Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Aspects of health among an employed population

This survey collected information on aspects of health amongst an employed population, employees in 14 different organisations in the West Midlands Regional Health Authority; and was a stratified sample of senior managers, middle managers and operatives. Nine hundred and sixty questionnaires were distributed asking for both quantitative and qualitative information on 58 questions covering health, work, family, leisure activities and life-style. A response rate of 48% (459 returned questionnaires) came from 290 men (63%), 165 women (36%) and four people (1%) who did not answer the gender question. The initial findings from this study are unique in that there has not been a specific review of the health of people at work. In answer to the main research questions, 92% felt they were healthy. Compared to others of a similar age, 34% felt their health was `above average', 58% `average', and 7&37 `below average'. Thirty two percent of respondents had visited their GP in the past 1-2 months; the highest reason given was disorders of the respiratory system, 20%. People's perceptions on the effects of work on their health were: good effect, 13% fair effect, 20% no effect, 27% poor effect, 27% and bad effect, 7%. The effects of leisure activities on health were thought to be more positive: good effect, 46% fair effect, 20% no effect, 21% poor effect, 3% and bad effect, 2%. The perceptions of effects of life-style on health were considered to be: good effect, 32% fair effect, 32% no effect, 20% poor effect, 9% and bad effect, 1%.  In this survey, leisure and life-style were seen by employees to have more beneficial effects on health than work. Future implications include a review of occupational health as a major policy development area within primary care. There is a need to influence the education and training of health care practitioners in order to affect their ability to practise effectively in this new and challenging area of work.

Subjective indicators of health held by the lay population:eudaimanistic model

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Health and population effects of rare gene knockouts in adult humans with related parents

Examining complete gene knockouts within a viable organism can inform on gene function. We sequenced the exomes of 3222 British Pakistani-heritage adults with high parental relatedness, discovering 1111 rare-variant homozygous genotypes with predicted loss of gene function (knockouts) in 781 genes. We observed 13.7% fewer than expected homozygous knockout genotypes, implying an average load of 1.6 recessive-lethal-equivalent LOF variants per adult. Linking genetic data to lifelong health records, knockouts were not associated with clinical consultation or prescription rate. In this dataset we identified a healthy PRDM9 knockout mother, and performed phased genome sequencing on her, her child and controls, which showed meiotic recombination sites localized away from PRDM9-dependent hotspots. Thus, natural LOF variants inform upon essential genetic loci, and demonstrate PRDM9 redundancy in humans.