Random Matrix Methods For Machine Learning

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Random Matrix Methods for Machine Learning

Author : Romain Couillet
Publisher : Cambridge University Press
ISBN 13 : 1009301896
Total Pages : 412 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Random Matrix Methods for Machine Learning by : Romain Couillet

Download or read book Random Matrix Methods for Machine Learning written by Romain Couillet and published by Cambridge University Press. This book was released on 2022-07-21 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A First Course in Random Matrix Theory

Author : Marc Potters
Publisher : Cambridge University Press
ISBN 13 : 1108488080
Total Pages : 371 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis A First Course in Random Matrix Theory by : Marc Potters

Download or read book A First Course in Random Matrix Theory written by Marc Potters and published by Cambridge University Press. This book was released on 2020-12-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.

An Introduction to Matrix Concentration Inequalities

Author : Joel Tropp
Publisher :
ISBN 13 : 9781601988386
Total Pages : 256 pages
Book Rating : 4.9/5 (883 download)

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Book Synopsis An Introduction to Matrix Concentration Inequalities by : Joel Tropp

Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp and published by . This book was released on 2015-05-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Methods in Data Mining and Pattern Recognition

Author : Lars Elden
Publisher : SIAM
ISBN 13 : 0898716268
Total Pages : 226 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Matrix Methods in Data Mining and Pattern Recognition by : Lars Elden

Download or read book Matrix Methods in Data Mining and Pattern Recognition written by Lars Elden and published by SIAM. This book was released on 2007-07-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Algorithms

Author : Ravindran Kannan
Publisher : Now Publishers Inc
ISBN 13 : 1601982747
Total Pages : 153 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Spectral Algorithms by : Ravindran Kannan

Download or read book Spectral Algorithms written by Ravindran Kannan and published by Now Publishers Inc. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

Asymptotic Statistics

Author : A. W. van der Vaart
Publisher : Cambridge University Press
ISBN 13 : 9780521784504
Total Pages : 470 pages
Book Rating : 4.7/5 (845 download)

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Book Synopsis Asymptotic Statistics by : A. W. van der Vaart

Download or read book Asymptotic Statistics written by A. W. van der Vaart and published by Cambridge University Press. This book was released on 2000-06-19 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.

Algorithmic Aspects of Machine Learning

Author : Ankur Moitra
Publisher : Cambridge University Press
ISBN 13 : 1107184584
Total Pages : 161 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Algorithmic Aspects of Machine Learning by : Ankur Moitra

Download or read book Algorithmic Aspects of Machine Learning written by Ankur Moitra and published by Cambridge University Press. This book was released on 2018-09-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.

Introduction to Random Matrices

Author : Giacomo Livan
Publisher : Springer
ISBN 13 : 3319708856
Total Pages : 122 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Introduction to Random Matrices by : Giacomo Livan

Download or read book Introduction to Random Matrices written by Giacomo Livan and published by Springer. This book was released on 2018-01-16 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.

High-Dimensional Covariance Matrix Estimation

Author : Aygul Zagidullina
Publisher : Springer Nature
ISBN 13 : 3030800652
Total Pages : 123 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis High-Dimensional Covariance Matrix Estimation by : Aygul Zagidullina

Download or read book High-Dimensional Covariance Matrix Estimation written by Aygul Zagidullina and published by Springer Nature. This book was released on 2021-10-29 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interpretable Machine Learning

Author : Christoph Molnar
Publisher : Lulu.com
ISBN 13 : 0244768528
Total Pages : 320 pages
Book Rating : 4.2/5 (447 download)

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Book Synopsis Interpretable Machine Learning by : Christoph Molnar

Download or read book Interpretable Machine Learning written by Christoph Molnar and published by Lulu.com. This book was released on 2020 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.

Hands-On Machine Learning with R

Author : Brad Boehmke
Publisher : CRC Press
ISBN 13 : 1000730433
Total Pages : 373 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Hands-On Machine Learning with R by : Brad Boehmke

Download or read book Hands-On Machine Learning with R written by Brad Boehmke and published by CRC Press. This book was released on 2019-11-07 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hands-on Machine Learning with R provides a practical and applied approach to learning and developing intuition into today’s most popular machine learning methods. This book serves as a practitioner’s guide to the machine learning process and is meant to help the reader learn to apply the machine learning stack within R, which includes using various R packages such as glmnet, h2o, ranger, xgboost, keras, and others to effectively model and gain insight from their data. The book favors a hands-on approach, providing an intuitive understanding of machine learning concepts through concrete examples and just a little bit of theory. Throughout this book, the reader will be exposed to the entire machine learning process including feature engineering, resampling, hyperparameter tuning, model evaluation, and interpretation. The reader will be exposed to powerful algorithms such as regularized regression, random forests, gradient boosting machines, deep learning, generalized low rank models, and more! By favoring a hands-on approach and using real word data, the reader will gain an intuitive understanding of the architectures and engines that drive these algorithms and packages, understand when and how to tune the various hyperparameters, and be able to interpret model results. By the end of this book, the reader should have a firm grasp of R’s machine learning stack and be able to implement a systematic approach for producing high quality modeling results. Features: · Offers a practical and applied introduction to the most popular machine learning methods. · Topics covered include feature engineering, resampling, deep learning and more. · Uses a hands-on approach and real world data.

