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.

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Validation of order rank scales based on compositional data analysis: a proposal

Usually, psychometricians apply classical factorial analysis to evaluate construct validity of order rank scales. Nevertheless, these scales have particular characteristics that must be taken into account: total scores and rank are highly relevant

Rank estimation of trajectory matrix in motion segmentation

A novel technique for estimating the rank of the trajectory matrix in the local subspace affinity (LSA) motion segmentation framework is presented. This new rank estimation is based on the relationship between the estimated rank of the trajectory matrix and the affinity matrix built with LSA. The result is an enhanced model selection technique for trajectory matrix rank estimation by which it is possible to automate LSA, without requiring any a priori knowledge, and to improve the final segmentation

Parámetros cuantitativos de la resonancia magnética cerebral en esclerosis múltiple y su correlación con la discapacidad

A pesar del amplio uso de la resonancia magnética en la esclerosis múltiple no se ha logrado una adecuada correlación clínico-imagenológica en esta enfermedad. Objetivo: Determinar la correlación del volumen normalizado de sustancia gris y del volumen de lesiones hipointensas en T1 obtenidos a partir de la resonancia magnética cerebral con la escala de discapacidad extendida en pacientes con diagnóstico de esclerosis múltiple. Materiales y métodos: Estudio retrospectivo en pacientes con diagnóstico de esclerosis múltiple de la Fundación Cardioinfantil. Se obtuvieron los resultados de la escala de discapacidad expandida así como análisis cuantitativo de las imágenes correspondientes de resonancia magnética por medio de la herramienta SIENA. Se cuantificaron el volumen del parénquima cerebral, sustancia gris, sustancia blanca y volumen de lesiones hipointensas en T1. Posteriormente, se relacionaron estos resultados con la escala de discapacidad extendida de Kurtzke previamente obtenida. Para el análisis estadístico se emplearon el test correlación de Spearman y t de Student y Hotelling. Resultados: Se incluyeron 58 pacientes, encontrándose correlaciones estadísticamente significativas entre la escala de discapacidad extendida y volumen de parénquima cerebral, volumen de sustancia gris y volumen de lesiones hipointensas en T1; de 0.384, 0.386 y 0.39. No se encontró una relación entre el volumen de sustancia blanca y la escala de discapacidad. Conclusiones: Existe una correlación clínico-imagenológica moderada en la esclerosis múltiple. La cuantificación de los parámetros propuestos en este estudio podría ser utilizada como herramienta en el seguimiento de la enfermedad y monitorización de nuevos tratamientos.

Resolución espontánea de reflujo vesicoureteral primario en niños: factores predictores y nomograma de predicción

Introducción: Determinamos la proporción de resolución espontánea de RVU primario en una población de niños menores de 5 años así como los factores que influyen y predicen tal resolución, con base en lo cual diseñamos un nomograma que permite determinar la posibilidad de resolución espontánea de cada grado de reflujo a los 3 años de su diagnóstico Metodología: Incluimos 407 niños con diagnóstico de RVU primario en un periodo de 10 años. Mediante análisis de asociación y comparaciones de promedios se determinaron las variables que se comportaron como factores de riesgo para fallar en obtener resolución espontanea y por un modelo de regresión logística binomial se confirmaron asociaciones. Se practicaron comparaciones mediante ANOVA o t-test y así como análisis de sobrevida mediante Log Rank Test para determinar las variables que influían también en el tiempo necesario para obtener resolución espontánea. Resultados: Las tasas de resolución espontánea fueron 92%, 85%, 56.4%, 21% y 5% para los grados I a V de reflujo respectivamente. En el análisis multivariado, Las variables nefropatía por reflujo (sig=0,000), Síndrome de evacuación disfuncional (SED) (sig=0,000) y bilateralidad (sig=0,006) fueron los factores de riesgo independientes para la falla del RVU en resolver espontáneamente. Sin embargo, en los análisis de sobrevida solo la variable SED demostró influir en el tiempo necesario para obtener resolución espontanea (sig=0,002). Discusión: Los hallazgos de este estudio ratifican la importancia de incluir variables como SED, nefropatía por reflujo y lateralidad en los modelos de predicción de resolución espontánea del RVU.

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Practice tests for IGCSE English as a second language : listening and speaking (Book 1) . Audio CDs extended level.

Dos CDs audio aprobados por la Universidad Cambridge International Examinations para la preparación del examen IGCSE (International General Certificate of Secondary Education) en la asignatura de 'Inglés como segundo idioma', y para ser usados junto al libro de texto 'Listening and speaking revised edition (Book 1)'. Los tests de compresión auditiva permitirán a los alumnos practicar la identificación de información concreta, la toma de notas esquemáticas y la compresión de significados, opiniones y actitudes más complejas.

A comparison of discriminant logistic regression and Item Response Theory Likelihood-Ratio Tests for Differential Item Functioning (IRTLRDIF) in polytomous short tests

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Establishing Winter Origins of Migrating Lesser Snow Geese Using Stable Isotopes

Increases in Snow Goose (Chen caerulescens) populations and large-scale habitat changes in North America have contributed to the concentration of migratory waterfowl on fewer wetlands, reducing resource availability, and enhancing risks of disease transmission. Predicting wintering locations of migratory individuals is critical to guide wildlife population management and habitat restoration. We used stable carbon (δ13C), nitrogen (δ15N), and hydrogen (δ2H) isotope ratios in muscle tissue of wintering Snow Geese to discriminate four major wintering areas, the Playa Lake Region, Texas Gulf Coast, Louisiana Gulf Coast, and Arkansas, and infer the wintering locations of individuals collected later during the 2007 and 2008 spring migrations in the Rainwater Basin (RWB) of Nebraska. We predicted the wintering ground derivation of migrating Snow Geese using a likelihood-based approach. Our three-isotope analysis provided an efficient discrimination of the four wintering areas. The assignment model predicted that 53% [95% CI: 37-69] of our sample of Snow Geese from the RWB in 2007 had most likely originated in Louisiana, 38% [23-54] had wintered on Texas Gulf Coast, and 9% [0-20] in Arkansas; the assessment suggested that 89% [73-100] of our 2008 sample had most likely come from Texas Gulf Coast, 9% [0-27] from Louisiana Gulf Coast, and 2% [0-9] from Arkansas. Further segregation of wintering grounds and additional sampling of spring migrating Snow Geese would refine overall assignment and help explain interannual variations in migratory connectivity. The ability to distinguish origins of northbound geese can support the development of spatially-adaptive management strategies for the midcontinent Snow Goose population. Establishing migratory connectivity using isotope assignment techniques can be extended to other waterfowl species to determine critical habitat, evaluate population energy requirements, and inform waterfowl conservation and management strategies.

Stratospheric Memory and Skill of Extended-Range Weather Forecasts

We use an empirical statistical model to demonstrate significant skill in making extended-range forecasts of the monthly-mean Arctic Oscillation (AO). Forecast skill derives from persistent circulation anomalies in the lowermost stratosphere and is greatest during boreal winter. A comparison to the Southern Hemisphere provides evidence that both the time scale and predictability of the AO depend on the presence of persistent circulation anomalies just above the tropopause. These circulation anomalies most likely affect the troposphere through changes to waves in the upper troposphere, which induce surface pressure changes that correspond to the AO.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.