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1

Tipton, James Edward. "Reproducing Kernel Hilbert spaces and complex dynamics." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2284.

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Both complex dynamics and the theory of reproducing kernel Hilbert spaces have found widespread application over the last few decades. Although complex dynamics started over a century ago, the gravity of it's importance was only recently realized due to B.B. Mandelbrot's work in the 1980's. B.B. Mandelbrot demonstrated to the world that fractals, which are chaotic patterns containing a high degree of self-similarity, often times serve as better models to nature than conventional smooth models. The theory of reproducing kernel Hilbert spaces also having started over a century ago, didn't pick u
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2

Bhujwalla, Yusuf. "Nonlinear System Identification with Kernels : Applications of Derivatives in Reproducing Kernel Hilbert Spaces." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0315/document.

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Cette thèse se concentrera exclusivement sur l’application de méthodes non paramétriques basées sur le noyau à des problèmes d’identification non-linéaires. Comme pour les autres méthodes non-linéaires, deux questions clés dans l’identification basée sur le noyau sont les questions de comment définir un modèle non-linéaire (sélection du noyau) et comment ajuster la complexité du modèle (régularisation). La contribution principale de cette thèse est la présentation et l’étude de deux critères d’optimisation (un existant dans la littérature et une nouvelle proposition) pou
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3

Struble, Dale William. "Wavelets on manifolds and multiscale reproducing kernel Hilbert spaces." Related electronic resource:, 2007. http://proquest.umi.com/pqdweb?did=1407687581&sid=1&Fmt=2&clientId=3739&RQT=309&VName=PQD.

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4

Quiggin, Peter Philip. "Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces." Thesis, Lancaster University, 1994. http://eprints.lancs.ac.uk/61962/.

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Pick's theorem states that there exists a function in H1, which is bounded by 1 and takes given values at given points, if and only if a certain matrix is positive. H1 is the space of multipliers of H2 and this theorem has a natural generalisation when H1 is replaced by the space of multipliers of a general reproducing kernel Hilbert space H(K) (where K is the reproducing kernel). J. Agler showed that this generalised theorem is true when H(K) is a certain Sobolev space or the Dirichlet space. This thesis widens Agler's approach to cover reproducing kernel Hilbert spaces in general and derives
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5

Marx, Gregory. "The Complete Pick Property and Reproducing Kernel Hilbert Spaces." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/24783.

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We present two approaches towards a characterization of the complete Pick property. We first discuss the lurking isometry method used in a paper by J.A. Ball, T.T. Trent, and V. Vinnikov. They show that a nondegenerate, positive kernel has the complete Pick property if $1/k$ has one positive square. We also look at the one-point extension approach developed by P. Quiggin which leads to a sufficient and necessary condition for a positive kernel to have the complete Pick property. We conclude by connecting the two characterizations of the complete Pick property.<br>Master of Science
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6

Giménez, Febrer Pere Joan. "Matrix completion with prior information in reproducing kernel Hilbert spaces." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/671718.

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In matrix completion, the objective is to recover an unknown matrix from a small subset of observed entries. Most successful methods for recovering the unknown entries are based on the assumption that the unknown full matrix has low rank. By having low rank, each of its entries are obtained as a function of a small number of coefficients which can be accurately estimated provided that there are enough available observations. Hence, in low-rank matrix completion the estimate is given by the matrix of minimum rank that fits the observed entries. Besides low rankness, the unknown matrix might
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7

Dieuleveut, Aymeric. "Stochastic approximation in Hilbert spaces." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE059/document.

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Le but de l’apprentissage supervisé est d’inférer des relations entre un phénomène que l’on souhaite prédire et des variables « explicatives ». À cette fin, on dispose d’observations de multiples réalisations du phénomène, à partir desquelles on propose une règle de prédiction. L’émergence récente de sources de données à très grande échelle, tant par le nombre d’observations effectuées (en analyse d’image, par exemple) que par le grand nombre de variables explicatives (en génétique), a fait émerger deux difficultés : d’une part, il devient difficile d’éviter l’écueil du sur-apprentissage lorsq
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8

Giulini, Ilaria. "Generalization bounds for random samples in Hilbert spaces." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0026/document.

