Minimum description length, regularisation and multi-modal data

Relationships between clustering, description length, and regularisation are pointed out, motivating the introduction of a cost function with a description length interpretation and the unusual and useful property of having its minimum approximated by the densest mode of a distribution. A simple inverse kinematics example is used to demonstrate that this property can be used to select and learn one branch of a multi-valued mapping. This property is also used to develop a method for setting regularisation parameters according to the scale on which structure is exhibited in the training data. The regularisation technique is demonstrated on two real data sets, a classification problem and a regression problem.

Minimum description length, regularisation and multi-modal data

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.

A comparison of the vocational training system of Britain and West Germany as experienced by minimum-age school leavers.

The sectoral and occupational structure of Britain and West Germany has increasingly changed over the last fifty years from a manual manufacturing based to a non-manual service sector based one. There has been a trend towards more managerial and less menial type occupations. Britain employs a higher proportion of its population in the service sector than in manufacturing compared to West Germany, except in retailing, where West Germany employs twice as many people as Britain. This is a stable sector of the economy in terms of employment, but the requirements of the workforce have changed in line with changes in the industry in both countries. School leavers in the two countries, faced with the same options (FE, training schemes or employment) have opted for the various options in different proportions: young Germans are staying longer in education before embarking on training and young Britons are now less likely to go straight into employment than ten years ago. Training is becoming more accepted as the normal route into employment with government policy leading the way, but public opinion still slow to respond. This study investigates how vocational training has adapted to the changing requirements of industry, often determined by technological advancements. In some areas e.g. manufacturing industry the changes have been radical, in others such as retailing they have not, but skill requirements, not necessarily influenced by technology have changed. Social-communicative skills, frequently not even considered skills and therefore not included in training are coming to the forefront. Vocational training has adapted differently in the two countries: in West Germany on the basis of an established over-defined system and in Britain on the basis of an out-dated ill-defined and almost non-existent system. In retailing German school leavers opt for two or three year apprenticeships whereas British school leavers are offered employment with or without formalised training. The publicly held view of the occupation of sales assistant is one of low-level skill, low intellectual demands and a job anyone can do. The traditional skills - product knowledge, selling and social-communicative skills have steadily been eroded. In the last five years retailers have recognised that a return to customer service, utilising the traditional skills was going to be needed of their staff to remain competitive. This requires training. The German retail training system responded by adapting its training regulations in a long consultative process, whereas the British experimented with YTS, a formalised training scheme nationwide being a new departure. The thesis evaluates the changes in these regulations. The case studies in four retail outlets demonstrate that it is indeed product knowledge and selling and social-communicative skills which are fundamental to being a successful and content sales assistant in either country. When the skills are recognised and taught well and systematically the foundations for career development in retailing are laid in a labour market which is continually looking for better qualified workers. Training, when planned and conducted professionally is appreciated by staff and customers and of benefit to the company. In retailing not enough systematic training, to recognisable standards is carried out in Britain, whereas in West Germany the training system is nevertheless better prepared to show innovative potential as a structure and is in place on which to build. In Britain the reputation of the individual company has a greater role to play, not ensuring a national provision of good training in retailing.

Optical link design for minimum power consumption and maximum capacity

Using a well-established analytic nonlinear signal-to-noise ratio noise model we show that there are very simple, fibre independent, amplifier gains which minimize the total energy requirement for amplified systems. Power savings of over 50% are shown to be possible by choosing appropriate amplifier gain and output power.

