Block GTM: Incorporating prior knowledge of covariance structure in data visualisation

Visualising data for exploratory analysis is a big challenge in scientific and engineering domains where there is a need to gain insight into the structure and distribution of the data. Typically, visualisation methods like principal component analysis and multi-dimensional scaling are used, but it is difficult to incorporate prior knowledge about structure of the data into the analysis. In this technical report we discuss a complementary approach based on an extension of a well known non-linear probabilistic model, the Generative Topographic Mapping. We show that by including prior information of the covariance structure into the model, we are able to improve both the data visualisation and the model fit.

Semi-analytical Q parameter estimate in linear and nonlinear transmission systems

We compare the Q parameter obtained from the semi-analytical model with scalar and vector models for two realistic transmission systems. First a linear system with a compensated dispersion map and second a soliton transmission system.

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

Studies on the generalisation of Gaussian processes and Bayesian neural networks

The assessment of the reliability of systems which learn from data is a key issue to investigate thoroughly before the actual application of information processing techniques to real-world problems. Over the recent years Gaussian processes and Bayesian neural networks have come to the fore and in this thesis their generalisation capabilities are analysed from theoretical and empirical perspectives. Upper and lower bounds on the learning curve of Gaussian processes are investigated in order to estimate the amount of data required to guarantee a certain level of generalisation performance. In this thesis we analyse the effects on the bounds and the learning curve induced by the smoothness of stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the tightness of the bounds are also discussed. The analysis is supported by several numerical simulations. The generalisation error of a Gaussian process is affected by the dimension of the input vector and may be decreased by input-variable reduction techniques. In conventional approaches to Gaussian process regression, the positive definite matrix estimating the distance between input points is often taken diagonal. In this thesis we show that a general distance matrix is able to estimate the effective dimensionality of the regression problem as well as to discover the linear transformation from the manifest variables to the hidden-feature space, with a significant reduction of the input dimension. Numerical simulations confirm the significant superiority of the general distance matrix with respect to the diagonal one.In the thesis we also present an empirical investigation of the generalisation errors of neural networks trained by two Bayesian algorithms, the Markov Chain Monte Carlo method and the evidence framework; the neural networks have been trained on the task of labelling segmented outdoor images.

Gabor-based region covariance matrices for face recognition

This paper presents a new method for human face recognition by utilizing Gabor-based region covariance matrices as face descriptors. Both pixel locations and Gabor coefficients are employed to form the covariance matrices. Experimental results demonstrate the advantages of this proposed method.

Statnote 31:analysis of covariance

Analysis of covariance (ANCOVA) is a useful method of ‘error control’, i.e., it can reduce the size of the error variance in an experimental or observational study. An initial measure obtained before the experiment, which is closely related to the final measurement, is used to adjust the final measurements, thus reducing the error variance. When this method is used to reduce the error term, the X variable must not itself be affected by the experimental treatments, because part of the treatment effect would then also be removed. Hence, the method can only be safely used when X is measured before an experiment. A further limitation of the analysis is that only the linear effect of Y on X is being removed and it is possible that Y could be a curvilinear function of X. A question often raised is whether ANCOVA should be used routinely in experiments rather than a randomized blocks or split-plot design, which may also reduce the error variance. The answer to this question depends on the relative precision of the difference methods with reference to each scenario. Considerable judgment is often required to select the best experimental design and statistical help should be sought at an early stage of an investigation.

Appropriate wage rate and estimate of labour availability for a public works based safety net in Cambodia

Employment generating public works (EGPW) are an important part of Royal Government of Cambodia’s (RGC’s) strategy being developed through Council for Agriculture and Rural Development (CARD) to develop a comprehensive social safety net (SSN) to provide a measure of protection from shocks for the poor and vulnerable and to contribute to poverty alleviation through short-term unskilled employment.

Simple eye-closure penalty estimate for amplitude noise-degraded signals

We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals. Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the model predictions and the results obtained from the conventional numerical estimation method over several thousand kilometers.

Using DEA to estimate potential savings at GP units at medical specialty level

The aim of this paper is to identify benchmark cost-efficient General Practitioner (GP) units at delivering health care in the Geriatric and General Medicine (GMG) specialty and estimate potential cost savings. The use of a single medical specialty makes it possible to reflect more accurately the medical condition of the List population of the Practice so as to contextualize its expenditure on care for patients. We use Data Envelopment Analysis (DEA) to estimate the potential for cost savings at GP units and to decompose these savings into those attributable to the reduction of resource use, to altering the mix of resources used and to those attributable to securing better resource 'prices'. The results reveal a considerable potential for savings of varying composition across GP units. © 2013 Elsevier Ltd.

Use of general practice prescribing data as a surrogate estimate of statin compliance

Background and Objective: To maximise the benefit from statin therapy, patients must maintain regular therapy indefinitely. Non-compliance is thought to be common in those taking medication at regular intervals over long periods of time, especially where they may perceive no immediate benefit (News editorial, 2002). This study extends previous work in which commonly held prescribing data is used as a surrogate marker of compliance and was designed to examine compliance in those stabilised on statins in a large General Practice. Design: Following ethical approval, details of all patients who had a single statin for 12 consecutive months with no changes in drug, frequency or dose, between December 1999 and March 2003, were obtained. Setting: An Eastern Birmingham Primary Care Trust GP surgery. Main Outcome Measures: A compliance ratio was calculated by dividing the number of days treatment by the number of doses prescribed. For a once daily regimen the ratio for full compliance_1. Results: 324 patients were identified. The average compliance ratio for the first six months of the study was 1.06 ± 0.01 (range 0.46 – 2.13) and for the full twelve months was 1.05 ± 0.01 (range 0.58 – 2.08). Conclusions: The data shown here indicates that as a group, long-term, stabilised statin users appear compliant. However, the range of values obtained show that there are identifiable subsets of patients who are not taking their therapy as prescribed. Although the apparent use of more doses than prescribed in some patients may result from medication hording, this cannot be the case in the patients who apparently take less. It has been demonstrated here that the compliance ratio can be used as an early indicator of problems allowing targeted compliance advice can be given where it will have the most benefit. References: News Editorial. Pharmacy records could be used to enhance statin compliance in elderly. Pharm. J. 2002; 269: 121.

Numerical estimate of BER in optical systems with strong patterning effects

A statistical approach to evaluate numerically transmission distances in optical communication systems was described. The proposed systems were subjected to strong patterning effects and strong intersymbol interference. The dependence of transmission distance on the total number of bits was described. Normal and Gaussian distributions were used to derive the error probability.

Simple eye-closure penalty estimate for amplitude noise-degraded signals

We present a simplified model for a simple estimation of the eye-closure penalty for amplitude noise-degraded signals. Using a typical 40-Gbit/s return-to-zero amplitude-shift-keying transmission, we demonstrate agreement between the model predictions and the results obtained from the conventional numerical estimation method over several thousand kilometers.