Rish / Grabarnik Sparse Modeling

Theory, Algorithms, and Applications
Erscheinungsjahr 2014
ISBN: 978-1-4398-2870-0
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 253 Seiten

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.

Zielgruppe

Researchers and graduate students in machine learning, data mining, statistics, signal processing, computational biology, computational neuroscience, image processing, finance, and systems management.

Autoren/Hrsg.

Rish, Irina

Grabarnik, Genady

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

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/l8 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.