Sparsity
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Sparsity
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Author : Jaroslav Nešetřil
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-24
Sparsity written by Jaroslav Nešetřil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-24 with Mathematics categories.
This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.
Statistical Learning With Sparsity
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Author : Trevor Hastie
language : en
Publisher: CRC Press
Release Date : 2015-05-07
Statistical Learning With Sparsity written by Trevor Hastie and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-07 with Business & Economics categories.
Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl
Estimation And Testing Under Sparsity
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Author : Sara van de Geer
language : en
Publisher: Springer
Release Date : 2016-06-28
Estimation And Testing Under Sparsity written by Sara van de Geer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Mathematics categories.
Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.
Algorithms For Sparsity Constrained Optimization
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Author : Sohail Bahmani
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-07
Algorithms For Sparsity Constrained Optimization written by Sohail Bahmani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-07 with Technology & Engineering categories.
This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.
Sparsity And Its Applications
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Author : David J. Evans
language : en
Publisher: CUP Archive
Release Date : 1985-01-10
Sparsity And Its Applications written by David J. Evans and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-10 with Mathematics categories.
Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Study On Signal Detection And Recovery Methods With Joint Sparsity
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Author : Xueqian Wang
language : en
Publisher: Springer Nature
Release Date : 2023-09-30
Study On Signal Detection And Recovery Methods With Joint Sparsity written by Xueqian Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-30 with Technology & Engineering categories.
The task of signal detection is deciding whether signals of interest exist by using their observed data. Furthermore, signals are reconstructed or their key parameters are estimated from the observations in the task of signal recovery. Sparsity is a natural characteristic of most of signals in practice. The fact that multiple sparse signals share the common locations of dominant coefficients is called by joint sparsity. In the context of signal processing, joint sparsity model results in higher performance of signal detection and recovery. This book focuses on the task of detecting and reconstructing signals with joint sparsity. The main contents include key methods for detection of joint sparse signals and their corresponding theoretical performance analysis, and methods for joint sparse signal recovery and their application in the context of radar imaging.
Sparse Sensing And Sparsity Sensed In Multi Sensor Array Applications
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Author : Xiangrong Wang
language : en
Publisher: Springer Nature
Release Date :
Sparse Sensing And Sparsity Sensed In Multi Sensor Array Applications written by Xiangrong Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Analyticity And Sparsity In Uncertainty Quantification For Pdes With Gaussian Random Field Inputs
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Author : Dinh Dũng
language : en
Publisher: Springer Nature
Release Date : 2023-11-16
Analyticity And Sparsity In Uncertainty Quantification For Pdes With Gaussian Random Field Inputs written by Dinh Dũng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-16 with Mathematics categories.
The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.
Inverse Problems With Sparsity Constraints
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Author : Dennis Trede
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2010
Inverse Problems With Sparsity Constraints written by Dennis Trede and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization
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Author : Jens Flemming
language : en
Publisher: Springer
Release Date : 2018-09-08
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization written by Jens Flemming and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.