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Discover New Methods for Dealing with High-Dimensional Data A 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 underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of ℓ1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

Discover New Methods for Dealing with High-Dimensional Data A 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 underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of ℓ1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

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This book provides practical approaches to the efficient use of sparsity--a key to solving large problems in many fields, including computational science and engineering, where mathematical models give rise to very large systems of linear equations. The emphasis is on practicality, with conclusions based on concrete experience. Non-numeric computing techniques have been included as well as frequent illustrations in an attempt to bridge the gap between the written word and the working computer code. Exercises have been included to strengthen understanding of the material as well as to extend it for students and researchers in engineering, mathematics, and computer science.

This book presents the state of the art in sparse and multiscale image and signal processing, covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Recent concepts of sparsity and morphological diversity are described and exploited for various problems such as denoising, inverse problem regularization, sparse signal decomposition, blind source separation, and compressed sensing. This book weds theory and practice in examining applications in areas such as astronomy, biology, physics, digital media, and forensics. A final chapter explores a paradigm shift in signal processing, showing that previous limits to information sampling and extraction can be overcome in very significant ways. Matlab and IDL code accompany these methods and applications to reproduce the experiments and illustrate the reasoning and methodology of the research available for download at the associated Web site.

Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.

Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.

One of the ironies of our time is the sparsity of useful analytic tools for understanding change and development within technology itself. For all the diatribes about the disastrous effects of technology on modern life, for all the equally uncritical paeans to technology as the panacea for human ills, the vociferous pro- and anti-technology movements have failed to illuminate the nature of technology. On a more scholarly level, in the midst of claims by Marxists and non-Marxists alike about the technological underpinnings of the major social and economic changes of the last couple of centuries, and despite advice given to government and industry about managing science and technology by a small army of consultants and policy analysts, technology itself remains locked inside an impenetrable black box, a deus ex machina to be invoked when all other explanations of puzzling social and economic pheoomena fail. The discipline that has probably done most to penetrate that black box in recent years by studying the 1 internal development of technology is history. Historians of technology and certain economic historians have carried out careful and detailed studies on the genesis and impact of technological innovations, and the structu-re of the social systems associated with those innovations. Within the past few decades tentative consensus about the periodization and the major traditions within the history of technology has begun to emerge, at least as far as Britain and America in the eighteenth and nineteenth century are concerned.

Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.

Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.