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Ce travail de thèse porte sur l'obtention de bornes de généralisation pour des échantillons statistiques à valeur dans des espaces de Hilbert définis par des noyaux reproduisants. L'approche consiste à obtenir des bornes non asymptotiques indépendantes de la dimension dans des espaces de dimension finie, en utilisant des inégalités PAC-Bayesiennes liées à une perturbation Gaussienne du paramètre et à les étendre ensuite aux espaces de Hilbert séparables. On se pose dans un premier temps la question de l'estimation de l'opérateur de Gram à partir d'un échantillon i. i. d. par un estimateur robu
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9

Paiva, António R. C. "Reproducing kernel Hilbert spaces for point processes, with applications to neural activity analysis." [Gainesville, Fla.] : University of Florida, 2008. http://purl.fcla.edu/fcla/etd/UFE0022471.

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10

Sabree, Aqeeb A. "Positive definite kernels, harmonic analysis, and boundary spaces: Drury-Arveson theory, and related." Diss., University of Iowa, 2019. https://ir.uiowa.edu/etd/7023.

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A reproducing kernel Hilbert space (RKHS) is a Hilbert space $\mathscr{H}$ of functions with the property that the values $f(x)$ for $f \in \mathscr{H}$ are reproduced from the inner product in $\mathscr{H}$. Recent applications are found in stochastic processes (Ito Calculus), harmonic analysis, complex analysis, learning theory, and machine learning algorithms. This research began with the study of RKHSs to areas such as learning theory, sampling theory, and harmonic analysis. From the Moore-Aronszajn theorem, we have an explicit correspondence between reproducing kernel Hilbert spaces (RKHS
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11

Barbian, Christoph [Verfasser], and Jörg [Akademischer Betreuer] Eschmeier. "Beurling-type representation of invariant subspaces in reproducing kernel Hilbert spaces / Christoph Barbian. Betreuer: Jörg Eschmeier." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2011. http://d-nb.info/1051285119/34.

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12

Barbosa, Victor Simões. "Universalidade e ortogonalidade em espaços de Hilbert de reprodução." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18032013-142251/.

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Neste trabalho analisamos o papel das funções layout de um núcleo positivo definido K sobre um espaço topológico de Hausdor E com relação a duas propriedades específicas: a universalidade de K e a ortogonalidade no espaço de Hilbert de reprodução de K a partir de suportes disjuntos. As funções layout sempre existem mas podem não ser únicas. De uma maneira geral, a função layout e uma aplicação que transfere, convenientemente, informações do espaço E para um espaço com produto interno de dimensão alta, onde métodos lineares podem ser usados. Tanto a universalidade quanto a ortogonalidade pressu
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13

Plumlee, Matthew. "Fast methods for identifying high dimensional systems using observations." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53544.

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This thesis proposes new analysis tools for simulation models in the presence of data. To achieve a representation close to reality, simulation models are typically endowed with a set of inputs, termed parameters, that represent several controllable, stochastic or unknown components of the system. Because these models often utilize computationally expensive procedures, even modern supercomputers require a nontrivial amount of time, money, and energy to run for complex systems. Existing statistical frameworks avoid repeated evaluations of deterministic models through an emulator, constructed
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14

Ferreira, José Claudinei. "Operadores integrais positivos e espaços de Hilbert de reprodução." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17082010-100716/.

