No description available.

No / Recently, automatic age progression has gained popularity due to its nu-merous applications. Among these is the search for missing people, in the UK alone up to 300,000 people are reported missing every year. Although many algorithms have been proposed, most of the methods are affected by image noise, illumination variations, and most importantly facial expres-sions. To this end we propose to build an age progression framework that utilizes image de-noising and expression normalizing capabilities of kernel principal component analysis (Kernel PCA). Here, Kernel PCA a nonlinear form of PCA that explores higher order correlations between input varia-bles, is used to build a model that captures the shape and texture variations of the human face. The extracted facial features are then used to perform age progression via a regression procedure. To evaluate the performance of the framework, rigorous tests are conducted on the FGNET ageing data-base. Furthermore, the proposed algorithm is used to progress images of Mary Boyle; a six-year-old that went missing over 39 years ago, she is considered Ireland’s youngest missing person. The algorithm presented in this paper could potentially aid, among other applications, the search for missing people worldwide.

This thesis aims to contribute to the area of kernel methods, which are a class of machine learning methods known for their wide applicability and state-of-the-art performance, but which suffer from high training and evaluation complexity. The work in this thesis utilizes the notion of reduced-set models to alleviate the training and testing complexities of these methods in a unified manner. In the first part of the thesis, we use recent results in kernel smoothing and integral-operator learning to design a generic strategy to speed up various kernel methods. In Chapter 3, we present a method to speed up kernel PCA (KPCA), which is one of the fundamental kernel methods for manifold learning, by using reduced-set density estimates (RSDE) of the data. The proposed method induces an integral operator that is an approximation of the ideal integral operator associated to KPCA. It is shown that the error between the ideal and approximate integral operators is related to the error between the ideal and approximate kernel density estimates of the data. In Chapter 4, we derive similar approximation algorithms for Gaussian process regression, diffusion maps, and kernel embeddings of conditional distributions. In the second part of the thesis, we use reduced-set models for kernel methods to tackle online learning in model-reference adaptive control (MRAC). In Chapter 5, we relate the properties of the feature spaces induced by Mercer kernels to make a connection between persistency-of-excitation and the budgeted placement of kernels to minimize tracking and modeling error. In Chapter 6, we use a Gaussian process (GP) formulation of the modeling error to accommodate a larger class of errors, and design a reduced-set algorithm to learn a GP model of the modeling error. Proofs of stability for all the algorithms are presented, and simulation results on a challenging control problem validate the methods.

<p>We write down explicit algebraic formulas for the Szeg\H{o}, Garabedian and Bergman kernels for specific two-connected planar domains. We use these results to derive integral representations for a biholomorphic invariant relating the Bergman and Szeg\H{o} kernels. We use the formulas to study the asymptotic behavior of these kernels as a family of two-connected domains approaches the unit disc. We derive an explicit formula for the Green's function for the Laplacian for special values on two-connected domains. Every two-connected domain is biholomorphic to a unique two-connected domain of the type we consider. This allows one to write down formulas for the kernel functions on a general two-connected domain.</p>

<p>Abstract：The kernel system of Windows is more thoroughly exposed to people. So, thekernel-level Rootkits techniques are now laid on greater emphasis. It is very importantto maintain the security of computers and to conduct an in-depth research on theoperational mechanism by using kernel-level Rootkits in hiding its traces. Since theinvolved core techniques are beginning to catch on nowadays, we should analyzesome new key techniques employed for application of Rootkits, discuss the specificmethods and propose a set of defense strategy for computer security.</p>

Three forms of multivariate analysis, one very classical and the other two relatively new and little-known, are showcased and enhanced: the first is the Singular Value Decomposition (SVD), which is at the heart of many statistical, and now geostatistical, techniques; the second is the method of Variogram Analysis, which is one way of investigating spatial correlation in one or several variables; and the third is the process of interpolation known as cokriging, a method for optimizing the estimation of multivariate data based on the information provided through variogram analysis. The SVD is described in detail, and it is shown that the SVD can be generalized from its familiar matrix (two-dimensional) case to three, and possibly n, dimensions. This generalization we call the "Tensor SVD" (or TSVD), and we demonstrate useful applications in the field of geostatistics (and indicate ways in which it will be useful in other areas). Applications of the SVD to the tools of geostatistics are described: in particular, applications dependent on the TSVD, including variogram modelling in coregionalization. Variogram analysis in general is explored, and we propose broader use of an old tool (which we call the "corhogram ", based on the variogram) which proves useful in helping one choose variables for multivariate interpolation. The reasoning behind kriging and cokriging is discussed, and a better algorithm for solving the cokriging equations is developed, which results in simultaneous kriging estimates for comparison with those obtained from cokriging. Links from kriging systems to kernel systems are made; discovering kerneIs equivalent to kriging systems will be useful in the case where data are plentiful. Finally, some results of the application of geostatistical techniques to a data set concerning nitrate pollution in the West Salt River Valley of Arizona are described.

No description available.

