Statistical Learning with Sparsity: The Lasso and Generalizations

Trevor Hastie, Robert Tibshirani, Martin Wainwright

May 7, 2015 by Chapman and Hall/CRC
Reference - 367 Pages - 99 Color Illustrations
ISBN 9781498712163 - CAT# K25103
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

USD$98.95

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Features

  • Explores the many advantages of sparsity
  • Shows how to effectively estimate parameters using the lasso and related methods
  • Covers both supervised and unsupervised learning problems
  • Presents first-order numerical methods for solving large-scale problems
  • Illustrates how compressed sensing is a powerful tool for image analysis

Summary

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 1 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.