Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

A representation of representation applied to a discussion of variable binding

States or state sequences in neural network models are made to represent concepts from applications. This paper motivates, introduces and discusses a formalism for denoting such representations; a representation for representations. The formalism is illustrated by using it to discuss the representation of variable binding and inference abstractly, and then to present four specific representations. One of these is an apparently novel hybrid of phasic and tensor-product representations which retains the desirable properties of each.

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

An illustration of variable precision rough sets model:an analysis of the findings of the UK Monopolies and Mergers Commission

This paper introduces a new technique in the investigation of limited-dependent variable models. This paper illustrates that variable precision rough set theory (VPRS), allied with the use of a modern method of classification, or discretisation of data, can out-perform the more standard approaches that are employed in economics, such as a probit model. These approaches and certain inductive decision tree methods are compared (through a Monte Carlo simulation approach) in the analysis of the decisions reached by the UK Monopolies and Mergers Committee. We show that, particularly in small samples, the VPRS model can improve on more traditional models, both in-sample, and particularly in out-of-sample prediction. A similar improvement in out-of-sample prediction over the decision tree methods is also shown.

Fixed or variable noise in contrast discrimination? The jury's still out

The ability to distinguish one visual stimulus from another slightly different one depends on the variability of their internal representations. In a recent paper on human visual-contrast discrimination, Kontsevich et al (2002 Vision Research 42 1771 - 1784) re-considered the long-standing question whether the internal noise that limits discrimination is fixed (contrast-invariant) or variable (contrast-dependent). They tested discrimination performance for 3 cycles deg-1 gratings over a wide range of incremental contrast levels at three masking contrasts, and showed that a simple model with an expansive response function and response-dependent noise could fit the data very well. Their conclusion - that noise in visual-discrimination tasks increases markedly with contrast - has profound implications for our understanding and modelling of vision. Here, however, we re-analyse their data, and report that a standard gain-control model with a compressive response function and fixed additive noise can also fit the data remarkably well. Thus these experimental data do not allow us to decide between the two models. The question remains open. [Supported by EPSRC grant GR/S74515/01]

Variable time-scale information processing

With the extensive use of pulse modulation methods in telecommunications, much work has been done in the search for a better utilisation of the transmission channel.The present research is an extension of these investigations. A new modulation method, 'Variable Time-Scale Information Processing', (VTSIP), is proposed.The basic principles of this system have been established, and the main advantages and disadvantages investigated. With the proposed system, comparison circuits detect the instants at which the input signal voltage crosses predetermined amplitude levels.The time intervals between these occurrences are measured digitally and the results are temporarily stored, before being transmitted.After reception, an inverse process enables the original signal to be reconstituted.The advantage of this system is that the irregularities in the rate of information contained in the input signal are smoothed out before transmission, allowing the use of a smaller transmission bandwidth. A disadvantage of the system is the time delay necessarily introduced by the storage process.Another disadvantage is a type of distortion caused by the finite store capacity.A simulation of the system has been made using a standard speech signal, to make some assessment of this distortion. It is concluded that the new system should be an improvement on existing pulse transmission systems, allowing the use of a smaller transmission bandwidth, but introducing a time delay.