Regression tasks belong to the set of core problems faced in statistics and machine learning and promising approaches can often be generalized to also deal with classification, interpolation or denoising problems. Whereas the most widely used classical statistical techniques place severe a priori constraints on the type of function that can be approximated (e.g. only lines, in the case of linear regression), the successes of sparse kernel learners, such as the SVM (support vector machine) demonstrate that good results may be obtained in a quite general framework by enforcing sparsity. Similarly, even very simple sparsity-based denoising techniques, such as classical wavelet shrinkage, can produce surprisingly good results on a wide variety of different signals, because, unlike noise, most signals of practical interest share vital characteristics (such as smoothness, or the ability to be well approximated by piece-wise linear polynomials of a low order) that allow a sparse representation in wavelet space. On the other hand results obtained from SVMs (and classical wavelet-shrinkage) suffer from a certain lack of interpretability, since one cannot straightforwardly attach probabilities to them. By contrast regression, and even more importantly classification, in a Bayesian context always entails a probabilistic measure of confidence in the results, which, provided the model assumptions are reasonably accurate, forms a basis for principled decision-making. The relevance vector machine (RVM) combines these strengths by explicitly encoding the criterion of model sparsity as a (Bayesian) prior over the model weights and offers a single, unified paradigm to efficiently deal with regression as well as classification tasks. However the lack of an explicit prior structure over the weight variances means that the degree of sparsity is to a large extent controlled by the choice of kernel (and kernel parameters). This can lead to severe overfitting or oversmoothing -- possibly even both at the same time (e.g. for the multiscale Doppler data). This thesis details an efficient scheme to control sparsity in Bayesian regression by incorporating a flexible noise-dependent smoothness prior into the RVM. The resultant smooth RVM (sRVM) encompasses the original RVM as a special case, but empirical results with a variety of popular data sets show that it can surpass RVM performance in terms of goodness of fit and achieved sparsity as well as computational performance in many cases. As the smoothness prior effectively makes it possible to use (highly efficient) wavelet kernels in an RVM setting this work also unveils a strong connection between Bayesian wavelet shrinkage and RVM regression and effectively further extends the applicability of the RVM to denoising tasks for up to millions of datapoints. We further discuss its applicability to classification tasks.

We study two different operational scenarios for a regional air ambulance service-company which has bases in Northern California. Two of these bases serve the land areas encompassed roughly in a circular area of radius 100 miles centered in Gilroy and Salinas, respectively; with a large part of their coverage areas reachable from either base. The base in Salinas currently operates one helicopter only from Thursday to Monday, whereas the base in Gilroy operates one helicopter 24/7. The company is considering extending the operation of one helicopter to 24/7 for its Salinas base. In this study we analyze the operational impacts of that extension, and develop a framework that can be applied towards the study of the ambulance assignment problem faced by small operators. / pa/cb Original. 10/06/05. updated 09/09/2011.

Magíster en Ciencias de la Ingeniería, Mención Eléctrica. Ingeniero Civil Eléctrico / El modelamiento de series de tiempo es un problema transversal a diferentes áreas de ingeniería y ciencias. Este tópico, visto a través del foco de aprendizaje de máquinas o aprendizaje estadístico, se reduce a elegir un modelo de regresión que sea lo suficientemente flexible sin que sobreajuste al conjunto de entrenamiento y, por ende, permita generalizar. No obstante, la elección de modelos flexibles suele venir de la mano de poca interpretabilidad de los mismos, como por ejemplo en modelos con estructura tipo \textit{caja negra}. Los modelos más flexibles son preferidos para problemas de alta complejidad, debido a su ajuste con mayor precisión a las observaciones. Más aún, el ajuste de los modelos predictivos es una componente crìtica para la regresión en línea aplicada a problemas reales. Es por ello que se decide abordar el tema del aprendizaje en línea para series de tiempo no lineales a través de un modelo flexible, que extiende la teoría del filtrado adaptivo lineal, al caso no lineal, haciendo uso de transformación de espacio de características basadas en \textit{kernel} reproductivos. Los objetivos de la investigación realizada son (i) presentar e interpretar el estimador de filtro de \textit{kernel} adaptivo (KAF) al contexto de regresión no lineal de series de tiempo, (ii) extender, en términos de mejoras sobre el algoritmo y el ajuste de sus hiperparámetros, la aplicación estándar de KAF validada sobre series sintéticas y datos reales y (iii) acercar la interpretabilidad y aplicabilidad de los métodos KAF para usuarios, validando la mejora tanto en desempeño predictivo como en ajuste de modelos con las extensiones propuestas. Para ello, este trabajo de investigación reúne los resultados principales de dos investigaciones previas, la primera enfocada en mejorar la predicción de KAF utilizando una entrada exógena de un sistema. En ese contexto se estudió el comportamiento de descarga de batería de ion-litio para una bicicleta eléctrica que utilizaba como entrada exógena mediciones de altitud derivadas a partir de coordenadas de geolocalización. El objetivo era caracterizar la posible dependencia oculta a través del descubrimiento automático de relevancia de las variables al momento de la predicción; para lo cual se usó un \textit{kernel} Gaussiano de Determinación de Relevancia Automática (ARD). Por otro lado, la segunda investigación se centró en la validación de una metodología para la inicialización de KAF extendiendo el estimador a una variante probabilística para mejorar su desempeño y entrenamiento, proponiendo hibridar la estimación en línea adicionando un entrenamiento en \textit{batch} que permite encontrar los hiperparámetros óptimos de la extensión propuesta. Adicionalmente, este enfoque permitió proponer un regularizador novedoso para abordar dos de los problemas más desafiantes de diseño según el estado del arte para KAF: el ajuste del hiperparámetro del \textit{kernel} Gaussiano y el tamaño del diccionario usado por el estimador. La metodología fue validada tanto en datos sintéticos, específicamente para el caso del atractor caótico de Lorentz, como en datos reales, los cuales correspondieron a una serie de viento extraída a partir de mediciones de anemométro. Ambos estudios mostraron resultados prometedores, acercando el uso de KAF a usuarios neófitos, tanto por las metodologías desarrolladas que quedan como guías metodológicas aplicadas, como por la interpretabilidad proporcionada a través de toda la investigación, caracterización y desarrollo del uso de KAF. Finalmente se dejan desafíos futuros con respecto a promover más aún la automatización con respecto a la selección de hiperparámetros del modelo, lo que culminaría con un desarrollo completamente adaptivo de estos métodos, vale decir, con intervención mínima del usuario en la selección de los hiperparámetros.