On the Noise Model of Support Vector Machine Regression

Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called Vapnik"s $epsilon$- insensitive loss function, which is similar to the "robust" loss functions introduced by Huber (Huber, 1981). The quadratic loss function is well justified under the assumption of Gaussian additive noise. However, the noise model underlying the choice of Vapnik's loss function is less clear. In this paper the use of Vapnik's loss function is shown to be equivalent to a model of additive and Gaussian noise, where the variance and mean of the Gaussian are random variables. The probability distributions for the variance and mean will be stated explicitly. While this work is presented in the framework of SVMR, it can be extended to justify non-quadratic loss functions in any Maximum Likelihood or Maximum A Posteriori approach. It applies not only to Vapnik's loss function, but to a much broader class of loss functions.

On the V(subscript gamma) Dimension for Regression in Reproducing Kernel Hilbert Spaces

This paper presents a computation of the $V_gamma$ dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression $epsilon$-insensitive loss function, and general $L_p$ loss functions. Finiteness of the RV_gamma$ dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the $L_epsilon$ or general $L_p$ loss functions. This paper presenta a novel proof of this result also for the case that a bias is added to the functions in the RKHS.

Time-series regression models to study the short-term effects of environmental factors on health

Time series regression models are especially suitable in epidemiology for evaluating short-term effects of time-varying exposures on health. The problem is that potential for confounding in time series regression is very high. Thus, it is important that trend and seasonality are properly accounted for. Our paper reviews the statistical models commonly used in time-series regression methods, specially allowing for serial correlation, make them potentially useful for selected epidemiological purposes. In particular, we discuss the use of time-series regression for counts using a wide range Generalised Linear Models as well as Generalised Additive Models. In addition, recently critical points in using statistical software for GAM were stressed, and reanalyses of time series data on air pollution and health were performed in order to update already published. Applications are offered through an example on the relationship between asthma emergency admissions and photochemical air pollutants

Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

An alternative method for dating unknown tephras based on a segmented regression model

In CoDaWork’05, we presented an application of discriminant function analysis (DFA) to 4 different compositional datasets and modelled the first canonical variable using a segmented regression model solely based on an observation about the scatter plots. In this paper, multiple linear regressions are applied to different datasets to confirm the validity of our proposed model. In addition to dating the unknown tephras by calibration as discussed previously, another method of mapping the unknown tephras into samples of the reference set or missing samples in between consecutive reference samples is proposed. The application of these methodologies is demonstrated with both simulated and real datasets. This new proposed methodology provides an alternative, more acceptable approach for geologists as their focus is on mapping the unknown tephra with relevant eruptive events rather than estimating the age of unknown tephra. Kew words: Tephrochronology; Segmented regression

Regression periods in infancy. A case study from Catalonia.

Based on Rijt-Plooij and Plooij’s (1992) research on emergence of regression periods in the first two years of life, the presence of such periods in a group of 18 babies (10 boys and 8 girls, aged between 3 weeks and 14 months) from a Catalonian population was analyzed. The measurements were a questionnaire filled in by the infants’ mothers, a semi-structured weekly tape-recorded interview, and observations in their homes. The procedure and the instruments used in the project follow those proposed by Rijt-Plooij and Plooij. Our results confirm the existence of the regression periods in the first year of children’s life. Inter-coder agreement for trained coders was 78.2% and within-coder agreement was 90.1 %. In the discussion, the possible meaning and relevance of regression periods in order to understand development from a psychobiological and social framework is commented upon

Use of multilevel logistic regression to identify the causes of differential item functioning

Resumen tomado de la publicaci??n

Regression-based techniques for statistical decision making in singlecase designs

Resumen tomado de la publicaci??n

PILT Threshold 1

Files used for and during the Threshold 1 workshop

PILT Threshold 2

Files used for and during the Threshold 2 workshop

Additional regression techniques_Solutions_2009.ppt (19)

PowerPoint Slides relating to theory and use of SPSS. Used in Research Skills for Biomedical Science

Capacidad aeróbica de bomberos aeronáuticos

Los bomberos aeronáuticos son los encargados de atender todas las emergencias en los aeropuertos y sus cercanías. Estas emergencias incluyen emergencias aéreas, en tierra, eventos con materiales peligros e incendios, entre otros. Su trabajo tiene como características la realización de actividades durante periodos largos de baja intensidad y periodos cortos de alta intensidad. De acuerdo con estas características, es necesario que los bomberos aeronáuticos tengan una buena condición física. El consumo máximo de oxígeno (VO2 máx) como indicador de capacidad aeróbica resulta indispensable para conocer el desempeño de los bomberos en su trabajo. El objetivo de este estudio es determinar la capacidad aeróbica de los bomberos aeronáuticos y sus factores determinantes. Por tanto se desarrolló un estudio transversal de tipo descriptivo en una muestra de 23 hombres bomberos aeronáuticos. Se obtuvo información acerca de sus variables socio-demográficas, se determinó el VO2 máx y umbral ventilatorio mediante análisis de gases espirados durante un protocolo de ejercicio máximo sobre tapiz rodante, se evaluó la composición corporal mediante adipometría y se determinó el nivel de actividad física mediante el cuestionario internacional de actividad física IPAQ. Se encontró que la muestra tenia una edad de 32,6 ± 4,8 años, peso de 78,4 ± 9,8 kg, porcentaje de grasa de 14,8 ± 3,8 %, índice de masa corporal de 25,7 ± 2,7 y VO2máx de 44,6 ± 6. No se encontraron cambios significativos del VO2máx con la edad, pero si con la actividad física, porcentaje de grasa e índice de masa corporal. Se sugiere que el entrenamiento de los bomberos aeronáuticos durante su jornada laboral sea de intervalos de alta intensidad y que se monitorice su nivel de actividad física y composición corporal.