Random Matrix Methods For Machine Learning
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Random Matrix Methods For Machine Learning
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Author : Romain Couillet
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-21
Random Matrix Methods For Machine Learning written by Romain Couillet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-21 with Computers categories.
This unified random matrix approach to large-dimensional machine learning covers applications from power detection to deep neural networks.
Random Matrix Methods For Machine Learning
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Author : Romain Couillet
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-21
Random Matrix Methods For Machine Learning written by Romain Couillet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-21 with Computers categories.
This book presents a unified theory of random matrices for applications in machine learning, offering a large-dimensional data vision that exploits concentration and universality phenomena. This enables a precise understanding, and possible improvements, of the core mechanisms at play in real-world machine learning algorithms. The book opens with a thorough introduction to the theoretical basics of random matrices, which serves as a support to a wide scope of applications ranging from SVMs, through semi-supervised learning, unsupervised spectral clustering, and graph methods, to neural networks and deep learning. For each application, the authors discuss small- versus large-dimensional intuitions of the problem, followed by a systematic random matrix analysis of the resulting performance and possible improvements. All concepts, applications, and variations are illustrated numerically on synthetic as well as real-world data, with MATLAB and Python code provided on the accompanying website.
An Introduction To Matrix Concentration Inequalities
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Author : Joel Tropp
language : en
Publisher:
Release Date : 2015-05-27
An Introduction To Matrix Concentration Inequalities written by Joel Tropp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-27 with Computers categories.
Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore 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.
A First Course In Random Matrix Theory
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Author : Marc Potters
language : en
Publisher: Cambridge University Press
Release Date : 2020-12-03
A First Course In Random Matrix Theory written by Marc Potters and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-03 with Computers categories.
An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Data Analytics And Ai For Quantitative Risk Assessment And Financial Computation
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Author : Galety, Mohammad Gouse
language : en
Publisher: IGI Global
Release Date : 2024-11-29
Data Analytics And Ai For Quantitative Risk Assessment And Financial Computation written by Galety, Mohammad Gouse and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-29 with Business & Economics categories.
In today's fast-paced financial landscape, professionals face an uphill battle in effectively integrating data analytics and artificial intelligence (AI) into quantitative risk assessment and financial computation. The constantly increasing volume, velocity, and variety of data generated by digital transactions, market exchanges, and social media platforms offer unparalleled financial analysis and decision-making opportunities. However, professionals need sophisticated AI technologies and data analytics methodologies to harness this data for predictive modeling, risk assessment, and algorithmic trading. Navigating this complex terrain can be daunting, and a comprehensive guide that bridges theory and practice is necessary. Data Analytics and AI for Quantitative Risk Assessment and Financial Computation is an all-encompassing reference for finance professionals, risk managers, data scientists, and students seeking to leverage the transformative power of AI and data analytics in finance. The book encapsulates this integration's theoretical underpinnings, practical applications, challenges, and future directions, empowering readers to enhance their analytical capabilities, make informed decisions, and stay ahead in the competitive financial landscape.
Random Matrix Methods For Wireless Communications
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Author : Romain Couillet
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29
Random Matrix Methods For Wireless Communications written by Romain Couillet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Technology & Engineering categories.
Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.
High Dimensional Covariance Matrix Estimation
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Author : Aygul Zagidullina
language : en
Publisher: Springer Nature
Release Date : 2021-10-29
High Dimensional Covariance Matrix Estimation written by Aygul Zagidullina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-29 with Business & Economics categories.
This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.
Matrix Methods In Data Mining And Pattern Recognition
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Author : Lars Elden
language : en
Publisher: SIAM
Release Date : 2007-07-12
Matrix Methods In Data Mining And Pattern Recognition written by Lars Elden and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Computers categories.
Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.
Determinantal Point Processes For Machine Learning
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Author : Alex Kulesza
language : en
Publisher: Now Pub
Release Date : 2012-11-29
Determinantal Point Processes For Machine Learning written by Alex Kulesza and has been published by Now Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-29 with Computers categories.
This monograph provides a comprehensible introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community.