Rish / Grabarnik Sparse Modeling

Theory, Algorithms, and Applications
Erscheinungsjahr 2014
ISBN: 978-1-4398-2870-0
Verlag: Taylor & Francis
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.