Margin-adaptive model selection in statistical learning

A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning framework. Actually, we consider a weaker version of this condition that allows one to take into account that learning within a small model can be much easier than within a large one. Requiring this “strong margin adaptivity” makes the model selection problem more challenging. We first prove, in a general framework, that some penalization procedures (including local Rademacher complexities) exhibit this adaptivity when the models are nested. Contrary to previous results, this holds with penalties that only depend on the data. Our second main result is that strong margin adaptivity is not always possible when the models are not nested: for every model selection procedure (even a randomized one), there is a problem for which it does not demonstrate strong margin adaptivity.

An approach to statistical lip modelling for speaker identification via chromatic feature extraction

This paper presents a novel technique for the tracking of moving lips for the purpose of speaker identification. In our system, a model of the lip contour is formed directly from chromatic information in the lip region. Iterative refinement of contour point estimates is not required. Colour features are extracted from the lips via concatenated profiles taken around the lip contour. Reduction of order in lip features is obtained via principal component analysis (PCA) followed by linear discriminant analysis (LDA). Statistical speaker models are built from the lip features based on the Gaussian mixture model (GMM). Identification experiments performed on the M2VTS¹ database, show encouraging results

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

Antiretroviral therapy (ART) adherence among people living with HIV/AIDS (PLHIV) in the north of Vietnam : a multi-method approach

The antiretroviral therapy (ART) program for People Living with HIV/AIDS (PLHIV) in Vietnam has been scaled up rapidly in recent years (from 50 clients in 2003 to almost 38,000 in 2009). ART success is highly dependent on the ability of the patients to fully adhere to the prescribed treatment regimen. Despite the remarkable extension of ART programs in Vietnam, HIV/AIDS program managers still have little reliable data on levels of ART adherence and factors that might promote or reduce adherence. Several previous studies in Vietnam estimated extremely high levels of ART adherence among their samples, although there are reasons to question the veracity of the conclusion that adherence is nearly perfect. Further, no study has quantitatively assessed the factors influencing ART adherence. In order to reduce these gaps, this study was designed to include several phases and used a multi-method approach to examine levels of ART non-adherence and its relationship to a range of demographic, clinical, social and psychological factors. The study began with an exploratory qualitative phase employing four focus group discussions and 30 in-depth interviews with PLHIV, peer educators, carers and health care providers (HCPs). Survey interviews were completed with 615 PLHIV in five rural and urban out-patient clinics in northern Vietnam using an Audio Computer Assisted Self-Interview (ACASI) and clinical records extraction. The survey instrument was carefully developed through a systematic procedure to ensure its reliability and validity. Cultural appropriateness was considered in the design and implementation of both the qualitative study and the cross sectional survey. The qualitative study uncovered several contrary perceptions between health care providers and HIV/AIDS patients regarding the true levels of ART adherence. Health care providers often stated that most of their patients closely adhered to their regimens, while PLHIV and their peers reported that “it is not easy” to do so. The quantitative survey findings supported the PLHIV and their peers’ point of view in the qualitative study, because non-adherence to ART was relatively common among the study sample. Using the ACASI technique, the estimated prevalence of onemonth non-adherence measured by the Visual Analogue Scale (VAS) was 24.9% and the prevalence of four-day not-on-time-adherence using the modified Adult AIDS Clinical Trials Group (AACTG) instrument was 29%. Observed agreement between the two measures was 84% and kappa coefficient was 0.60 (SE=0.04 and p<0.0001). The good agreement between the two measures in the current study is consistent with those found in previous research and provides evidence of cross-validation of the estimated adherence levels. The qualitative study was also valuable in suggesting important variables for the survey conceptual framework and instrument development. The survey confirmed significant correlations between two measures of ART adherence (i.e. dose adherence and time adherence) and many factors identified in the qualitative study, but failed to find evidence of significant correlations of some other factors and ART adherence. Non-adherence to ART was significantly associated with untreated depression, heavy alcohol use, illicit drug use, experiences with medication side-effects, chance health locus of control, low quality of information from HCPs, low satisfaction with received support and poor social connectedness. No multivariate association was observed between ART adherence and age, gender, education, duration of ART, the use of adherence aids, disclosure of ART, patients’ ability to initiate communication with HCPs or distance between clinic and patients’ residence. This is the largest study yet reported in Asia to examine non-adherence to ART and its possible determinants. The evidence strongly supports recent calls from other developing nations for HIV/AIDS services to provide screening, counseling and treatment for patients with depressive symptoms, heavy use of alcohol and substance use. Counseling should also address fatalistic beliefs about chance or luck determining health outcomes. The data suggest that adherence could be enhanced by regularly providing information on ART and assisting patients to maintain social connectedness with their family and the community. This study highlights the benefits of using a multi-method approach in examining complex barriers and facilitators of medication adherence. It also demonstrated the utility of the ACASI interview method to enhance open disclosure by people living with HIV/AIDS and thus, increase the veracity of self-reported data.