Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

GLM-beamformer method demonstrates stationary field, alpha ERD and gamma ERS co-localisation with fMRI BOLD response in visual cortex

Recently, we introduced a new 'GLM-beamformer' technique for MEG analysis that enables accurate localisation of both phase-locked and non-phase-locked neuromagnetic effects, and their representation as statistical parametric maps (SPMs). This provides a useful framework for comparison of the full range of MEG responses with fMRI BOLD results. This paper reports a 'proof of principle' study using a simple visual paradigm (static checkerboard). The five subjects each underwent both MEG and fMRI paradigms. We demonstrate, for the first time, the presence of a sustained (DC) field in the visual cortex, and its co-localisation with the visual BOLD response. The GLM-beamformer analysis method is also used to investigate the main non-phase-locked oscillatory effects: an event-related desynchronisation (ERD) in the alpha band (8-13 Hz) and an event-related synchronisation (ERS) in the gamma band (55-70 Hz). We show, using SPMs and virtual electrode traces, the spatio-temporal covariance of these effects with the visual BOLD response. Comparisons between MEG and fMRI data sets generally focus on the relationship between the BOLD response and the transient evoked response. Here, we show that the stationary field and changes in oscillatory power are also important contributors to the BOLD response, and should be included in future studies on the relationship between neuronal activation and the haemodynamic response. © 2005 Elsevier Inc. All rights reserved.

Method for characterisation of weakly guiding waveguides by measuring mode field diameter

In this paper, we described an efficient theoretical approach to determine the integral characteristics such as Mode Field Diameter (MFD) and V-parameter of the Weakly guiding waveguides. To test the described method we measured MFD for the commercially available step index single mode fibre with known parameters. The results of these measurements are presented for two different wavelengths. It is worth noting that the developed approach implies infinite cladding, thus care should be taken to avoid influence of finiteness of cladding when MFD compares to cladding diamete.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Method for characterisation of weakly guiding waveguides by measuring mode field diameter

In this paper, we described an efficient theoretical approach to determine the integral characteristics such as Mode Field Diameter (MFD) and V-parameter of the Weakly guiding waveguides. To test the described method we measured MFD for the commercially available step index single mode fibre with known parameters. The results of these measurements are presented for two different wavelengths. It is worth noting that the developed approach implies infinite cladding, thus care should be taken to avoid influence of finiteness of cladding when MFD compares to cladding diamete.

Gaussian processes and SVM: Mean field results and leave-one-out

In this chapter, we elaborate on the well-known relationship between Gaussian processes (GP) and Support Vector Machines (SVM). Secondly, we present approximate solutions for two computational problems arising in GP and SVM. The first one is the calculation of the posterior mean for GP classifiers using a `naive' mean field approach. The second one is a leave-one-out estimator for the generalization error of SVM based on a linear response method. Simulation results on a benchmark dataset show similar performances for the GP mean field algorithm and the SVM algorithm. The approximate leave-one-out estimator is found to be in very good agreement with the exact leave-one-out error.

Online approximations for wind-field models

We study online approximations to Gaussian process models for spatially distributed systems. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data. Our approach combines a sequential update of a Gaussian approximation to the posterior with a sparse representation that allows to treat problems with a large number of observations.

A method for profiling biometric changes during disaccommodation

PURPOSE: To demonstrate the application of low-coherence reflectometry to the study of biometric changes during disaccommodation responses in human eyes after cessation of a near task and to evaluate the effect of contact lenses on low-coherence reflectometry biometric measurements. METHODS: Ocular biometric parameters of crystalline lens thickness (LT) and anterior chamber depth (ACD) were measured with the LenStar device during and immediately after a 5 D accommodative task in 10 participants. In a separate trial, accommodation responses were recorded with a Shin-Nippon WAM-5500 optometer in a subset of two participants. Biometric data were interleaved to form a profile of post-task anterior segment changes. In a further experiment, the effect of soft contact lenses on LenStar measurements was evaluated in 15 participants. RESULTS: In 10 adult participants, increased LT and reduced ACD was seen during the 5 D task. Post-task, during fixation of a 0 D target, a profile of the change in LT and ACD against time was observed. In the two participants with accommodation data (one a sufferer of nearwork-induced transient myopia and other a non-sufferer), the post-task changes in refraction compared favorably with the interleaved LenStar biometry data. The insertion of soft contact lenses did not have a significant effect on LenStar measures of ACD or LT (mean change: -0.007 mm, p = 0.265 and + 0.001 mm, p = 0.875, respectively). CONCLUSIONS: With the addition of a relatively simple stimulus modification, the LenStar instrument can be used to produce a profile of post-task changes in LT and ACD. The spatial and temporal resolution of the system is sufficient for the investigation of nearwork-induced transient myopia from a biometric viewpoint. LenStar measurements of ACD and LT remain valid after the fitting of soft contact lenses.

Description and critical appraisal of principal components analysis (PCA) methodology applied to pulsed-field gel electrophoresis profiles of methicillin-resistant Staphylococcus aureus isolates

Principal components analysis (PCA) has been described for over 50 years; however, it is rarely applied to the analysis of epidemiological data. In this study PCA was critically appraised in its ability to reveal relationships between pulsed-field gel electrophoresis (PFGE) profiles of methicillin- resistant Staphylococcus aureus (MRSA) in comparison to the more commonly employed cluster analysis and representation by dendrograms. The PFGE type following SmaI chromosomal digest was determined for 44 multidrug-resistant hospital-acquired methicillin-resistant S. aureus (MR-HA-MRSA) isolates, two multidrug-resistant community-acquired MRSA (MR-CA-MRSA), 50 hospital-acquired MRSA (HA-MRSA) isolates (from the University Hospital Birmingham, NHS Trust, UK) and 34 community-acquired MRSA (CA-MRSA) isolates (from general practitioners in Birmingham, UK). Strain relatedness was determined using Dice band-matching with UPGMA clustering and PCA. The results indicated that PCA revealed relationships between MRSA strains, which were more strongly correlated with known epidemiology, most likely because, unlike cluster analysis, PCA does not have the constraint of generating a hierarchic classification. In addition, PCA provides the opportunity for further analysis to identify key polymorphic bands within complex genotypic profiles, which is not always possible with dendrograms. Here we provide a detailed description of a PCA method for the analysis of PFGE profiles to complement further the epidemiological study of infectious disease. © 2005 Elsevier B.V. All rights reserved.