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Este trabalho é dedicado ao estudo de propriedades teóricas dos operadores integrais positivos em \'L POT. 2\' (X; u), quando X é um espaço topológico localmente compacto ou primeiro enumerável e u é uma medida estritamente positiva. Damos ênfase à análise de propriedades espectrais relacionadas com extensões do Teorema de Mercer e ao estudo dos espaços de Hilbert de reprodução relacionados. Como aplicação, estudamos o decaimento dos autovalores destes operadores, em um contexto especial. Finalizamos o trabalho com a análise de propriedades de suavidade das funções do espaço de Hilbert de
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15

Niedzialomski, Robert. "Extension of positive definite functions." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/2595.

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Let $\Omega\subset\mathbb{R}^n$ be an open and connected subset of $\mathbb{R}^n$. We say that a function $F\colon \Omega-\Omega\to\mathbb{C}$, where $\Omega-\Omega=\{x-y\colon x,y\in\Omega\}$, is positive definite if for any $x_1,\ldots,x_m\in\Omega$ and any $c_1,\ldots,c_m\in \mathbb{C}$ we have that $\sum_{j,k=1}^m F(x_j-x_k)c_j\overline{c_k}\geq 0$. Let $F\colon\Omega-\Omega\to\mathbb{C}$ be a continuous positive definite function. We give necessary and sufficient conditions for $F$ to have an extension to a continuous
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16

Kingravi, Hassan. "Reduced-set models for improving the training and execution speed of kernel methods." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51799.

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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
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17

Santana, Júnior Ewaldo éder Carvalho. "EXTRAÇÃO CEGA DE SINAIS COM ESTRUTURAS TEMPORAIS UTILIZANDO ESPAÇOS DE HILBERT REPRODUZIDOS POR KERNEIS." Universidade Federal do Maranhão, 2012. http://tedebc.ufma.br:8080/jspui/handle/tede/476.

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Made available in DSpace on 2016-08-17T14:53:18Z (GMT). No. of bitstreams: 1 Dissertacao Ewaldo.pdf: 1169300 bytes, checksum: fc5d4b9840bbafe39d03cd1221da615e (MD5) Previous issue date: 2012-02-10<br>This work derives and evaluates a nonlinear method for Blind Source Extraction (BSE) in a Reproducing Kernel Hilbert Space (RKHS) framework. For extracting the desired signal from a mixture a priori information about the autocorrelation function of that signal translated in a linear transformation of the Gram matrix of the nonlinearly transformed data to the Hilbert space. Our method proved to
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18

Benelmadani, Djihad. "Contribution à la régression non paramétrique avec un processus erreur d'autocovariance générale et application en pharmacocinétique." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAM034/document.

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Dans cette thèse, nous considérons le modèle de régression avec plusieurs unités expérimentales, où les erreurs forment un processus d'autocovariance dans un cadre générale, c'est-à-dire, un processus du second ordre (stationnaire ou non stationnaire) avec une autocovariance non différentiable le long de la diagonale. Nous sommes intéressés, entre autres, à l'estimation non paramétrique de la fonction de régression de ce modèle.Premièrement, nous considérons l'estimateur classique proposé par Gasser et Müller. Nous étudions ses performances asymptotiques quand le nombre d'unités expérimentales
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19

Varagnolo, Damiano. "Distributed Parametric-Nonparametric Estimation in Networked Control Systems." Doctoral thesis, Università degli studi di Padova, 2011. http://hdl.handle.net/11577/3421610.

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In the framework of parametric and nonparametric distributed estimation, we introduce and mathematically analyze some consensus-based regression strategies characterized by a guess of the number of agents in the network as a parameter. The parametric estimators assume a-priori information about the finite set of parameters to be estimated, while the the nonparametric use a reproducing kernel Hilbert space as the hypothesis space. The analysis of the proposed distributed regressors offers some sufficient conditions assuring the estimators to perform better, under the variance of the estimation
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20

Ren, Haobo. "Functional inverse regression and reproducing kernel Hilbert space." Diss., Texas A&M University, 2005. http://hdl.handle.net/1969.1/4203.

