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 18 of 18 for “"low-dimensional structure"”.
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On the low-dimensional structure of Bayesian inference
… characterizing the associated high-dimensional and non-Gaussian posterior distributions remains a challenging task. While the Bayesian formulation is quite general, essential features of a statistical model can bring additional structure to the Bayesian update. For instance, the …
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Robust learning with low-dimensional structure: theory,algorithms and applications
In this thesis, we study the robust learning of low-dimensional structures when there are uncertainties in the data. In particular, we consider two structures that are common in real problems: ?low-rank subspace model? that underlies matrix completion and Robust PCA, and ?union-of-subspace model? …
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Approximation of signals and functions in high dimensions with low dimensional structure: finite-valued sparse signals and generalized ridge functions
In this thesis, we consider the class of high dimensional functions which contains functions which are defined in high-dimensional spaces but are known to be constant along some unknown manifolds. We study different reconstruction problems under additional assumptions. In the papers [54, 41, 56] …
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Manifold aligned density estimation
… today is growing in both the scale and the dimensionality dramatically. It thus raises new challenges for some traditional machine learning tasks. This thesis is mainly concerned with manifold aligned density estimation problems. In particular, the work presented in this thesis includes …
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Gradient-based dimension reduction for Bayesian inverse problems and simulation-based inference
… inference: in both settings, the high dimensionality of model parameters and/or data can render naïve posterior exploration intractable. We address this challenge by developing gradient-based methods that discover and exploit several notions of low-dimensional structure in inference, …
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The Geometry and Dynamics of Context
… semantic context spaces exhibit a two-scaled and low dimensional structure. Finally, we use Takens' delay embedding theorem to show that the low dimension structure is directly related to the dynamics of how people move from one context to another. We discuss these results in the light of the …
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Exploring the dimensionality of speech using manifold learning and dimensionality reduction methods
… have indicated that speech data has inherent low-dimensional structure and that it may be possible to efficiently represent speech using only a small number of parameters. This view is motivated by the fact that articulatory movement is limited by physiological constraints and thus the speech …
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Harnessing Sparse and Low-Dimensional Structures for Robust Clustering of Imagery Data
… show that, by properly harnessing the intrinsic low-dimensional structure of the data, these kinds of practical problems can be dealt with in a uniform fashion. In particular, we propose two robust segmentation algorithms: an algebraic method for data from multiple quadratic manifolds, and an …
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Integrating Feature and Graph Learning with Factorization Models for Low-Rank Data Representation
Representing and handling high-dimensional data has been increasingly ubiquitous in many real world-applications, such as computer vision, machine learning, and data mining. High-dimensional data usually have intrinsic low-dimensional structures, which are suitable for subsequent data processing. …
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Spectral Regression: A Regression Framework for Efficient Regularized Subspace Learning
… have recently emerged as a powerful tool for dimensionality reduction and manifold learning. These methods use information contained in the eigenvectors of a data affinity (\ie, item-item similarity) matrix to reveal the low dimensional structure in the high dimensional data. The most popular …
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Learning from partially labeled data
… walk representation that exploits clusters and low-dimensional structure in the data in a robust and probabilistic manner. Thirdly, we introduce information regularization, a non-parametric technique based on minimizing information about labels over regions covering the domain. Information …
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Efficient Learning and Inference for High-dimensional Lagrangian Systems
… challenges and opportunities owing to the unique structure associated with such systems. Many physical systems of practical interest in engineering are high-dimensional, which prohibits the application of standard learning methods to such problems. This first part of this work proposes therefore …
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First-principles structure prediction of extreme nanowires
Low-dimensional systems are an important and intensely studied area of condensed matter physics. When a material is forced to adopt a low-dimensional structure, its behaviour is often dramatically different to that of the bulk phase. It is vital to predict the structures of low-dimensional systems …
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Computational modeling of intrinsic dissipation in nano-structure
… modes, is provided. We, then, study damping is low dimensional structure. We first consider the case of two dimensional graphene sheet and under in-plane stretching. We show that the coupling between the in-plane and the out-of-plane motions plays an important role in the loss of mechanical …
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Semiparametric Methods for Two Problems in Causal Inference using Machine Learning
… forms the basis for constraint-based causal structure learning, but it has been shown that any test which controls size for all null distributions has no power against any alternative. For this reason it is necessary to restrict the null space, and it is convenient to do so in terms of the …