Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical resultsfor the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these results tothe Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smoothing propagation,while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimensionality ofthe state-space model in a variety of synthetic problems and one real high-dimensional data set. 1 Introduction Bayesian approaches to machine learning have several desirable properties. Bayesian integration does not suffer overfitting (since nothing is fit to the data). Prior knowledge canbe incorporated naturally and all uncertainty is manipulated in a consistent manner. Moreover it is possible to learn model structures and readily compare between model classes. Unfortunately, for most models of interest a full Bayesian analysis is computationally intractable.

Theneurons in these networks are the random variables, whereas the connections between them model the causal dependencies. Usually, some of the nodes have a direct relation with the random variables in the problem and are called'visibles'. The other nodes, known as'hiddens', are used to model more complex probability distributions. Learning in graphical models can be done as long as the likelihood that the visibles correspond to a pattern in the data set, can be computed. In general the time it takes, scales exponentially with the number of hidden neurons.

The principle of maximizing mutual information is applied to learning overcomplete and recurrent representations. The underlying model consists ofa network of input units driving a larger number of output units with recurrent interactions. In the limit of zero noise, the network is deterministic andthe mutual information can be related to the entropy of the output units.

Igor V. Cadez Information and Computer Science University of California Irvine, CA 92697-3425, U.S.A. PadhraicSmyth Information and Computer Science University of California Irvine, CA 92697-3425, U.S.A. Abstract We investigate a general characteristic of the tradeoff in learning problems between goodness-of-fit and model complexity. Specifically wecharacterize a general class of learning problems where the goodness-of-fit function can be shown to be convex within firstorder asa function of model complexity. This general property of "diminishing returns" is illustrated on a number of real data sets and learning problems, including finite mixture modeling and multivariate linear regression. 1 Introduction, Motivation, and Related Work Assume we have a data set D Such learning tasks can typically be characterized by the existence of a model and a loss function. A fitted model of complexity k is a function of the data points D and depends on a specific set of fitted parameters B. The loss function (goodnessof-fit) isa functional of the model and maps each specific model to a scalar used to evaluate the model, e.g., likelihood for density estimation or sum-of-squares for regression. Figure 1 illustrates a typical empirical curve for loss function versus complexity, for mixtures of Markov models fitted to a large data set of 900,000 sequences.

In this paper, we discuss some new research directions in automatic speech recognition (ASR), and which somewhat deviate from the usual approaches. More specifically, we will motivate and briefly describe new approaches based on multi-stream and multi/band ASR. These approaches extend the standard hidden Markov model (HMM) based approach by assuming that the different (frequency) channels representing the speech signal are processed by different (independent) "experts", each expert focusing on a different characteristic ofthe signal, and that the different stream likelihoods (or posteriors) are combined at some (temporal) stage to yield a global recognition output. As a further extension to multi-stream ASR, we will finally introduce a new approach, referred to as HMM2, where the HMM emission probabilities are estimated via state specific featurebased HMMs responsible for merging the stream information andmodeling their possible correlation.

Stimulus arrays are inevitably presented at different positions on the retina in visual tasks, even those that nominally require fixation.

Visual input, providedby a video camera on a miniature robot, is preprocessed by a set of Gabor filters on 31 nodes of a log-polar retinotopic graph. Unsupervised Hebbianlearning is employed to incrementally build a population of localized overlapping place fields. Place cells serve as basis functions forreinforcement learning. Experimental results for goal-oriented navigation of a mobile robot are presented.

In this communication we present a new algorithm for solving Support Vector Classifiers (SVC) with large training data sets. The new algorithm is based on an Iterative Re-Weighted Least Squares procedure which is used to optimize the SVc. Moreover, a novel sample selection strategy for the working set is presented, which randomly chooses the working set among the training samples that do not fulfill the stopping criteria. The validity of both proposals, the optimization procedure and sample selection strategy, is shown by means of computer experiments using well-known data sets.

We present a novel method for clustering using the support vector machine approach.Data points are mapped to a high dimensional feature space, where support vectors are used to define a sphere enclosing them. The boundary of the sphere forms in data space a set of closed contours containing the data. Data points enclosed by each contour are defined as a cluster. As the width parameter of the Gaussian kernel is decreased, these contours fit the data more tightly and splitting of contours occurs. The algorithm works by separating clusters according to valleys in the underlying probabilitydistribution, and thus clusters can take on arbitrary geometrical shapes.

E lRP such as to achieve minimum Bayes error (or probability of misclassification). Two avenues will be explored: the first is to maximize the ()-average divergence between the class densities and the second is to minimize the union Bhattacharyya bound in the range of (). While both approaches yield similar performance in practice, they outperform standardLDA features and show a 10% relative improvement in the word error rate over state-of-the-art cepstral features on a large vocabulary telephony speech recognition task. 1 Introduction Modern speech recognition systems use cepstral features characterizing the short-term spectrum of the speech signal for classifying frames into phonetic classes. These features are augmented with dynamic information from the adjacent frames to capture transient spectral events in the signal.