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The basic philosophy of Functional Data Analysis (FDA) is to think of the observed data functions as elements of a possibly infinite-dimensional function space. Most of the current research topics on FDA focus on advancing theoretical tools and extending existing multivariate techniques to accommodate the infinite-dimensional nature of data. This dissertation reports contributions on both fronts, where a unifying inverse regression theory for both the multivariate setting (Li 1991) and functional data from a Reproducing Kernel Hilbert Space (RKHS) prospective is developed. We proposed a functi
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21

Kamari, Halaleh. "Qualité prédictive des méta-modèles construits sur des espaces de Hilbert à noyau auto-reproduisant et analyse de sensibilité des modèles complexes." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASE010.

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Ce travail porte sur le problème de l'estimation d'un méta-modèle d'un modèle complexe, noté m. Le modèle m dépend de d variables d'entrées X1,...,Xd qui sont indépendantes et ont une loi connue. Le méta-modèle, noté f∗, approche la décomposition de Hoeffding de m et permet d'estimer ses indices de Sobol. Il appartient à un espace de Hilbert à noyau auto-reproduisant (RKHS), noté H, qui est construit comme une somme directe d'espaces de Hilbert (Durrande et al. (2013)). L'estimateur du méta-modèle, noté f^, est calculé en minimisant un critère des moindres carrés pénalisé par la somme de la no
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22

Amaya, Austin J. "Beurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versions." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27636.

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Given a full-range simply-invariant shift-invariant subspace <i>M</i> of the vector-valued <i>L<sup>2</sup></i> space on the unit circle, the classical Beurling-Lax-Halmos (BLH) theorem obtains a unitary operator-valued function <i>W</i> so that <i>M</i> may be represented as the image of of the Hardy space <i>H<sup>2</sup></i> on the disc under multiplication by <i>W</i>. The work of Ball-Helton later extended this result to find a single function representing a so-called dual shift-invariant pair of subspaces <i>(M,M<sup>Ã </sup>)</i> which together form a direct-sum decomposition of <i>L<su
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23

Das, Suporna. "Frames and reproducing kernels in a Hilbert space." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ54293.pdf.

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24

Zhang, Xinhua, and xinhua zhang cs@gmail com. "Graphical Models: Modeling, Optimization, and Hilbert Space Embedding." The Australian National University. ANU College of Engineering and Computer Sciences, 2010. http://thesis.anu.edu.au./public/adt-ANU20100729.072500.

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Over the past two decades graphical models have been widely used as powerful tools for compactly representing distributions. On the other hand, kernel methods have been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. Graphical models are a powerful underlying formalism in machine learning. Their graph theoretic properties provide both an intuitive modular interface to model the interacting factors, and a data structure facilitating efficient learning and inference. T
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25

Leon, Ralph Daniel. "Module structure of a Hilbert space." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2469.

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This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.
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26

Jordão, Thaís. "Diferenciabilidade em espaços de Hilbert de reprodução sobre a esfera." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-29032012-103159/.

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Um espaço de Hilbert de reprodução (EHR) é um espaço de Hilbert de funções construído de maneira específica e única a partir de um núcleo positivo definido. As funções do EHR tem a seguinte peculiaridade: seus valores podem ser reproduzidos através de uma operação elementar envolvendo a própria função, o núcleo gerador e o produto interno do espaço. Neste trabalho, consideramos EHR gerados por núcleos positivos definidos sobre a esfera unitária m-dimensional usual. Analisamos quais propriedades são herdadas pelos elementos do espaço, quando o núcleo gerador possui alguma hipótese de diferencia
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27

Tullo, Alessandra. "Apprendimento automatico con metodo kernel." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23200/.

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Il seguente lavoro ha come obbiettivo lo studio dei metodi kernel nell'apprendimento automatico. Partendo dalla definizione di spazi di Hilbert a nucleo riproducente vengono esaminate le funzioni kernel e i metodi kernel. In particolare vengono analizzati il kernel trick e il representer theorem. Infine viene dato un esempio di problema dell'apprendimento automatico supervisionato, il problema di regressione lineare del kernel, risolto attraverso il representer theorem.
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28

Agrawal, Devanshu. "The Complete Structure of Linear and Nonlinear Deformations of Frames on a Hilbert Space." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3003.

