Mathematical Theories of Machine Learning - Theory and Applications

Mathematical Theories of Machine Learning - Theory and Applications

Author: Bin Shi

Publisher: Springer

Published: 2019-06-12

Total Pages: 133

ISBN-13: 3030170764

DOWNLOAD EBOOK

This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.


Book Synopsis Mathematical Theories of Machine Learning - Theory and Applications by : Bin Shi

Download or read book Mathematical Theories of Machine Learning - Theory and Applications written by Bin Shi and published by Springer. This book was released on 2019-06-12 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection.

Machine Learning

Machine Learning

Author: Seyedeh Leili Mirtaheri

Publisher: CRC Press

Published: 2022

Total Pages: 0

ISBN-13: 9781000737721

DOWNLOAD EBOOK

The book reviews core concepts of machine learning (ML) while focusing on modern applications. It is aimed at those who want to advance their understanding of ML by providing technical and practical insights. It does not use complicated mathematics to explain how to benefit from ML algorithms. Unlike the existing literature, this work provides the core concepts with emphasis on fresh ideas and real application scenarios. It starts with the basic concepts of ML and extends the concepts to the different deep learning algorithms. The book provides an introduction and main elements of evaluation tools with Python and walks you through the recent applications of ML in self-driving cars, cognitive decision making, communication networks, security, and signal processing. The concept of generative networks is also presented and focuses on GANs as a tool to improve the performance of existing algorithms. In summary, this book provides a comprehensive technological path from fundamental theories to the categorization of existing algorithms, covers state-of-the-art, practical evaluation tools and methods to empower you to use synthetic data to improve the performance of applications.


Book Synopsis Machine Learning by : Seyedeh Leili Mirtaheri

Download or read book Machine Learning written by Seyedeh Leili Mirtaheri and published by CRC Press. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews core concepts of machine learning (ML) while focusing on modern applications. It is aimed at those who want to advance their understanding of ML by providing technical and practical insights. It does not use complicated mathematics to explain how to benefit from ML algorithms. Unlike the existing literature, this work provides the core concepts with emphasis on fresh ideas and real application scenarios. It starts with the basic concepts of ML and extends the concepts to the different deep learning algorithms. The book provides an introduction and main elements of evaluation tools with Python and walks you through the recent applications of ML in self-driving cars, cognitive decision making, communication networks, security, and signal processing. The concept of generative networks is also presented and focuses on GANs as a tool to improve the performance of existing algorithms. In summary, this book provides a comprehensive technological path from fundamental theories to the categorization of existing algorithms, covers state-of-the-art, practical evaluation tools and methods to empower you to use synthetic data to improve the performance of applications.

Innovations in Machine Learning

Innovations in Machine Learning

Author: Dawn E. Holmes

Publisher: Springer

Published: 2006-02-28

Total Pages: 285

ISBN-13: 3540334866

DOWNLOAD EBOOK

Machine learning is currently one of the most rapidly growing areas of research in computer science. In compiling this volume we have brought together contributions from some of the most prestigious researchers in this field. This book covers the three main learning systems; symbolic learning, neural networks and genetic algorithms as well as providing a tutorial on learning casual influences. Each of the nine chapters is self-contained. Both theoreticians and application scientists/engineers in the broad area of artificial intelligence will find this volume valuable. It also provides a useful sourcebook for Postgraduate since it shows the direction of current research.


Book Synopsis Innovations in Machine Learning by : Dawn E. Holmes

Download or read book Innovations in Machine Learning written by Dawn E. Holmes and published by Springer. This book was released on 2006-02-28 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning is currently one of the most rapidly growing areas of research in computer science. In compiling this volume we have brought together contributions from some of the most prestigious researchers in this field. This book covers the three main learning systems; symbolic learning, neural networks and genetic algorithms as well as providing a tutorial on learning casual influences. Each of the nine chapters is self-contained. Both theoreticians and application scientists/engineers in the broad area of artificial intelligence will find this volume valuable. It also provides a useful sourcebook for Postgraduate since it shows the direction of current research.

Theory of Information and its Value

Theory of Information and its Value

Author: Ruslan L. Stratonovich

Publisher: Springer Nature

Published: 2020-01-14

Total Pages: 419

ISBN-13: 3030228339

DOWNLOAD EBOOK

This English version of Ruslan L. Stratonovich’s Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.


