimates over knowledge-free approaches.

Agakov System Engineering Research Group Chair of Manufacturing Technology Universitiit Erlangen-Niirnberg 91058 Erlangen, Germany F.Agakov@lft·uni-erlangen.de Stephen N. Felderhof Division of Informatics University of Edinburgh Edinburgh EH1 2QL, UK stephenf@dai.ed.ac.uk Abstract Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data. Below weconsider PoE models in which each expert is a Gaussian. Although the product of Gaussians is also a Gaussian, if each Gaussian hasa simple structure the product can have a richer structure. We examine (1) Products of Gaussian pancakes which give rise to probabilistic Minor Components Analysis, (2) products of I-factor PPCA models and (3) a products of experts construction for an AR(l) process. Recently Hinton (1999) has introduced the Products of Experts (PoE) model in which several individual probabilistic models for data are combined to provide an overall model of the data.

The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propagation. Lastly,we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classification anddensity estimation with Gaussian processes and on an independent componentanalysis problem.