Download or read book Linear Algebra and Optimization for Machine Learning written by Charu C. Aggarwal and published by Springer Nature. This book was released on 2020-05-13 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Linear Algebra And Optimization With Applications To Machine Learning Volume Ii Fundamentals Of Optimization Theory With Applications To Machine Learning written by Quaintance Jocelyn and published by World Scientific. This book was released on 2020-03-16 with total page 896 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.

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Download or read book Numerical Linear Algebra And Optimization written by Philip E. Gill and published by Westview Press. This book was released on 1991-07-22 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical linear algebra and opt./Gill, P.E.- v.1

Download or read book Optimization for Machine Learning written by Suvrit Sra and published by MIT Press. This book was released on 2012 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.

Download or read book Linear Algebra and Learning from Data written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2019-01-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Download or read book Hands On Mathematics for Deep Learning written by Jay Dawani and published by Packt Publishing Ltd. This book was released on 2020-06-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to getting well-versed with the mathematical techniques for building modern deep learning architectures Key FeaturesUnderstand linear algebra, calculus, gradient algorithms, and other concepts essential for training deep neural networksLearn the mathematical concepts needed to understand how deep learning models functionUse deep learning for solving problems related to vision, image, text, and sequence applicationsBook Description Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL. What you will learnUnderstand the key mathematical concepts for building neural network modelsDiscover core multivariable calculus conceptsImprove the performance of deep learning models using optimization techniquesCover optimization algorithms, from basic stochastic gradient descent (SGD) to the advanced Adam optimizerUnderstand computational graphs and their importance in DLExplore the backpropagation algorithm to reduce output errorCover DL algorithms such as convolutional neural networks (CNNs), sequence models, and generative adversarial networks (GANs)Who this book is for This book is for data scientists, machine learning developers, aspiring deep learning developers, or anyone who wants to understand the foundation of deep learning by learning the math behind it. Working knowledge of the Python programming language and machine learning basics is required.

Download or read book Basics of Linear Algebra for Machine Learning written by Jason Brownlee and published by Machine Learning Mastery. This book was released on 2018-01-24 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Deep Learning written by Ian Goodfellow and published by MIT Press. This book was released on 2016-11-10 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

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 Publishing Company. This book was released on 2020-01-15 with total page 550 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.

Download or read book Fundamentals of Linear Algebra written by J.S. Chahal and published by CRC Press. This book was released on 2018-12-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Linear Algebra is like no other book on the subject. By following a natural and unified approach to the subject it has, in less than 250 pages, achieved a more complete coverage of the subject than books with more than twice as many pages. For example, the textbooks in use in the United States prove the existence of a basis only for finite dimensional vector spaces. This book proves it for any given vector space. With his experience in algebraic geometry and commutative algebra, the author defines the dimension of a vector space as its Krull dimension. By doing so, most of the facts about bases when the dimension is finite, are trivial consequences of this definition. To name one, the replacement theorem is no longer needed. It becomes obvious that any two bases of a finite dimensional vector space contain the same number of vectors. Moreover, this definition of the dimension works equally well when the geometric objects are nonlinear. Features: Presents theories and applications in an attempt to raise expectations and outcomes The subject of linear algebra is presented over arbitrary fields Includes many non-trivial examples which address real-world problems About the Author: Dr. J.S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published a number of papers about number theory. For hobbies, he likes to travel and hike, the reason he accepted the position at Brigham Young University

Download or read book Applied Linear Algebra and Optimization Using MATLAB written by Rizwan Butt and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM contains ... "all of the figures, code, and m-files for all of the programs."--Page 4 of cover.

Download or read book Neural Networks and Deep Learning written by Charu C. Aggarwal and published by Springer. This book was released on 2018-08-25 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of deep learning. The theory and algorithms of neural networks are particularly important for understanding important concepts, so that one can understand the important design concepts of neural architectures in different applications. Why do neural networks work? When do they work better than off-the-shelf machine-learning models? When is depth useful? Why is training neural networks so hard? What are the pitfalls? The book is also rich in discussing different applications in order to give the practitioner a flavor of how neural architectures are designed for different types of problems. Applications associated with many different areas like recommender systems, machine translation, image captioning, image classification, reinforcement-learning based gaming, and text analytics are covered. The chapters of this book span three categories: The basics of neural networks: Many traditional machine learning models can be understood as special cases of neural networks. An emphasis is placed in the first two chapters on understanding the relationship between traditional machine learning and neural networks. Support vector machines, linear/logistic regression, singular value decomposition, matrix factorization, and recommender systems are shown to be special cases of neural networks. These methods are studied together with recent feature engineering methods like word2vec. Fundamentals of neural networks: A detailed discussion of training and regularization is provided in Chapters 3 and 4. Chapters 5 and 6 present radial-basis function (RBF) networks and restricted Boltzmann machines. Advanced topics in neural networks: Chapters 7 and 8 discuss recurrent neural networks and convolutional neural networks. Several advanced topics like deep reinforcement learning, neural Turing machines, Kohonen self-organizing maps, and generative adversarial networks are introduced in Chapters 9 and 10. The book is written for graduate students, researchers, and practitioners. Numerous exercises are available along with a solution manual to aid in classroom teaching. Where possible, an application-centric view is highlighted in order to provide an understanding of the practical uses of each class of techniques.

Download or read book Linear Algebra for Everyone written by Gilbert Strang and published by Wellesley-Cambridge Press. This book was released on 2020-11-26 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Practical Linear Algebra for Machine Learning written by Amirsina Torfi and published by . This book was released on 2019-12-26 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning is everywhere these days and a lot of fellows desire to learn it and even master it! This burning desire creates a sense of impatience. We are looking for shortcuts and willing to ONLY jump to the main concept. If you do a simple search on the web, you see thousands of people asking "How can I learn Machine Learning?", "What is the fastest approach to learn Machine Learning?", and "What are the best resources to start Machine Learning?" \textit. Mastering a branch of science is NOT just a feel-good exercise. It has its own requirements.One of the most critical requirements for Machine Learning is Linear Algebra. Basically, the majority of Machine Learning is working with data and optimization. How can you want to learn those without Linear Algebra? How would you process and represent data without vectors and matrices? On the other hand, Linear Algebra is a branch of mathematics after all. A lot of people trying to avoid mathematics or have the temptation to "just learn as necessary." I agree with the second approach, though. \textit: You cannot escape Linear Algebra if you want to learn Machine Learning and Deep Learning. There is NO shortcut.The good news is there are numerous resources out there. In fact, the availability of numerous resources made me ponder whether writing this book was necessary? I have been blogging about Machine Learning for a while and after searching and searching I realized there is a deficiency of an organized book which \textbf teaches the most used Linear Algebra concepts in Machine Learning, \textbf provides practical notions using everyday used programming languages such as Python, and \textbf be concise and NOT unnecessarily lengthy.In this book, you get all of what you need to learn about Linear Algebra that you need to master Machine Learning and Deep Learning.

Download or read book Linear Algebra Problem Book written by Paul R. Halmos and published by American Mathematical Soc.. This book was released on 1995-12-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.