Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"Reproducing kernel Hilbert space"”.
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Calibration of Option Pricing in Reproducing Kernel Hilbert Space
… a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. We discuss the existence of the minimizer by using regu- larized reproducing kernel method and show …
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Functional regression models in the frame work of reproducing kernel Hilbert space
… distance between the null and the alternative space that still allows a possible test. The lower bound of the minimax decay rate of this distance is derived, and test with a distance that decays faster than the lower bound would be impossible. It is shown that the minimax optimal rate is …
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Design and Simulation of a Model Reference Adaptive Control System Employing Reproducing Kernel Hilbert Space for Enhanced Flight Control of a Quadcopter
This thesis presents the integration of reproducing kernel Hilbert spaces (RKHSs) into the model reference adaptive control (MRAC) framework to enhance the control systems of quadcopters. Traditional MRAC systems, while robust under predictable conditions, can struggle with the dynamic …
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Signal detection in fractional Gaussian noise and an RKHS approach to robust detection and estimation
… of this problem, several results related to the reproducing kernel Hilbert space of fractional Brownian motion are presented. In particular, this reproducing kernel Hilbert space is characterized completely and an alternative characterization for the restriction of this class of functions to a …
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Direct and inverse problems in machine learning
… Our estimators are all constructed by kernel methods, which depend on a Reproducing Kernel Hilbert Space structure using spectral regularization methods. A first main result establishes upper and lower bounds for the rate of convergence under a given source condition assumption, …
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Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces
… 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 …
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Essays on Algorithmic Learning and Uncertainty Quantification
… in non-convex models. The second essay, titled “Kernel Ridge Regression Inference,” introduces a new technique for deriving sharp, non-asymptotic, uniform Gaussian approximation for partial sums in a reproducing kernel Hilbert space, which is then applied to construct uniform confidence bands for …
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Data-Driven, Non-Parametric Model Reference Adaptive Control Methods for Autonomous Underwater Vehicles
… control (MRAC) algorithms which make use of kernel functions for learning functional uncertainty present in the system dynamics. The first method extends recent results on model reference adaptive control using reproducing kernel Hilbert space (RKHS) learning techniques for some general cases …
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Spectral Regression: A Regression Framework for Efficient Regularized Subspace Learning
… problem by seeking an embedding function in reproducing kernel Hilbert space. However, a disadvantage of all these approaches is that their computations usually involve eigen-decomposition of dense matrices which is expensive in both time and memory. In this thesis, we introduce a novel …
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Everything old is new again : a fresh look at historical approaches in machine learning
… loss on a training set and small norm in a Reproducing Kernel Hilbert Space. The choice of loss function determines the learning scheme. Using the hinge loss gives rise to the now well-known Support Vector Machine algorithm. We present SvmFu, a state-of-the-art SVM solver developed as part …
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Sequential decision making with feature-linear models
… that model the reward as linear in some feature space. We consider a bandit problem, where the rewards are linear in a reproducing kernel Hilbert space, and a reinforcement learning setting with features given by a neural network. The thesis is split into two parts accordingly. In part I, we …
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Modeling and Estimation of Motion Over Manifolds with Motion Capture Data
… from statistical learning theory over Euclidean spaces to estimating functions over manifolds. Experimental results are presented for estimating reptilian motion using motion capture data. The second study in this dissertation utilizes reproducing kernel Hilbert space (RKHS) formulations and …
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Modeling and Estimation of Linear and Nonlinear Piezoelectric Systems
… An adaptive estimation method, that uses reproducing kernel Hilbert space (RKHS) embedding methods, can estimate the underlying nonlinear function that governs the system's dynamics. A model built by such a method can overcome some of the limitations of the modeling approaches mentioned …
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Contributions to statistical learning and its applications in personalized medicine
… with functional predictors. We focused on the Reproducing Kernel Hilbert space approach and show that regardless the generality of the method, minimax optimal convergence rates are achieved. In order to derive the asymptotic analysis of the estimator, we developed a simultaneous diagonalization …
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Essays on Decision Making Under Uncertainty
… In Chapter 3, "Data-Driven Optimization: A Reproducing Kernel Hilbert Space Approach," we present two methods, based on regression in reproducing kernel Hilbert spaces, for solving an optimization problem with uncertain parameters for which we have historical data, including auxiliary data. …
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Modeling, Approximation, and Control for a Class of Nonlinear Systems
… of nonlinear systems whose state evolves in space $mathbb{R}^n times H$, where $mathbb{R}^n$ is a n-dimensional Euclidean space and $H$ is a infinite dimensional Hilbert space. Specifically, two classes of nonlinear systems are studied in this dissertation. The first topic develops a novel …
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Modelos de cuantización en variedades
… conexas orientables de curvatura cero (euclidean space form) se muestra que existe un isomorfismo natural entre el espacio de Hilbert de funciones de cuadrado integrable en el espacio de configuración y el espacio de funciones holomorfas de cuadrado integrable en el espacio fase. Los productos …
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Convergence of Kernel Methods for Modeling and Estimation of Dynamical Systems
… dissertation analyzes the convergence of two kernel-based, data-driven modeling methods, the reproducing kernel Hilbert space (RKHS) embedding method and the empirical-analytical Lagrangian (EAL) model. RKHS embedding is a non-parametric extension of the classical adaptive estimation method …
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Nonparametric Anomaly Detection and Secure Communication
… generating typical samples. For both problems, kernel-based tests are proposed, which are based on maximum mean discrepancy (MMD) that measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space. These tests are nonparametric without exploiting the …
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Asymptotic theory for Bayesian nonparametric inference in statistical models arising from partial differential equations
… corresponds to a Tikhonov regulariser with a reproducing kernel Hilbert space norm penalty. We prove a semiparametric Bernstein–von Mises theorem for a large collection of linear functionals of the unknown, implying that semiparametric posterior estimation and uncertainty quantification are …
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