We propose a new Markov Chain Monte Carlo algorithm which is a generalization of the stochastic dynamics method. The algorithm performs exploration of the state space using its intrinsic geometric structure, facilitating efficient sampling of complex distributions. Applied to Bayesian learning in neural networks, our algorithm was found to perform at least as well as the best state-of-the-art method while consuming considerably less time. 1 Introduction

In this paper, we consider the problem of active learning in trigonometric polynomial networks and give a necessary and sufficient condition of sample points to provide the optimal generalization capability. By analyzing the condition from the functional analytic point of view, we clarify the mechanism of achieving the optimal generalization capability. We also show that a set of training examples satisfying the condition does not only provide the optimal generalization but also reduces the computational complexity and memory required for the calculation of learning results. Finally, examples of sample points satisfying the condition are given and computer simulations are performed to demonstrate the effectiveness of the proposed active learning method.

An important issue in neural computing concerns the description of learning dynamics with macroscopic dynamical variables. Recent progress on online learning only addresses the often unrealistic case of an infinite training set. We introduce a new framework to model batch learning of restricted sets of examples, widely applicable to any learning cost function, and fully taking into account the temporal correlations introduced by the recycling of the examples. For illustration we analyze the effects of weight decay and early stopping during the learning of teacher-generated examples.

The performance of regular and irregular Gallager-type errorcorrecting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of nonzero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity may be saturated in equilibrium for many of the regular codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding. We show that irregular codes may saturate Shannon's capacity but with improved dynamical properties. 1 Introduction The ever increasing information transmission in the modern world is based on reliably communicating messages through noisy transmission channels; these can be telephone lines, deep space, magnetic storing media etc. Error-correcting codes play a significant role in correcting errors incurred during transmission; this is carried out by encoding the message prior to transmission and decoding the corrupted received code-word for retrieving the original message.

Hierarchical learning machines are non-regular and non-identifiable statistical models, whose true parameter sets are analytic sets with singularities. Using algebraic analysis, we rigorously prove that the stochastic complexity of a non-identifiable learning machine is asymptotically equal to '1 log n - (ml - 1) log log n

A latent variable generative model with finite noise is used to describe several different algorithms for Independent Components Analysis (lCA). In particular, the Fixed Point ICA algorithm is shown to be equivalent to the Expectation-Maximization algorithm for maximum likelihood under certain constraints, allowing the conditions for global convergence to be elucidated. The algorithms can also be explained by their generic behavior near a singular point where the size of the optimal generative bases vanishes. An expansion of the likelihood about this singular point indicates the role of higher order correlations in determining the features discovered by ICA. The application and convergence of these algorithms are demonstrated on a simple illustrative example.

This paper describes bidirectional recurrent mixture density networks, which can model multi-modal distributions of the type P(Xt Iyf) and P(Xt lXI, X2,...,Xt-l, yf) without any explicit assumptions about the use of context. These expressions occur frequently in pattern recognition problems with sequential data, for example in speech recognition. Experiments show that the proposed generative models give a higher likelihood on test data compared to a traditional modeling approach, indicating that they can summarize the statistical properties of the data better. 1 Introduction Many problems of engineering interest can be formulated as sequential data problems in an abstract sense as supervised learning from sequential data, where an input vector (dimensionality D) sequence X xf {X!,X2,...,XT_!,XT} living in space X has to be mapped to an output vector (dimensionality J) target sequence T tf {tl' t 2,..., tT

Gaussian Processes are powerful regression models specified by parametrized mean and covariance functions. Standard approaches to estimate these parameters (known by the name Hyperparameters) are Maximum Likelihood (ML) and Maximum APosterior (MAP) approaches. In this paper, we propose and investigate predictive approaches, namely, maximization of Geisser's Surrogate Predictive Probability (GPP) and minimization of mean square error with respect to GPP (referred to as Geisser's Predictive mean square Error (GPE)) to estimate the hyperparameters. We also derive results for the standard Cross-Validation (CV) error and make a comparison. These approaches are tested on a number of problems and experimental results show that these approaches are strongly competitive to existing approaches. 1 Introduction Gaussian Processes (GPs) are powerful regression models that have gained popularity recently, though they have appeared in different forms in the literature for years.

This paper revisits the classical neuroscience paradigm of Hebbian learning. We find that a necessary requirement for effective associative memory learning is that the efficacies of the incoming synapses should be uncorrelated. This requirement is difficult to achieve in a robust manner by Hebbian synaptic learning, since it depends on network level information. Effective learning can yet be obtained by a neuronal process that maintains a zero sum of the incoming synaptic efficacies. This normalization drastically improves the memory capacity of associative networks, from an essentially bounded capacity to one that linearly scales with the network's size.

This question was recently shown in [9] to be a special case of a much more fundamental problem: What are the features of the variable X that are relevant for the prediction of another, relevance, variable Y?