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 12 of 12 for “"Low-Rank Matrices"”.
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Applications of low-rank matrix recovery methods in computer vision
… In this thesis, we harness recent advances in low-rank matrix recovery via convex optimization techniques to solve real problems in computer vision. This thesis also provides some theoretical analysis that extends existing results to new observation models. Low-rank matrix approximations are a …
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Matrix completion algorithms with applications in biomedicine, e-commerce and social science
… matrix completion algorithms work well for low rank matrices. Such matrices find many applications in recommender systems and social network analysis. On the other hand, biological networks often yield high rank matrices. For example, the adjacency matrix representing interactions between …
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Low-rank completion and recovery of correlation matrices
… for sparsely populated and partially observed 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 …
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Compressed absorbing boundary conditions for the Helmholtz equation
… condition, with a complexity that grows slowly (often, logarithmically) in the frequency parameter. We then obtain a fast (nearly linear in the dimension of the matrix) algorithm for the application of the absorbing boundary condition using partitioned low rank matrices. The result, modulo …
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Methods and Theory for Nonparametric Inference In High-dimensional Settings
… have theoretically optimal estimators that allow incorporation of flexible machine learning techniques and yield wald-type confidence intervals. In the second project, we propose a nonparametric parameter to measure the linear association between the outcome and explanatory variables. This …
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Flows, Submodularity, Sparsity, and Beyond: Continuous Optimization Insights for Discrete Problems
… first runtime improvement for the minimum cost flow problem in more than 10 years, as well as faster algorithms for problems like negative-weight shortest path and minimum cost perfect matching. In the second part of the thesis, we investigate efficient optimization algorithms for problems …
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Learning from Commerce Data: from Theory to Practice
… nearly complete solution to this problem that allows for the rate-optimal recovery of treatment effects. Our work generalizes the outcome model of the difference-in-difference paradigm and expands the applicability of the synthetic-control paradigm. In doing so, we provide a novel de-biasing …
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Algorithms for Large-scale Data Analytics and Applications to the COVID-19 Pandemic
… impact, we need both scalable algorithms that allow us to extract insights from an ever-increasing amount of data, and also important applications to apply our insights to the world. In this thesis, we demonstrate both sides of the coin. In the first part of the thesis, we focus on building …
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Time series estimation in a spiked signal regime
… problem and the signal model that it follows. It then presents a survey of both standard and the state-of-the-art techniques in addition to an analysis of TSCC. These methods are used to solve the problem of estimating the state of dynamical system, with partial, noisy observations. …
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Convex optimization methods for graphs and statistical modeling
… learning. The specific contributions are as follows: -- We propose a convex optimization method for decomposing the sum of a sparse matrix and a low-rank matrix into the individual components. Based on new rank-sparsity uncertainty principles, we give conditions under which the convex program …
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Geometric optimization algorithms for linear regression on fixed-rank matrices
… search space of main interest will be the set of low-rank matrices. Learning a low-rank matrix is a typical approach to cope with high-dimensional problems. The low-rank constraint is expected to force the learning algorithm to capture a limited number of dominant factors that mostly influence the …
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Fast MRI with sparse sampling: models, algorithms, and applications
… a novel constrained image model, the joint low-rank and sparse model, to enable dynamic image reconstruction from highly undersampled (k, t)-space data. Low-rank and sparse models are two low-dimensional signal structures, each of which parsimoniously models dynamic imaging data. Here, we …