An Introduction to Matrix Concentration Inequalities
Copyright policy )An Introduction to Matrix Concentration Inequalities
Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.
- California Institute of Technology United States
FOS: Computer and information sciences, Data Structures and Algorithms, Information Theory, Machine Learning (stat.ML), Randomness in computation, Randomized algorithms in signal processing, Sparse representations, 510, Machine Learning, Dimensionality reduction, Kernel methods, Randomness in computation, Design and analysis of algorithms, Information theory and computer science, Information theory and statistics, Quantum information processing, Randomized algorithms in signal processing, Sparse representations, Statistical signal processing, Quantum information processing, FOS: Mathematics, Data Structures and Algorithms (cs.DS), Probability, Numerical Analysis, Information Theory (cs.IT), Information theory and statistics, Probability (math.PR), Kernel methods, 500, Numerical Analysis (math.NA), Information theory and computer science, Dimensionality reduction, Statistical signal processing, Design and analysis of algorithms, Primary: 60B20. Secondary: 60F10, 60G50, 60G42
FOS: Computer and information sciences, Data Structures and Algorithms, Information Theory, Machine Learning (stat.ML), Randomness in computation, Randomized algorithms in signal processing, Sparse representations, 510, Machine Learning, Dimensionality reduction, Kernel methods, Randomness in computation, Design and analysis of algorithms, Information theory and computer science, Information theory and statistics, Quantum information processing, Randomized algorithms in signal processing, Sparse representations, Statistical signal processing, Quantum information processing, FOS: Mathematics, Data Structures and Algorithms (cs.DS), Probability, Numerical Analysis, Information Theory (cs.IT), Information theory and statistics, Probability (math.PR), Kernel methods, 500, Numerical Analysis (math.NA), Information theory and computer science, Dimensionality reduction, Statistical signal processing, Design and analysis of algorithms, Primary: 60B20. Secondary: 60F10, 60G50, 60G42
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