The model structure is an abstrac- tion of the hippocampus or the olfactory cortex. We propose a simple generalized Hebbian rule, using temporal-activity-dependent LTP and LTD, to encode both magnitudes and phases of oscillatory patterns into the synapses in the network. After learning, the model responds resonantly to inputs which have been learned (or, for networks which operate essentially linearly, to linear combinations of learned inputs), but negligibly to other input patterns. Encoding both amplitude and phase enhances computational capacity, for which the price is having to learn both the excitatory-to-excitatory and the excitatory-to-inhibitory connections. Our model puts contraints on the form of the learning kernal A(r) that should be experimenally observed, e.g., for small oscillation frequencies, it requires that the overall LTP dominates the overall LTD, but this requirement should be modified if the stored oscillations are of high frequencies.

We develop an approach for a sparse representation for Gaussian Process (GP) models in order to overcome the limitations of GPs caused by large data sets. The method is based on a combination of a Bayesian online algorithm togetherwith a sequential construction of a relevant subsample of the data which fully specifies the prediction of the model. Experimental resultson toy examples and large real-world datasets indicate the efficiency of the approach.

We estimate a statistical model of typical activities from a large set of 3D periodic human motion data by segmenting these data automatically into "cycles". Then the mean and the principal componentsof the cycles are computed using a new algorithm that accounts for missing information and enforces smooth transitions betweencycles. The learned temporal model provides a prior probability distribution over human motions that can be used in a Bayesian framework for tracking human subjects in complex monocular video sequences and recovering their 3D motion. 1 Introduction The modeling and tracking of human motion in video is important for problems as varied as animation, video database search, sports medicine, and human-computer interaction. Technically, the human body can be approximated by a collection of articulated limbs and its motion can be thought of as a collection of time-series describing the joint angles as they evolve over time. A key challenge in modeling these joint angles involves decomposing the time-series into suitable temporal primitives.

We investigate a new kernel-based classifier: the Kernel Fisher Discriminant (KFD).A mathematical programming formulation based on the observation thatKFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm.

The Bayesian paradigm apparently only sometimes gives rise to Occam's Razor; at other times very large models perform well. We give simple examples of both kinds of behaviour. The two views are reconciled when measuring complexity of functions, rather than of the machinery used to implement them. We analyze the complexity of functions for some linear in the parameter models that are equivalent to Gaussian Processes, and always find Occam's Razor at work. 1 Introduction Occam's Razor is a well known principle of "parsimony of explanations" which is influential inscientific thinking in general and in problems of statistical inference in particular. In this paper we review its consequences for Bayesian statistical models, where its behaviour can be easily demonstrated and quantified.

A new form of covariance modelling for Gaussian mixture models and hidden Markov models is presented. This is an extension to an efficient form of covariance modelling used in speech recognition, semi-tied covariance matrices.In the standard form of semi-tied covariance matrices the covariance matrix is decomposed into a highly shared decorrelating transform and a component-specific diagonal covariance matrix. The use of a factored decorrelating transform is presented in this paper. This factoring effectivelyincreases the number of possible transforms without increasing thenumber of free parameters. Maximum likelihood estimation schemes for all the model parameters are presented including the component/transform assignment,transform and component parameters. This new model form is evaluated on a large vocabulary speech recognition task. It is shown that using this factored form of covariance modelling reduces the word error rate. 1 Introduction A standard problem in machine learning is to how to efficiently model correlations in multidimensional data.Solutions should be efficient both in terms of number of model parameters and cost of the likelihood calculation. For speech recognition this is particularly important due to the large number of Gaussian components used, typically in the tens of thousands, and the relatively large dimensionality of the data, typically 30-60.

Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves for Gaussian processregression models. The approximation works well in the large sample size limit and for arbitrary dimensionality of the input space. We explain how the approximation can be systematically improvedand argue that similar techniques can be applied to general likelihood models. 1 Introduction Gaussian process (GP) models have gained considerable interest in the Neural Computation Community(see e.g.[I, 2, 3, 4]) in recent years. Being nonparametric models by construction their theoretical understanding seems to be less well developed comparedto simpler parametric models like neural networks. We are especially interested in developing theoretical approaches which will at least give good approximations togeneralization errors when the number of training data is sufficiently large. In this paper we present a step in this direction which is based on a statistical mechanics approach.In contrast to most previous applications of statistical mechanics to learning theory we are not limited to the so called "thermodynamic" limit which would require a high dimensional input space.

In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters toobtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particlefiltering and other nonlinear filtering methods very substantially.

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.

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