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 15 of 15 for “"low-rank approximations"”.
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CONVERGENGE ANALYSIS ON SVD-BASED ALGORITHMS FOR TENSOR LOW RANK APPROXIMATIONS
… a few problems on tensor decompositions and approximations in real space. Among other things, we revisit the classical problem of finding the best rank-R CANDECOMP/PARAFAC(CP) approximation with diff erent cases R > 1 and R = 1 respectively. Unlike the rank-1 approximation is theoretically …
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Towards high-resolution magnetic resonance spectroscopic imaging: spatiotemporal denoising and echo-time selection
… addresses two issues, that is the problem of low SNR and the problem of TE selection. To address SNR limitations of MRSI, we first investigate a new scheme for denoising MRSI data, incorporating both an anatomically adapted spatial-smoothness constraint and an autoregressive spectral …
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Low-rank completion and recovery of correlation matrices
… the problem of matrix completion within a low-rank framework is of particular significance. This dissertation presents the methods of spectral completion and convex relaxation, which have been successfully applied to the particular problem of lowrank completion and recovery of valid …
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Hessian-based model reduction with applications to initial-condition inverse problems
… to those computed with high-fidelity models and low-rank approximations. Initial condition estimates are then formed with limited observational data to demonstrate that predictions of system state using reduced models are possible given relatively short measurement time windows. We show that …
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Efficient ML Inference via Matrix-Vector Approximations
… comparing quantization, sparsification, and low-rank approximations. Our analysis spans four perspectives: (1) how different methods trade off ℓ₂ error and compression, (2) how weight statistics and input distributions shape error, (3) how well ℓ₂ error predicts classification accuracy, and …
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Pushing the Limits of Active Data Selection with Gradient Matching
… variants using restricted-layer gradients, low-rank approximations, and gradient quantization. We also analyze GIST’s selection behavior, showing that it implicitly balances classes and repeatedly selects high-utility examples—two factors that enhance both robustness and learning efficiency. …
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Theoretical and practical aspects of linear and nonlinear model order reduction techniques
… iteration with alternate directions) and uses low-rank approximations of a system's gramians. This method is shown to be advantageous over the common approach of independently approximating the controllability and observability gramians, as such independent approximation methods can be …
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Bayesian Linear Modeling in High Dimensions: Advances in Hierarchical Modeling, Inference, and Evaluation
… fast, accurate inferences by leveraging (i) low rank approximations of data or (ii) parallelism across a certain class of Markov chain Monte Carlo algorithms. The final part of the thesis addresses the challenge of evaluation. Modern statistics provides an expansive toolkit for estimating …
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A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation
… matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem is formulated as a meta-optimization problem. Best values for parameters such as sensor location are obtained by optimizing a performance …
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On the low-dimensional structure of Bayesian inference
… a rigorous mathematical characterization of low-dimensional structures that enable efficient Bayesian inference in high-dimensional and continuous parameter spaces; and (2) exploit this characterization to devise new structure-exploiting and computationally efficient inference algorithms. Our …
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Complex data analytics via sparse, low-rank matrix approximation
… Specifically, we have achieved the following: 1) we develop Exemplar-based low-rank sparse Matrix Decomposition (EMD), a novel method for fast clustering large-scale data by incorporating low-rank approximations into matrix decomposition-based clustering; 2) we propose ECKF, a general …
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Algorithmic advances in learning from large dimensional matrices and scientific data
… spectrum related problems such as numerical rank estimation, matrix function trace estimation including log-determinants, Schatten norms, and other spectral sums. We also propose a new method which simultaneously estimates the dimension of the dominant subspace of covariance matrices and …
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Bayesian learning for high-dimensional nonlinear dynamical systems : methodologies, numerics and applications to fluid flows
… range of transient phenomena including fluid flows, heat transfer, biogeochemical dynamics, and other advection-diffusion-reaction-based transport processes. Even though such models often express the differential form of fundamental laws, they commonly contain uncertainty in their initial and …
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Matrix probing, skeleton decompositions, and sparse Fourier transform
… algorithms that help to solve matrices, compute low rank approximations and perform the Fast Fourier Transform. Matrix probing and its conditioning When a matrix A with n columns is known to be well approximated by a linear combination of basis matrices B1,... , Bp, we can apply A to a random …
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Applications of low-rank approximation: complex networks and inverse problems
The use of low-rank approximation is crucial when one is interested in solving problems of large dimension. In this case, the matrix with reduced rank can be obtained starting from the singular value decomposition considering only the largest components. This thesis describes how the use of the …