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A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show that
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29

Wang, Roy Chih Chung. "Adaptive Kernel Functions and Optimization Over a Space of Rank-One Decompositions." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36975.

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The representer theorem from the reproducing kernel Hilbert space theory is the origin of many kernel-based machine learning and signal modelling techniques that are popular today. Most kernel functions used in practical applications behave in a homogeneous manner across the domain of the signal of interest, and they are called stationary kernels. One open problem in the literature is the specification of a non-stationary kernel that is computationally tractable. Some recent works solve large-scale optimization problems to obtain such kernels, and they often suffer from non-identifiability iss
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30

Gräf, Manuel. "Efficient Algorithms for the Computation of Optimal Quadrature Points on Riemannian Manifolds." Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-115287.

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We consider the problem of numerical integration, where one aims to approximate an integral of a given continuous function from the function values at given sampling points, also known as quadrature points. A useful framework for such an approximation process is provided by the theory of reproducing kernel Hilbert spaces and the concept of the worst case quadrature error. However, the computation of optimal quadrature points, which minimize the worst case quadrature error, is in general a challenging task and requires efficient algorithms, in particular for large numbers of points. The focus
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31

Pan, Yue. "Currents- and varifolds-based registration of lung vessels and lung surfaces." Thesis, University of Iowa, 2016. https://ir.uiowa.edu/etd/2257.

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This thesis compares and contrasts currents- and varifolds-based diffeomorphic image registration approaches for registering tree-like structures in the lung and surface of the lung. In these approaches, curve-like structures in the lung—for example, the skeletons of vessels and airways segmentation—and surface of the lung are represented by currents or varifolds in the dual space of a Reproducing Kernel Hilbert Space (RKHS). Currents and varifolds representations are discretized and are parameterized via of a collection of momenta. A momenta corresponds to a line segment via the coordinates o
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32

Shin, Hyejin. "Infinite dimensional discrimination and classification." Texas A&M University, 2003. http://hdl.handle.net/1969.1/5832.

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Modern data collection methods are now frequently returning observations that should be viewed as the result of digitized recording or sampling from stochastic processes rather than vectors of finite length. In spite of great demands, only a few classification methodologies for such data have been suggested and supporting theory is quite limited. The focus of this dissertation is on discrimination and classification in this infinite dimensional setting. The methodology and theory we develop are based on the abstract canonical correlation concept of Eubank and Hsing (2005), and motivated by the
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33

Bui, Thi Thien Trang. "Modèle de régression pour des données non-Euclidiennes en grande dimension. Application à la classification de taxons en anatomie computationnelle." Thesis, Toulouse, INSA, 2019. http://www.theses.fr/2019ISAT0021.

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Dans cette thèse, nous étudions un modèle de régression avec des entrées de type distribution et le problème de test d'hypothèse pour la détection de signaux dans un modèle de régression. Nos modèles ont été appliqués aux données de sensibilité auditive mesurées par otoémissions acoustiques, cette mesure biologique contenant potentiellement des informations annexes sur l'individu (age, sexe, population/espèce).Dans la première partie, un nouveau modèle de régression de distribution pour les distributions de probabilité est introduit. Ce modèle est basé sur un cadre de régression RKHS, dans leq
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34

Ke, Chenlu. "A NEW INDEPENDENCE MEASURE AND ITS APPLICATIONS IN HIGH DIMENSIONAL DATA ANALYSIS." UKnowledge, 2019. https://uknowledge.uky.edu/statistics_etds/41.

