Linear Algebra And Learning From Data

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Linear Algebra and Learning from Data

Gilbert Strang

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 446 pages
File Size : 54,8 Mb
Release : 2019-01-31
Category : Computers
ISBN : 0692196382

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Linear Algebra and Learning from Data by Gilbert Strang Pdf

Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.

Linear Algebra and Optimization for Machine Learning

Charu C. Aggarwal

Author : Charu C. Aggarwal
Publisher : Springer Nature
Page : 507 pages
File Size : 43,8 Mb
Release : 2020-05-13
Category : Computers
ISBN : 9783030403447

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Linear Algebra and Optimization for Machine Learning by Charu C. Aggarwal Pdf

This textbook introduces linear algebra and optimization in the context of machine learning. Examples and exercises are provided throughout the book. A solution manual for the exercises at the end of each chapter is available to teaching instructors. This textbook targets graduate level students and professors in computer science, mathematics and data science. Advanced undergraduate students can also use this textbook. The chapters for this textbook are organized as follows: 1. Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2. Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization, and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to back propagation in neural networks. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning.

Linear Algebra for Everyone

Gilbert Strang

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 368 pages
File Size : 47,8 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 1733146636

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Linear Algebra for Everyone by Gilbert Strang Pdf

Linear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

Mathematics for Machine Learning

Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong

Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Publisher : Cambridge University Press
Page : 391 pages
File Size : 54,9 Mb
Release : 2020-04-23
Category : Computers
ISBN : 9781108470049

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Mathematics for Machine Learning by Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong Pdf

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

Basics of Linear Algebra for Machine Learning

Jason Brownlee

Author : Jason Brownlee
Publisher : Machine Learning Mastery
Page : 211 pages
File Size : 42,8 Mb
Release : 2018-01-24
Category : Computers
ISBN : 8210379456XXX

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Basics of Linear Algebra for Machine Learning by Jason Brownlee Pdf

Linear algebra is a pillar of machine learning. You cannot develop a deep understanding and application of machine learning without it. In this laser-focused Ebook, you will finally cut through the equations, Greek letters, and confusion, and discover the topics in linear algebra that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover what linear algebra is, the importance of linear algebra to machine learning, vector, and matrix operations, matrix factorization, principal component analysis, and much more.

Introduction to Applied Linear Algebra

Stephen Boyd,Lieven Vandenberghe

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 53,7 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Grokking Deep Learning

Andrew W. Trask

Author : Andrew W. Trask
Publisher : Simon and Schuster
Page : 475 pages
File Size : 48,9 Mb
Release : 2019-01-23
Category : Computers
ISBN : 9781638357209

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Grokking Deep Learning by Andrew W. Trask Pdf

Summary Grokking Deep Learning teaches you to build deep learning neural networks from scratch! In his engaging style, seasoned deep learning expert Andrew Trask shows you the science under the hood, so you grok for yourself every detail of training neural networks. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology Deep learning, a branch of artificial intelligence, teaches computers to learn by using neural networks, technology inspired by the human brain. Online text translation, self-driving cars, personalized product recommendations, and virtual voice assistants are just a few of the exciting modern advancements possible thanks to deep learning. About the Book Grokking Deep Learning teaches you to build deep learning neural networks from scratch! In his engaging style, seasoned deep learning expert Andrew Trask shows you the science under the hood, so you grok for yourself every detail of training neural networks. Using only Python and its math-supporting library, NumPy, you'll train your own neural networks to see and understand images, translate text into different languages, and even write like Shakespeare! When you're done, you'll be fully prepared to move on to mastering deep learning frameworks. What's inside The science behind deep learning Building and training your own neural networks Privacy concepts, including federated learning Tips for continuing your pursuit of deep learning About the Reader For readers with high school-level math and intermediate programming skills. About the Author Andrew Trask is a PhD student at Oxford University and a research scientist at DeepMind. Previously, Andrew was a researcher and analytics product manager at Digital Reasoning, where he trained the world's largest artificial neural network and helped guide the analytics roadmap for the Synthesys cognitive computing platform. Table of Contents Introducing deep learning: why you should learn it Fundamental concepts: how do machines learn? Introduction to neural prediction: forward propagation Introduction to neural learning: gradient descent Learning multiple weights at a time: generalizing gradient descent Building your first deep neural network: introduction to backpropagation How to picture neural networks: in your head and on paper Learning signal and ignoring noise:introduction to regularization and batching Modeling probabilities and nonlinearities: activation functions Neural learning about edges and corners: intro to convolutional neural networks Neural networks that understand language: king - man + woman == ? Neural networks that write like Shakespeare: recurrent layers for variable-length data Introducing automatic optimization: let's build a deep learning framework Learning to write like Shakespeare: long short-term memory Deep learning on unseen data: introducing federated learning Where to go from here: a brief guide