Book Synopsis Theory of Information and its Value by : Ruslan L. Stratonovich

Download or read book Theory of Information and its Value written by Ruslan L. Stratonovich and published by Springer Nature. This book was released on 2020-01-14 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English version of Ruslan L. Stratonovich’s Theory of Information (1975) builds on theory and provides methods, techniques, and concepts toward utilizing critical applications. Unifying theories of information, optimization, and statistical physics, the value of information theory has gained recognition in data science, machine learning, and artificial intelligence. With the emergence of a data-driven economy, progress in machine learning, artificial intelligence algorithms, and increased computational resources, the need for comprehending information is essential. This book is even more relevant today than when it was first published in 1975. It extends the classic work of R.L. Stratonovich, one of the original developers of the symmetrized version of stochastic calculus and filtering theory, to name just two topics. Each chapter begins with basic, fundamental ideas, supported by clear examples; the material then advances to great detail and depth. The reader is not required to be familiar with the more difficult and specific material. Rather, the treasure trove of examples of stochastic processes and problems makes this book accessible to a wide readership of researchers, postgraduates, and undergraduate students in mathematics, engineering, physics and computer science who are specializing in information theory, data analysis, or machine learning.

Fundamental Mathematical Concepts for Machine Learning in Science

Fundamental Mathematical Concepts for Machine Learning in Science

Author: Umberto Michelucci

Publisher: Springer

Published: 2024-05-17

Total Pages: 0

ISBN-13: 9783031564307

DOWNLOAD EBOOK

This book is for individuals with a scientific background who aspire to apply machine learning within various natural science disciplines—such as physics, chemistry, biology, medicine, psychology and many more. It elucidates core mathematical concepts in an accessible and straightforward manner, maintaining rigorous mathematical integrity. For readers more versed in mathematics, the book includes advanced sections that are not prerequisites for the initial reading. It ensures concepts are clearly defined and theorems are proven where it's pertinent. Machine learning transcends the mere implementation and training of algorithms; it encompasses the broader challenges of constructing robust datasets, model validation, addressing imbalanced datasets, and fine-tuning hyperparameters. These topics are thoroughly examined within the text, along with the theoretical foundations underlying these methods. Rather than concentrating on particular algorithms this book focuses on the comprehensive concepts and theories essential for their application. It stands as an indispensable resource for any scientist keen on integrating machine learning effectively into their research. Numerous texts delve into the technical execution of machine learning algorithms, often overlooking the foundational concepts vital for fully grasping these methods. This leads to a gap in using these algorithms effectively across diverse disciplines. For instance, a firm grasp of calculus is imperative to comprehend the training processes of algorithms and neural networks, while linear algebra is essential for the application and efficient training of various algorithms, including neural networks. Absent a solid mathematical base, machine learning applications may be, at best, cursory, or at worst, fundamentally flawed. This book lays the foundation for a comprehensive understanding of machine learning algorithms and approaches.


Book Synopsis Fundamental Mathematical Concepts for Machine Learning in Science by : Umberto Michelucci

Download or read book Fundamental Mathematical Concepts for Machine Learning in Science written by Umberto Michelucci and published by Springer. This book was released on 2024-05-17 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for individuals with a scientific background who aspire to apply machine learning within various natural science disciplines—such as physics, chemistry, biology, medicine, psychology and many more. It elucidates core mathematical concepts in an accessible and straightforward manner, maintaining rigorous mathematical integrity. For readers more versed in mathematics, the book includes advanced sections that are not prerequisites for the initial reading. It ensures concepts are clearly defined and theorems are proven where it's pertinent. Machine learning transcends the mere implementation and training of algorithms; it encompasses the broader challenges of constructing robust datasets, model validation, addressing imbalanced datasets, and fine-tuning hyperparameters. These topics are thoroughly examined within the text, along with the theoretical foundations underlying these methods. Rather than concentrating on particular algorithms this book focuses on the comprehensive concepts and theories essential for their application. It stands as an indispensable resource for any scientist keen on integrating machine learning effectively into their research. Numerous texts delve into the technical execution of machine learning algorithms, often overlooking the foundational concepts vital for fully grasping these methods. This leads to a gap in using these algorithms effectively across diverse disciplines. For instance, a firm grasp of calculus is imperative to comprehend the training processes of algorithms and neural networks, while linear algebra is essential for the application and efficient training of various algorithms, including neural networks. Absent a solid mathematical base, machine learning applications may be, at best, cursory, or at worst, fundamentally flawed. This book lays the foundation for a comprehensive understanding of machine learning algorithms and approaches.