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This dissertation has three consecutive topics. First, we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. The index is also applicable when both variables are continuous. Second, we develop a sufficient variable selection procedure based on the new measure in a large p small
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35

Henchiri, Yousri. "L'approche Support Vector Machines (SVM) pour le traitement des données fonctionnelles." Thesis, Montpellier 2, 2013. http://www.theses.fr/2013MON20187/document.

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L'Analyse des Données Fonctionnelles est un domaine important et dynamique en statistique. Elle offre des outils efficaces et propose de nouveaux développements méthodologiques et théoriques en présence de données de type fonctionnel (fonctions, courbes, surfaces, ...). Le travail exposé dans cette thèse apporte une nouvelle contribution aux thèmes de l'apprentissage statistique et des quantiles conditionnels lorsque les données sont assimilables à des fonctions. Une attention particulière a été réservée à l'utilisation de la technique Support Vector Machines (SVM). Cette technique fait interv
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Saide, Chafic. "Filtrage adaptatif à l’aide de méthodes à noyau : application au contrôle d’un palier magnétique actif." Thesis, Troyes, 2013. http://www.theses.fr/2013TROY0018/document.

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L’estimation fonctionnelle basée sur les espaces de Hilbert à noyau reproduisant demeure un sujet de recherche actif pour l’identification des systèmes non linéaires. L'ordre du modèle croit avec le nombre de couples entrée-sortie, ce qui rend cette méthode inadéquate pour une identification en ligne. Le critère de cohérence est une méthode de parcimonie pour contrôler l’ordre du modèle. Le modèle est donc défini à partir d'un dictionnaire de faible taille qui est formé par les fonctions noyau les plus pertinentes.Une fonction noyau introduite dans le dictionnaire y demeure même si la non-stat
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37

Ammanouil, Rita. "Contributions au démélange non-supervisé et non-linéaire de données hyperspectrales." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4079/document.

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Le démélange spectral est l’un des problèmes centraux pour l’exploitation des images hyperspectrales. En raison de la faible résolution spatiale des imageurs hyperspectraux en télédetection, la surface représentée par un pixel peut contenir plusieurs matériaux. Dans ce contexte, le démélange consiste à estimer les spectres purs (les end members) ainsi que leurs fractions (les abondances) pour chaque pixel de l’image. Le but de cette thèse estde proposer de nouveaux algorithmes de démélange qui visent à améliorer l’estimation des spectres purs et des abondances. En particulier, les algorithmes
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38

Kuo, David, and 郭立維. "Reproducing Kernel Hilbert Spaces and Reproducing Kernel Hilbert Spacesand Feichtinger’s Conjecture." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/76783081720520823585.

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碩士<br>逢甲大學<br>應用數學所<br>93<br>We will prove a theorem on a class of unitary operators between a Hilbert space and related reproducing kernel Hilbert space. Using this theorem, we then prove that every bounded frame is a finite union of Riesz sequences, which have been conjectured by Feichtinger. This in turn will imply that for any WH-frame the modulation constant must be irrational.
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39

Evgeniou, Theodoros, and Massimiliano Pontil. "On the V(subscript gamma) Dimension for Regression in Reproducing Kernel Hilbert Spaces." 1999. http://hdl.handle.net/1721.1/7262.

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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.
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Girosi, Federico. "An Equivalence Between Sparse Approximation and Support Vector Machines." 1997. http://hdl.handle.net/1721.1/7289.

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In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of
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41

Bhattacharjee, Monojit. "Analytic Models, Dilations, Wandering Subspaces and Inner Functions." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4241.

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This thesis concerns dilation theory, analytic models, joint invariant subspaces, reproducing kernelHilbert spaces and multipliers associated to commuting tuples of bounded linear operators on Hilbert spaces. The main contribution of this thesis is twofold: dilation and analytic model theory for n-tuples of (1) commuting contractions (in the setting of the unit polydisc), and (2) commuting row contractions (in the setting of the unit ball). On n-tuples of commuting contractions: We study analytic models of operators with some positivity assumptions and quotient modules of function Hilbert spac
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42

Zhang, Xinhua. "Graphical Models: Modeling, Optimization, and Hilbert Space Embedding." Phd thesis, 2010. http://hdl.handle.net/1885/49340.

