We present the embedded trees algorithm, an iterative technique for estimation of Gaussian processes defined on arbitrary graphs. By exactly solving a series of modified problems on embedded spanning trees, it computes the conditional means with an efficiency comparable to or better than other techniques. Unlike other methods, the embedded trees algorithm also computes exact error covariances. The error covariance computation is most efficient for graphs in which removing a small number of edges reveals an embedded tree. In this context, we demonstrate that sparse loopy graphs can provide a significant increase in modeling power relative to trees, with only a minor increase in estimation complexity.

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 effectively increases the number of possible transforms without increasing the number of free parameters.

Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoretical results for 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 to the 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 of the 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.

In multi-service communications networks, such as Asynchronous Transfer Mode (ATM) networks, resource control is of crucial importance for the network operator as well as for the users. The objective is to maintain the service quality while maximizing the operator's revenue. At the call level, service quality (Grade of Service) is measured in terms of call blocking probabilities, and the key resource to be controlled is bandwidth. Network routing and call admission control (CAC) are two such resource control problems. Markov decision processes offer a framework for optimal CAC and routing [1]. By modelling the dynamics of the network with traffic and computing control policies using dynamic programming [2], resource control is optimized. A standard assumption in such models is that calls arrive according to Poisson processes. This makes the models of the dynamics relatively simple. Although the Poisson assumption is valid for most user-initiated requests in communications networks, a number of studies [3, 4, 5] indicate that many types of arrival similar.

We introduce stagewise processing in error-correcting codes and image restoration, by extracting information from the former stage and using it selectively to improve the performance of the latter one. Both mean-field analysis using the cavity method and simulations show that it has the advantage of being robust against uncertainties in hyperparameter estimation. 1 Introduction In error-correcting codes [1] and image restoration [2], the choice of the so-called hyperparameters is an important factor in determining their performances. Hyperparameters refer to the coefficients weighing the biases and variances of the tasks. In error correction, they determine the statistical significance given to the paritychecking terms and the received bits. Similarly in image restoration, they determine the statistical weights given to the prior knowledge and the received data.

We analyze the bit error probability of multiuser demodulators for directsequence binary phase-shift-keying (DSIBPSK) CDMA channel with additive gaussian noise. The problem of multiuser demodulation is cast into the finite-temperature decoding problem, and replica analysis is applied to evaluate the performance of the resulting MPM (Marginal Posterior Mode) demodulators, which include the optimal demodulator and the MAP demodulator as special cases. An approximate implementation of demodulators is proposed using analog-valued Hopfield model as a naive mean-field approximation to the MPM demodulators, and its performance is also evaluated by the replica analysis. Results of the performance evaluation shows effectiveness of the optimal demodulator and the mean-field demodulator compared with the conventional one, especially in the cases of small information bit rate and low noise level.

We present a computational model of the neural mechanisms in the parietal and temporal lobes that support spatial navigation, recall of scenes and imagery of the products of recall. Long term representations are stored in the hippocampus, and are associated with local spatial and object-related features in the parahippocampal region. Viewer-centered representations are dynamically generated from long term memory in the parietal part of the model. The model thereby simulates recall and imagery of locations and objects in complex environments. After parietal damage, the model exhibits hemispatial neglect in mental imagery that rotates with the imagined perspective of the observer, as in the famous Milan Square experiment [1]. Our model makes novel predictions for the neural representations in the parahippocampal and parietal regions and for behavior in healthy volunteers and neuropsychological patients.

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 in scientific 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.

For example, priming in a subliminal perception task was found to be confined to a quadrant of the visual field [16]. The notion that the representation of an object may be tied to a particular location in the visual field where it is first observed is compatible with the concept of object file, a hypothetical record created by the visual system for every encountered object, which persists as long as the object is observed. Moreover, location (as it figures in the CoF model) should be interpreted relative to the focus of attention, rather than retinotopically [17]. The idea that global relationships (hence, large-scale structure) have precedence over local ones [18], which is central to our approach, has withstood extensive testing in the past two decades. Even with the perceptual salience of the global and local structure equated, subjects are able to process the relations among elements before the elements themselves are identified [19]. More generally, humans are limited in their ability to represent spatial structure, in that the representation of spatial relations requires spatial attention.

In this paper we show that the kernel peA algorithm of Sch6lkopf et al (1998) can be interpreted as a form of metric multidimensional scaling (MDS) when the kernel function k(x, y) is isotropic, i.e. it depends only on Ilx - yll. This leads to a metric MDS algorithm where the desired configuration of points is found via the solution of an eigenproblem rather than through the iterative optimization of the stress objective function. The question of kernel choice is also discussed.