The valuation of travel time savings in least developed countries:theoretical and empirical challenges and results from a field study

In developed countries travel time savings can account for as much as 80% of the overall benefits arising from transport infrastructure and service improvements. In developing countries they are generally ignored in transport project appraisals, notwithstanding their importance. One of the reasons for ignoring these benefits in the developing countries is that there is insufficient empirical evidence to support the conventional models for valuing travel time where work patterns, particularly of the poor, are diverse and it is difficult to distinguish between work and non-work activities. The exclusion of time saving benefits may lead to a bias against investment decisions that benefit the poor and understate the poverty reduction potential of transport investments in Least Developed Countries (LDCs). This is because the poor undertake most travel and transport by walking and headloading on local roads, tracks and paths and improvements of local infrastructure and services bring large time saving benefits for them through modal shifts. The paper reports on an empirical study to develop a methodology for valuing rural travel time savings in the LDCs. Apart from identifying the theoretical and empirical issues in valuing travel time savings in the LDCs, the paper presents and discusses the results of an analysis of data from Bangladesh. Some of the study findings challenge the conventional wisdom concerning the time saving values. The Bangladesh study suggests that the western concept of dividing travel time savings into working and non-working time savings is broadly valid in the developing country context. The study validates the use of preference methods in valuing non-working time saving values. However, stated preference (SP) method is more appropriate than revealed preference (RP) method.

A study of field emission from cadmium sulphide

It was decided to investigate field emission from cadmium sulphide because many workers have found that the agreement between theory and experiment for this material, and other semiconductors, is poor. An electron energy analyser, similar to those used in most of the previously reported experiments, was, therefore, built. The performance of the analyser was thoroughly investigated both theoretically and practically and the results of these investigations were used in conjunction with a tungsten emitter. Excellent agreement was obtained between the usually accepted total energy distribution for tungsten and the corresponding .distribution measured with the present analyser. A method of obtaining reliable cadmium sulphide emitter was developed. These emitters were then used in the analyser and it was found that the agreement between theory and experiment was poor. Previous explanations of the lack of agreement are considered and are found to be doubtful. The theory of field emission from semiconductors is reviewed and possible reasons for the discrepancy between theory and experiment are proposed. Finally, further experiments are described which should prove or disprove the conclusions arrived at in this work.

Low spatial frequencies are suppressively masked across spatial scale, orientation, field position, and eye of origin

Masking is said to occur when a mask stimulus interferes with the visibility of a target (test) stimulus. One widely held view of this process supposes interactions between mask and test mechanisms (cross-channel masking), and explicit models (e.g., J. M. Foley, 1994) have proposed that the interactions are inhibitory. Unlike a within-channel model, where masking involves the combination of mask and test stimulus within a single mechanism, this cross-channel inhibitory model predicts that the mask should attenuate the perceived contrast of a test stimulus. Another possibility is that masking is due to an increase in noise, in which case, perception of contrast should be unaffected once the signal exceeds detection threshold. We use circular patches and annuli of sine-wave grating in contrast detection and contrast matching experiments to test these hypotheses and investigate interactions across spatial frequency, orientation, field position, and eye of origin. In both types of experiments we found substantial effects of masking that can occur over a factor of 3 in spatial frequency, 45° in orientation, across different field positions and between different eyes. We found the effects to be greatest at the lowest test spatial frequency we used (0.46 c/deg), and when the mask and test differed in all four dimensions simultaneously. This is surprising in light of previous work where it was concluded that suppression from the surround was strictly monocular (C. Chubb, G. Sperling, & J. A. Solomon, 1989). The results confirm that above detection threshold, cross-channel masking involves contrast suppression and not (purely) mask-induced noise. We conclude that cross-channel masking can be a powerful phenomenon, particularly at low test spatial frequencies and when mask and test are presented to different eyes. © 2004 ARVO.

The influence of age on the pattern and flash visual evoked field

We have investigated the effect of ageing on the visual system using the relatively new technique of magentoencephalography (MEG). This technique measures the magnetic signals produced by the visual system using a SQUID magnetometer. The magnetic visual evoked field (VEF) was measured over the occipital cortex to pattern and flash stimuli in 86 normal subjects aged 15 - 86 years. Factors that influenced subject defocussing or defixating the stimulus or selective attention were controlled as far as possible. The latency of the major positive component to the pattern reversal stimulus (P100M) increased with age particularly after the age of 55 years while the amplitude of the P100M decreased over the life span. The latency of the major flash component (P2M) increased much more slowly with age, while its amplitude decreased in only a proportion of elderly subjects. Changes in the P100M with age may reflect senile changes in the eye and optic nerve, e.g. senile miosis or degenerative changes in the retina. The P2M may be more susceptible to senile changes in the retina. The data suggest that the spatial frequency channels deteriorate more rapidly with age than the luminance channels and that MEG may be an effective method of studying ageing in the visual system.