The Random Matrix Theory of the Classical Compact Groups

Author : Elizabeth S. Meckes
Publisher : Cambridge University Press
ISBN 13 : 1108317995
Total Pages : 225 pages
Book Rating : 4.1/5 (83 download)

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Book Synopsis The Random Matrix Theory of the Classical Compact Groups by : Elizabeth S. Meckes

Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.

An Introduction to Wishart Matrix Moments

Author : Adrian N. Bishop
Publisher : Foundations and Trends (R) in Machine Learning
ISBN 13 : 9781680835069
Total Pages : 134 pages
Book Rating : 4.8/5 (35 download)

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Book Synopsis An Introduction to Wishart Matrix Moments by : Adrian N. Bishop

Download or read book An Introduction to Wishart Matrix Moments written by Adrian N. Bishop and published by Foundations and Trends (R) in Machine Learning. This book was released on 2018-12-07 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written in lecture note style, provides a comprehensive and self-contained introduction to the analysis of Wishart matrix moments. It can act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition of Wishart matrix moments.

Graph Representation Learning

Author : William L. William L. Hamilton
Publisher : Springer Nature
ISBN 13 : 3031015886
Total Pages : 141 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Graph Representation Learning by : William L. William L. Hamilton

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Machine Learning with Python Cookbook

Author : Chris Albon
Publisher : "O'Reilly Media, Inc."
ISBN 13 : 1491989335
Total Pages : 285 pages
Book Rating : 4.4/5 (919 download)

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Book Synopsis Machine Learning with Python Cookbook by : Chris Albon

Download or read book Machine Learning with Python Cookbook written by Chris Albon and published by "O'Reilly Media, Inc.". This book was released on 2018-03-09 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide provides nearly 200 self-contained recipes to help you solve machine learning challenges you may encounter in your daily work. If you’re comfortable with Python and its libraries, including pandas and scikit-learn, you’ll be able to address specific problems such as loading data, handling text or numerical data, model selection, and dimensionality reduction and many other topics. Each recipe includes code that you can copy and paste into a toy dataset to ensure that it actually works. From there, you can insert, combine, or adapt the code to help construct your application. Recipes also include a discussion that explains the solution and provides meaningful context. This cookbook takes you beyond theory and concepts by providing the nuts and bolts you need to construct working machine learning applications. You’ll find recipes for: Vectors, matrices, and arrays Handling numerical and categorical data, text, images, and dates and times Dimensionality reduction using feature extraction or feature selection Model evaluation and selection Linear and logical regression, trees and forests, and k-nearest neighbors Support vector machines (SVM), naïve Bayes, clustering, and neural networks Saving and loading trained models

Determinantal Point Processes for Machine Learning

Author : Alex Kulesza
Publisher : Now Pub
ISBN 13 : 9781601986283
Total Pages : 178 pages
Book Rating : 4.9/5 (862 download)

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Book Synopsis Determinantal Point Processes for Machine Learning by : Alex Kulesza

Download or read book Determinantal Point Processes for Machine Learning written by Alex Kulesza and published by Now Pub. This book was released on 2012-11-29 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensible introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community.

Foundations of Machine Learning, second edition

Author : Mehryar Mohri
Publisher : MIT Press
ISBN 13 : 0262351366
Total Pages : 505 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Foundations of Machine Learning, second edition by : Mehryar Mohri

Download or read book Foundations of Machine Learning, second edition written by Mehryar Mohri and published by MIT Press. This book was released on 2018-12-25 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of a graduate-level machine learning textbook that focuses on the analysis and theory of algorithms. This book is a general introduction to machine learning that can serve as a textbook for graduate students and a reference for researchers. It covers fundamental modern topics in machine learning while providing the theoretical basis and conceptual tools needed for the discussion and justification of algorithms. It also describes several key aspects of the application of these algorithms. The authors aim to present novel theoretical tools and concepts while giving concise proofs even for relatively advanced topics. Foundations of Machine Learning is unique in its focus on the analysis and theory of algorithms. The first four chapters lay the theoretical foundation for what follows; subsequent chapters are mostly self-contained. Topics covered include the Probably Approximately Correct (PAC) learning framework; generalization bounds based on Rademacher complexity and VC-dimension; Support Vector Machines (SVMs); kernel methods; boosting; on-line learning; multi-class classification; ranking; regression; algorithmic stability; dimensionality reduction; learning automata and languages; and reinforcement learning. Each chapter ends with a set of exercises. Appendixes provide additional material including concise probability review. This second edition offers three new chapters, on model selection, maximum entropy models, and conditional entropy models. New material in the appendixes includes a major section on Fenchel duality, expanded coverage of concentration inequalities, and an entirely new entry on information theory. More than half of the exercises are new to this edition.