Sparse Modeling: Theory, Algorithms, and Applications

Sparse modeling is an important issue in many applications of machine learning and statistics where the main objective is discovering predictive patterns in data to enhance understanding of underlying physical, biological, and other natural processes. This book surveys recent advances in statistics, machine learning, and signal processing related to sparse modeling. It provides a comprehensive introduction to recent developments in sparse modeling research, including the theoretical basis for sparse modeling, algorithmic approaches, and applications to computational biology, medicine, neuroscience, graphical model selection, and compressed sensing.

By:   Irina Rish (IBM Yorktown Heights New York USA), Genady Grabarnik (St. John's University, Queens, NY)
Imprint:   CRC Press Inc
Country of Publication:   United States
Dimensions:   Height: 235mm,  Width: 156mm,  Spine: 18mm
Weight:   522g
ISBN:   9781439828694
ISBN 10:   1439828695
Pages:   253
Publication Date:   December 2014
Audience:   College/higher education ,  College/higher education ,  Primary ,  Primary
Format:   Hardback
Publisher's Status:   Active

Introduction Motivating Examples Sparse Recovery in a Nutshell Statistical Learning versus Compressed Sensing Sparse Recovery: Problem Formulations Noiseless Sparse Recovery Approximations Convexity: Brief Review Relaxations of (P0) Problem The Effect of lq-Regularizer on Solution Sparsity l1-norm Minimization as Linear Programming Noisy Sparse Recovery A Statistical View of Sparse Recovery Beyond LASSO: Other Loss Functions and Regularizers Theoretical Results (Deterministic Part) The Sampling Theorem Surprising Empirical Results Signal Recovery from Incomplete Frequency Information Mutual Coherence Spark and Uniqueness of (P0) Solution Null Space Property and Uniqueness of (P1) Solution Restricted Isometry Property (RIP) Square Root Bottleneck for the Worst-Case Exact Recovery Exact Recovery Based on RIP Theoretical Results (Probabilistic Part) When Does RIP Hold? Johnson-Lindenstrauss Lemma and RIP for Subgaussian Random Matrices Random Matrices Satisfying RIP RIP for Matrices with Independent Bounded Rows and Matrices with Random Rows of Fourier Transform Algorithms for Sparse Recovery Problems Univariate Thresholding is Optimal for Orthogonal Designs Algorithms for l0-norm Minimization Algorithms for l1-norm Minimization (LASSO) Beyond LASSO: Structured Sparsity The Elastic Net Fused LASSO Group LASSO: l1/l2 Penalty Simultaneous LASSO: l1/lâ Penalty Generalizations Applications Beyond LASSO: Other Loss Functions Sparse Recovery from Noisy Observations Exponential Family, GLMs, and Bregman Divergences Sparse Recovery with GLM Regression Sparse Graphical Models Background Markov Networks Learning and Inference in Markov Networks Learning Sparse Gaussian MRFs Sparse Matrix Factorization: Dictionary Learning and Beyond Dictionary Learning Sparse PCA Sparse NMF for Blind Source Separation Epilogue Appendix: Mathematical Background Bibliography Index A Summary and Bibliographical Notes appear at the end of each chapter.

... an excellent introductory book for branching off into aspects of sparse modeling; it is also good for advanced students since it is contains an appendix with some of the mathematical background needed to learn from this book, including topics such as eigentheory, discrete Fourier transform, and subgaussian random variables. I very much recommend this book for researchers and students alike. -Computing Reviews, May 2015 A comprehensive, clear, and well-articulated book on sparse modeling. This book will stand as a prime reference to the research community for many years to come. -Ricardo Vilalta, Department of Computer Science, University of Houston This book provides a modern introduction to sparse methods for machine learning and signal processing, with a comprehensive treatment of both theory and algorithms. Sparse Modeling is an ideal book for a first-year graduate course. -Francis Bach, INRIA - Ecole Normale Superieure, Paris