Supervised Classification Using Sparse Fisher's LDA

It is well known that in a supervised classification setting when the number of features is smaller than the number of observations, Fisher's linear discriminant rule is asymptotically Bayes. However, there are numerous modern applications where classification is needed in the high-dimensional setting. Naive implementation of Fisher's rule in this case fails to provide good results because the sample covariance matrix is singular. Moreover, by constructing a classifier that relies on all features the interpretation of the results is challenging. Our goal is to provide robust classification that relies only on a small subset of important features and accounts for the underlying correlation structure. We apply a lasso-type penalty to the discriminant vector to ensure sparsity of the solution and use a shrinkage type estimator for the covariance matrix. The resulting optimization problem is solved using an iterative coordinate ascent algorithm. Furthermore, we analyze the effect of nonconvexity on the sparsity level of the solution and highlight the difference between the penalized and the constrained versions of the problem. The simulation results show that the proposed method performs favorably in comparison to alternatives. The method is used to classify leukemia patients based on DNA methylation features

Laplace Approximated EM Microarray Analysis: An Empirical Bayes Approach for Comparative Microarray Experiments

A two-groups mixed-effects model for the comparison of (normalized) microarray data from two treatment groups is considered. Most competing parametric methods that have appeared in the literature are obtained as special cases or by minor modification of the proposed model. Approximate maximum likelihood fitting is accomplished via a fast and scalable algorithm, which we call LEMMA (Laplace approximated EM Microarray Analysis). The posterior odds of treatment $\times$ gene interactions, derived from the model, involve shrinkage estimates of both the interactions and of the gene specific error variances. Genes are classified as being associated with treatment based on the posterior odds and the local false discovery rate (f.d.r.) with a fixed cutoff. Our model-based approach also allows one to declare the non-null status of a gene by controlling the false discovery rate (FDR). It is shown in a detailed simulation study that the approach outperforms well-known competitors. We also apply the proposed methodology to two previously analyzed microarray examples. Extensions of the proposed method to paired treatments and multiple treatments are also discussed.Comment: Published in at http://dx.doi.org/10.1214/10-STS339 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Crossing boundaries: :learning to teach in Further Education. An action research study of how Further Education-based teacher educators and trainee teachers model values.

Teacher educators in further education are preparing trainees to teach students aged sixteen and above, from entry level to level 6, in colleges, sixth form colleges, prisons, the workplace and in adult and community learning. They hold a substantial responsibility in terms of their impact on those who are learning to teach. This study illuminates the work of further education-based teacher educators and the process of learning to teach as trainees navigate the boundaries between formal and workplace learning. It posits that teacher educators model values both within and outside the classroom and that these impact the development of values in trainee teachers and their students. These concepts have been explored through a second person action research study in collaboration with teacher educators and trainee teachers in a further education college in the North of England. Data were collected over a period of twenty-six months, and involved semi-structured interviews, films of the teacher educators’ and trainee teachers’ classes, stimulated recall interviews and focus groups with three teacher educators and ten trainee teachers. Using a thematic analysis approach and the theoretical concepts of practice architectures, modelling and a layered pedagogy of teacher education, the practices of teacher educators and of learning to teach have been explored. The findings suggest that teacher educators have an orientation to values which influences the way they model values through their practice including managing a class and the construction of professional relationships. Whilst the modelling of values is implicit, it has a significant impact on trainee teachers and in turn, on students. This suggests that attention should be paid to the recruitment, induction and support of further education-based teacher educators in terms of their orientation to values

Simulating molecular cloud regulated star formation in Galaxies

This thesis is primarily concerned with understanding the process of galaxy formation via the simulation of the interstellar medium, star formation and supernova feedback. In order to probe galaxy formation it is necessary that we first obtain a basic knowledge of the cosmological framework in which we are working. Therefore in chapter 1 we provide a brief overview of the salient features of the current cosmological paradigm in addition to discussing in some detail the physics of the interstellar medium. In chapter 2 we focus on the numerical methods necessary to perform accurate cosmological simulations. We begin by providing an overview of the different simulation techniques currently in use in the field before performing comparisons of two simulation codes that work via two completely different methods. We then introduce a code for generating high-resolution initial conditions for the simulation of individual objects and investigate the numerical effects of mass resolution in cosmological simulation. In chapter 3 we describe a statistical model of the interstellar medium, in which the conversion of cooling gas to stars in the multiphase interstellar medium is governed by the rate at which molecular clouds are formed and destroyed. In the model, clouds form from thermally unstable ambient gas and get destroyed by star formation, feedback and thermal conduction. In chapter 4 this statistical model is applied to the simulation of isolated disk galaxies. We show that it naturally produces a multiphase medium with cold clouds, a warm disk and hot supernova bubbles. We illustrate this by evolving an isolated Milky Way like galaxy. Many observed properties of disk galaxies are reproduced well, including the molecular cloud mass spectrum, the molecular fraction as a function of radius, the Schmidt law, the stellar density profile and the appearance of a galactic fountain. Finally in chapter 5 we perform an investigation into more dynamic situations, namely the evolution of gravitationally interacting disk galaxies and the formation of a galaxy in a fully cosmological simulation. It is found that the sticky particle model does a good job of reproducing many of the observed properties of interacting galaxies, including the properties of the ISM in the resulting elliptical galaxy

A dialectical approach for argument-based judgment aggregation

The current paper provides a dialectical interpretation of the argumentation-based judgment aggregation operators of Caminada and Pigozzi. In particular, we define discussion-based proof procedures for the foundational concepts of down-admissible and up-complete. We then show how these proof procedures can be used as the basis of dialectical proof procedures for the sceptical, credulous and super credulous judgment aggregation operators

Effects of repeated consumption on sensory-enhanced satiety

Previous research suggests that sensory characteristics of a drink modify the acute satiating effects of its nutrients, with enhanced satiety evident when a high energy drink was thicker and tasted creamier. The present study tested whether this modulation of satiety by sensory context was altered by repeated consumption. Participants (n=48) consumed one of four drinks mid-morning on seven non-consecutive days with satiety responses measured pre-exposure (day 1), post-exposure (day 6) and at a one month follow-up. Drinks combined two levels of energy (lower energy, LE, 326 KJ: higher energy, HE, 1163KJ) with two levels of satiety-predictive sensory characteristics (low-sensory, LS, or enhanced sensory, ES). Test lunch intake 90 minutes after drink consumption depended on both the energy content and sensory characteristics of the drink before exposure, but on energy content alone at post-exposure and the follow-up. The largest change was an increase in test meal intake over time in the LE/LS condition. Effects on intake were reflected in appetite ratings, with rated hunger and expected filling affected by sensory characteristics and energy content pre-exposure, but were largely determined by energy content post exposure and at follow up. In contrast, a measure of expected satiety reflected sensory characteristics regardless of energy content on all three test days. Overall these data suggest that some aspects of the sensory-modulation of satiety are changed by repeated consumption, with covert energy becoming more effective in suppressing appetite over time, but also suggest that these behavioural changes are not readily translated into expectations of satiety