Manifold Learning Theory and Applications

Manifold Learning Theory and Applications

Author: Yunqian Ma

Publisher: CRC Press

Published: 2011-12-20

Total Pages: 410

ISBN-13: 1466558873

DOWNLOAD EBOOK

Trained to extract actionable information from large volumes of high-dimensional data, engineers and scientists often have trouble isolating meaningful low-dimensional structures hidden in their high-dimensional observations. Manifold learning, a groundbreaking technique designed to tackle these issues of dimensionality reduction, finds widespread


Book Synopsis Manifold Learning Theory and Applications by : Yunqian Ma

Download or read book Manifold Learning Theory and Applications written by Yunqian Ma and published by CRC Press. This book was released on 2011-12-20 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trained to extract actionable information from large volumes of high-dimensional data, engineers and scientists often have trouble isolating meaningful low-dimensional structures hidden in their high-dimensional observations. Manifold learning, a groundbreaking technique designed to tackle these issues of dimensionality reduction, finds widespread

Metaheuristics in Machine Learning: Theory and Applications

Metaheuristics in Machine Learning: Theory and Applications

Author: Diego Oliva

Publisher: Springer

Published: 2021-08-19

Total Pages: 769

ISBN-13: 9783030705411

DOWNLOAD EBOOK

This book is a collection of the most recent approaches that combine metaheuristics and machine learning. Some of the methods considered in this book are evolutionary, swarm, machine learning, and deep learning. The chapters were classified based on the content; then, the sections are thematic. Different applications and implementations are included; in this sense, the book provides theory and practical content with novel machine learning and metaheuristic algorithms. The chapters were compiled using a scientific perspective. Accordingly, the book is primarily intended for undergraduate and postgraduate students of Science, Engineering, and Computational Mathematics and is useful in courses on Artificial Intelligence, Advanced Machine Learning, among others. Likewise, the book is useful for research from the evolutionary computation, artificial intelligence, and image processing communities.


Book Synopsis Metaheuristics in Machine Learning: Theory and Applications by : Diego Oliva

Download or read book Metaheuristics in Machine Learning: Theory and Applications written by Diego Oliva and published by Springer. This book was released on 2021-08-19 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of the most recent approaches that combine metaheuristics and machine learning. Some of the methods considered in this book are evolutionary, swarm, machine learning, and deep learning. The chapters were classified based on the content; then, the sections are thematic. Different applications and implementations are included; in this sense, the book provides theory and practical content with novel machine learning and metaheuristic algorithms. The chapters were compiled using a scientific perspective. Accordingly, the book is primarily intended for undergraduate and postgraduate students of Science, Engineering, and Computational Mathematics and is useful in courses on Artificial Intelligence, Advanced Machine Learning, among others. Likewise, the book is useful for research from the evolutionary computation, artificial intelligence, and image processing communities.

Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

Author: Jean H Gallier

Publisher: World Scientific

Published: 2020-01-22

Total Pages: 823

ISBN-13: 9811206414

DOWNLOAD EBOOK

This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields.


Book Synopsis Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning by : Jean H Gallier

Download or read book Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning written by Jean H Gallier and published by World Scientific. This book was released on 2020-01-22 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields.

Linear Algebra and Optimization with Applications to Machine Learning

Linear Algebra and Optimization with Applications to Machine Learning

Author: Jean Gallier

Publisher: World Scientific Publishing Company

Published: 2020-03-06

Total Pages: 895

ISBN-13: 9789811216565

DOWNLOAD EBOOK

Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.


Book Synopsis Linear Algebra and Optimization with Applications to Machine Learning by : Jean Gallier

Download or read book Linear Algebra and Optimization with Applications to Machine Learning written by Jean Gallier and published by World Scientific Publishing Company. This book was released on 2020-03-06 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.

Variational Bayesian Learning Theory

Variational Bayesian Learning Theory

Author: Shinichi Nakajima

Publisher: Cambridge University Press

Published: 2019-07-11

Total Pages: 561

ISBN-13: 1316997219

DOWNLOAD EBOOK

Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to Bayesian learning.


Book Synopsis Variational Bayesian Learning Theory by : Shinichi Nakajima

Download or read book Variational Bayesian Learning Theory written by Shinichi Nakajima and published by Cambridge University Press. This book was released on 2019-07-11 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to Bayesian learning.