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Showing 1 to 15 of 15 for “"reproducing kernel Hilbert spaces"”.
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Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces
… 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 …
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The Complete Pick Property and Reproducing Kernel Hilbert Spaces
… 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 …
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Noncommutative Kernels
Positive kernels and their associated reproducing kernel Hilbert spaces have played a key role in the development of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject …
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Frames and reproducing kernels in a Hilbert space
Let H be a Hilbert space. A set of vectors [Special characters omitted.] ∈ H, i = 1, 2,..., n , x ∈ X , where X is a locally compact space with Borel measure v on it, constitute a rank-n continuous frame, F ([Special characters omitted.] , A, n ) if for each x ∈ X the set [Special characters …
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Nonparametric sparse learning of dynamical systems
… the system dynamics via transfer operators in reproducing kernel Hilbert spaces (RKHS). Compared with methods using fixed parametric structures, the proposed nonparametric representation does not require manually engineered features, and the model grows and adjusts with the amount of training …
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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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High-throughput machine learning algorithms
… theory of the symmetric group of permutations in reproducing kernel Hilbert spaces, resulting in improved analysis of Monte Carlo methods for Shapley value estimation and new, computationally more efficient algorithms based on kernel herding and Bayesian quadrature. We also utilise reproducing …
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Stochastic Processes and Multi-Resolution Analysis: A Trigonometric Moment Problem Approach and an Analysis of the Expenditure Trends for Diabetic Patients
… theory of realization of rational functions, and reproducing kernel Hilbert spaces. A novel form of multiresolution analysis is formulated in the discrete case that is used to study some stochastic processes. Using the trigonometric moment problem, we associate with a vector-valued wide-sense …
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Converting to Optimization in Machine Learning: Perturb-and-MAP, Differential Privacy, and Program Synthesis
… into an optimization problem using the theory of Reproducing Kernel Hilbert Spaces. Finally, the fourth case study casts the challenging discrete search problem of program synthesis from input-output examples as a supervised learning task that can be efficiently tackled using gradient-based …
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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
… 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 framework for adaptive estimation of nonlinear systems using reproducing kernel Hilbert spaces. A nonlinear adaptive …
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Stochastic Optimization For Multi-Agent Statistical Learning And Control
… the design of stochastic optimization tools in reproducing kernel Hilbert spaces that yield optimal, accurate, and affordable complexity statistical learning for a multi-agent network. To obtain this result, we first explore the relative merits and drawbacks of different function class …
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Models and methods for computer simulations as a resource in plant breeding
… of supervised principal component analysis and reproducing kernel Hilbert spaces regression, with versions for traits with no/low epistasis, pRKHS-NE, to high epistasis, pRKHS-E. Compared to RR-BLUP, BayesA, BayesB, and RKHS, pRKHS delivers greater predictive ability, particularly when epistasis …
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Identification of Dendritic Processing in Spiking Neural Circuits
… processor is fully captured by one or more kernels, which provide a characterization of the signal processing that is consistent with the broader cable theory description of dendritic trees. We prove that the neural identification problem, stated in terms of identifying the kernels of the …
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Beurling-Lax Representations of Shift-Invariant Spaces, Zero-Pole Data Interpolation, and Dichotomous Transfer Function Realizations: Half-Plane/Continuous-Time Versions
… 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<sup>2</sup></i>. In the case where the pair <i>(M,M<sup>Ã </sup>)</i> are finite-dimensional perturbations of the Hardy space <i>H<sup>2</sup></i> and its …