Common variants of the TCF7L2 gene are associated with increased risk of type 2 diabetes mellitus in a UK-resident South Asian population

Background - Recent studies have implicated variants of the transcription factor 7-like 2 (TCF7L2) gene in genetic susceptibility to type 2 diabetes mellitus in several different populations. The aim of this study was to determine whether variants of this gene are also risk factors for type 2 diabetes development in a UK-resident South Asian cohort of Punjabi ancestry. Methods - We genotyped four single nucleotide polymorphisms (SNPs) of TCF7L2 (rs7901695, rs7903146, rs11196205 and rs12255372) in 831 subjects with diabetes and 437 control subjects. Results - The minor allele of each variant was significantly associated with type 2 diabetes; the greatest risk of developing the disease was conferred by rs7903146, with an allelic odds ratio (OR) of 1.31 (95% CI: 1.11 – 1.56, p = 1.96 × 10-3). For each variant, disease risk associated with homozygosity for the minor allele was greater than that for heterozygotes, with the exception of rs12255372. To determine the effect on the observed associations of including young control subjects in our data set, we reanalysed the data using subsets of the control group defined by different minimum age thresholds. Increasing the minimum age of our control subjects resulted in a corresponding increase in OR for all variants of the gene (p ≤ 1.04 × 10-7). Conclusion - Our results support recent findings that TCF7L2 is an important genetic risk factor for the development of type 2 diabetes in multiple ethnic groups.

Multi-model fitting based on minimum spanning tree

This paper presents a novel approach to the computation of primitive geometrical structures, where no prior knowledge about the visual scene is available and a high level of noise is expected. We based our work on the grouping principles of proximity and similarity, of points and preliminary models. The former was realized using Minimum Spanning Trees (MST), on which we apply a stable alignment and goodness of fit criteria. As for the latter, we used spectral clustering of preliminary models. The algorithm can be generalized to various model fitting settings, without tuning of run parameters. Experiments demonstrate the significant improvement in the localization accuracy of models in plane, homography and motion segmentation examples. The efficiency of the algorithm is not dependent on fine tuning of run parameters like most others in the field.

Association of SNPs in LCP1 and CTIF with hearing in 11 year old children:findings from the Avon Longitudinal Study of Parents and Children (ALSPAC) birth cohort and the G-EAR consortium

BACKGROUND: The genetic basis of hearing loss in humans is relatively poorly understood. In recent years, experimental approaches including laboratory studies of early onset hearing loss in inbred mouse strains, or proteomic analyses of hair cells or hair bundles, have suggested new candidate molecules involved in hearing function. However, the relevance of these genes/gene products to hearing function in humans remains unknown. We investigated whether single nucleotide polymorphisms (SNPs) in the human orthologues of genes of interest arising from the above-mentioned studies correlate with hearing function in children. METHODS: 577 SNPs from 13 genes were each analysed by linear regression against averaged high (3, 4 and 8 kHz) or low frequency (0.5, 1 and 2 kHz) audiometry data from 4970 children in the Avon Longitudinal Study of Parents and Children (ALSPAC) birth-cohort at age eleven years. Genes found to contain SNPs with low p-values were then investigated in 3417 adults in the G-EAR study of hearing. RESULTS: Genotypic data were available in ALSPAC for a total of 577 SNPs from 13 genes of interest. Two SNPs approached sample-wide significance (pre-specified at p = 0.00014): rs12959910 in CBP80/20-dependent translation initiation factor (CTIF) for averaged high frequency hearing (p = 0.00079, β = 0.61 dB per minor allele); and rs10492452 in L-plastin (LCP1) for averaged low frequency hearing (p = 0.00056, β = 0.45 dB). For low frequencies, rs9567638 in LCP1 also enhanced hearing in females (p = 0.0011, β = -1.76 dB; males p = 0.23, β = 0.61 dB, likelihood-ratio test p = 0.006). SNPs in LCP1 and CTIF were then examined against low and high frequency hearing data for adults in G-EAR. Although the ALSPAC results were not replicated, a SNP in LCP1, rs17601960, is in strong LD with rs9967638, and was associated with enhanced low frequency hearing in adult females in G-EAR (p = 0.00084). CONCLUSIONS: There was evidence to suggest that multiple SNPs in CTIF may contribute a small detrimental effect to hearing, and that a sex-specific locus in LCP1 is protective of hearing. No individual SNPs reached sample-wide significance in both ALSPAC and G-EAR. This is the first report of a possible association between LCP1 and hearing function.