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Showing 1 to 10 of 10 for “"Matrix completion problem"”.
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Ultraconnected and Critical Graphs
… graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is preserved by Cartesian products. We completely characterize when adding a vertex to an ultraconnected graph …
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Low rank matrix completion
We consider the problem of recovering a low rank matrix given a sampling of its entries. Such problems are of considerable interest in a diverse set of fields including control, system identification, statistics and signal processing. Although the general low rank matrix completion problem is …
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Algorithms for Large-scale Data Analytics and Applications to the COVID-19 Pandemic
… 1, we consider a novel reformulation of the matrix completion problem and developed a projected stochastic gradient descent method, fastImpute, to solve matrix completion 20x faster than state-of-the-art methods while providing optimality guarantees. In Chapter 2, we introduce the …
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Learning to Predict End-to-End Network Performance
… There are three main contributions. First, the problem of network performance prediction is formulated as a matrix completion problem where the matrix contains performance measures between network nodes with some of them known and the others unknown and thus to be filled. This new formulation is …
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Efficient and guaranteed algorithms for sparse inverse problems
… algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common sensing matrix. In a favorable situation, the unknown matrix, which consists of the …
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Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization
… their application to Newton-type optimization. A matrix is called triadic if it has at most two nonzero off-diagonal elements in each column. Tridiagonal matrices are a special case of these. We prove that the triadic structure is preserved in the Cholesky-related factorizations We analyze its …
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Optimism and Robustness: Learning From Structured and Semi-Random Inputs
… the two. In this thesis, we study several problems and their algorithms under appropriate beyond worst-case models, aiming to provide more realistic and practically relevant performance guarantees. In the first part of this thesis, we focus on improving algorithm performance on …
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Joint Equalization and Decoding via Convex Optimization
… of new solutions for decoding and inference problems based on convex optimization methods. Th first part considers the joint detection and decoding problem for low-density parity-check (LDPC) codes on finite-state channels (FSCs). Hard-disk drives (or magnetic recording systems), where the …
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Voltooiingsprobleme vir klasse van reële simmetriese matrikse wat geslote konvekse keëls vorm
The goal of any completion problem in matrix theory is to determine when a partial matrix can be completed to a matrix that conforms to certain conditions, where a partial matrix is a matrix with some unspecified entries. We consider the completion problem of a few classes of symmetric matrices …
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Advances in Sparse and Low Rank Matrix Optimization for Machine Learning Applications
Numerous fundamental problems in operations research, machine learning, and statistics exhibit natural formulations as cardinality or rank constrained optimization problems. Sparse solutions are desirable for their interpretability and storage benefits. Moreover, in the machine learning setting, …