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Over the past two decades graphical models have been widely used as a powerful tool for compactly representing distributions. On the other hand, kernel methods have also been used extensively to come up with rich representations. This thesis aims to combine graphical models with kernels to produce compact models with rich representational abilities. The following four areas are our focus. 1. Conditional random fields for multi-agent reinforcement learning. Conditional random fields (CRFs) are graphical models for modeling the probability of labels given the observations. They have traditio
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43

Hota, Tapan Kumar. "Subnormality and Moment Sequences." Thesis, 2012. http://etd.iisc.ac.in/handle/2005/3242.

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In this report we survey some recent developments of relationship between Hausdorff moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorff moment sequences may not be a Hausdorff moment sequence, but Hausdorff convolution of two moment sequences is always a moment sequence. Observing from the Berg and Dur´an result that the multiplication operator on Is subnormal, we discuss further work on the subnormality of the multiplication operator on a reproducing kernel Hilbert space, whose kernel is a point-wise product of two diagonal po
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44

Hota, Tapan Kumar. "Subnormality and Moment Sequences." Thesis, 2012. http://hdl.handle.net/2005/3242.

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In this report we survey some recent developments of relationship between Hausdorff moment sequences and subnormality of an unilateral weighted shift operator. Although discrete convolution of two Haudorff moment sequences may not be a Hausdorff moment sequence, but Hausdorff convolution of two moment sequences is always a moment sequence. Observing from the Berg and Dur´an result that the multiplication operator on Is subnormal, we discuss further work on the subnormality of the multiplication operator on a reproducing kernel Hilbert space, whose kernel is a point-wise product of two diagonal po
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45

Rieger, Christian. "Sampling Inequalities and Applications." Doctoral thesis, 2008. http://hdl.handle.net/11858/00-1735-0000-0006-B3B9-0.

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46

Vito, Ernesto De, and Andrea Caponnetto. "Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels." 2005. http://hdl.handle.net/1721.1/30543.

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We show that recent results in [3] on risk bounds for regularized least-squares on reproducing kernel Hilbert spaces can be straightforwardly extended to the vector-valued regression setting. We first briefly introduce central concepts on operator-valued kernels. Then we show how risk bounds can be expressed in terms of a generalization of effective dimension.
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47

Scheuerer, Michael. "A Comparison of Models and Methods for Spatial Interpolation in Statistics and Numerical Analysis." Doctoral thesis, 2009. http://hdl.handle.net/11858/00-1735-0000-0006-B3D5-1.

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48

Oesting, Marco. "Spatial Interpolation and Prediction of Gaussian and Max-Stable Processes." Doctoral thesis, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F069-0.

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49

Caponnetto, Andrea, and Ernesto De Vito. "Fast Rates for Regularized Least-squares Algorithm." 2005. http://hdl.handle.net/1721.1/30539.

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We develop a theoretical analysis of generalization performances of regularized least-squares on reproducing kernel Hilbert spaces for supervised learning. We show that the concept of effective dimension of an integral operator plays a central role in the definition of a criterion for the choice of the regularization parameter as a function of the number of samples. In fact, a minimax analysis is performed which shows asymptotic optimality of the above-mentioned criterion.
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50

Lessig, Christian. "Modern Foundations of Light Transport Simulation." Thesis, 2012. http://hdl.handle.net/1807/32808.

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Light transport simulation aims at the numerical computation of the propagation of visible electromagnetic energy in macroscopic environments. In this thesis, we develop the foundations for a modern theory of light transport simulation, unveiling the geometric structure of the continuous theory and providing a formulation of computational techniques that furnishes remarkably efficacy with only local information. Utilizing recent results from various communities, we develop the physical and mathematical structure of light transport from Maxwell's equations by studying a lifted representation of
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