Differential Equations and Linear Algebra

Gilbert Strang

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 0 pages
File Size : 47,8 Mb
Release : 2015-02-12
Category : Mathematics
ISBN : 0980232791

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Differential Equations and Linear Algebra by Gilbert Strang Pdf

Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

Linear Algebra Problem Book

Paul R. Halmos

Author : Paul R. Halmos
Publisher : American Mathematical Soc.
Page : 333 pages
File Size : 46,7 Mb
Release : 1995-12-31
Category : Mathematics
ISBN : 9781614442127

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Linear Algebra Problem Book by Paul R. Halmos Pdf

Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.

Linear Algebra Done Right

Sheldon Axler

Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 41,6 Mb
Release : 1997-07-18
Category : Mathematics
ISBN : 0387982590

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Linear Algebra Done Right by Sheldon Axler Pdf

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

The Mathematics of Data

Michael W. Mahoney,John C. Duchi,Anna C. Gilbert

Author : Michael W. Mahoney,John C. Duchi,Anna C. Gilbert
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 41,6 Mb
Release : 2018-11-15
Category : Big data
ISBN : 9781470435752

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The Mathematics of Data by Michael W. Mahoney,John C. Duchi,Anna C. Gilbert Pdf

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Linear Algebra With Machine Learning and Data

Crista Arangala

Author : Crista Arangala
Publisher : CRC Press
Page : 310 pages
File Size : 55,5 Mb
Release : 2023-05-09
Category : Mathematics
ISBN : 9781000856163

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Linear Algebra With Machine Learning and Data by Crista Arangala Pdf

This textbook attempts to revolutionize the Advanced Linear Algebra course by offering the integration of data analysis through case studies. Many schools are trying to find ways to incorporate data analysis into the undergrad math curriculum. The author presents a real alternative to standard textbooks. The use of case studies to demonstrate how linear algebra can be used in data analysis separates this text from all others currently available from any major publisher.

Coding the Matrix

Philip N. Klein

Author : Philip N. Klein
Publisher : Unknown
Page : 530 pages
File Size : 52,8 Mb
Release : 2013-07
Category : Algebras, Linear
ISBN : 061585673X

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Coding the Matrix by Philip N. Klein Pdf

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.

Deep Learning for Coders with fastai and PyTorch

Jeremy Howard,Sylvain Gugger

Author : Jeremy Howard,Sylvain Gugger
Publisher : O'Reilly Media
Page : 624 pages
File Size : 51,8 Mb
Release : 2020-06-29
Category : Computers
ISBN : 9781492045496

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Deep Learning for Coders with fastai and PyTorch by Jeremy Howard,Sylvain Gugger Pdf

Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala

Numerical Matrix Analysis

Ilse C. F. Ipsen

Author : Ilse C. F. Ipsen
Publisher : SIAM
Page : 135 pages
File Size : 43,8 Mb
Release : 2009-07-23
Category : Mathematics
ISBN : 9780898716764

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Numerical Matrix Analysis by Ilse C. F. Ipsen Pdf

Matrix analysis presented in the context of numerical computation at a basic level.

Linear Algebra And Learning From Data

Linear Algebra and Learning from Data by Gilbert Strang Pdf

Linear Algebra and Optimization for Machine Learning by Charu C. Aggarwal Pdf

Linear Algebra for Everyone by Gilbert Strang Pdf

Mathematics for Machine Learning by Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong Pdf

Basics of Linear Algebra for Machine Learning by Jason Brownlee Pdf

Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

Grokking Deep Learning by Andrew W. Trask Pdf

Differential Equations and Linear Algebra by Gilbert Strang Pdf

Linear Algebra Problem Book by Paul R. Halmos Pdf

Linear Algebra Done Right by Sheldon Axler Pdf

The Mathematics of Data by Michael W. Mahoney,John C. Duchi,Anna C. Gilbert Pdf

Linear Algebra With Machine Learning and Data by Crista Arangala Pdf

Coding the Matrix by Philip N. Klein Pdf

Deep Learning for Coders with fastai and PyTorch by Jeremy Howard,Sylvain Gugger Pdf

Numerical Matrix Analysis by Ilse C. F. Ipsen Pdf

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