Linear Algebra and Optimization for Machine Learning
Linear Algebra and Optimization for Machine Learning

Author: Charu C. Aggarwal

Publisher: Springer Nature

Published: 2020-05-13

Total Pages: 507

ISBN-13: 3030403440

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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.

Optimization for Machine Learning
Optimization for Machine Learning

Author: Suvrit Sra

Publisher: MIT Press

Published: 2012

Total Pages: 509

ISBN-13: 026201646X

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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.

Mathematics for Machine Learning
Mathematics for Machine Learning

Author: Marc Peter Deisenroth

Publisher: Cambridge University Press

Published: 2020-04-23

Total Pages: 392

ISBN-13: 1108569323

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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.

Introduction to Applied Linear Algebra
Introduction to Applied Linear Algebra

Author: Stephen Boyd

Publisher: Cambridge University Press

Published: 2018-06-07

Total Pages: 477

ISBN-13: 1316518965

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

Linear Algebra and Learning from Data
Linear Algebra and Learning from Data

Author: Gilbert Strang

Publisher: Wellesley-Cambridge Press

Published: 2019-01-31

Total Pages: 0

ISBN-13: 9780692196380

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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.

Basics of Linear Algebra for Machine Learning
Basics of Linear Algebra for Machine Learning

Author: Jason Brownlee

Publisher: Machine Learning Mastery

Published: 2018-01-24

Total Pages: 211

ISBN-13:

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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.

Hands-On Mathematics for Deep Learning
Hands-On Mathematics for Deep Learning

Author: Jay Dawani

Publisher: Packt Publishing Ltd

Published: 2020-06-12

Total Pages: 347

ISBN-13: 183864184X

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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.

Deep Learning
Deep Learning

Author: Ian Goodfellow

Publisher: MIT Press

Published: 2016-11-10

Total Pages: 801

ISBN-13: 0262337371

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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.

Neural Networks and Deep Learning
Neural Networks and Deep Learning

Author: Charu C. Aggarwal

Publisher: Springer

Published: 2018-08-25

Total Pages: 512

ISBN-13: 3319944630

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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.

Machine Learning for Text
Machine Learning for Text

Author: Charu C. Aggarwal

Publisher: Springer

Published: 2018-03-19

Total Pages: 510

ISBN-13: 3319735314

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Text analytics is a field that lies on the interface of information retrieval,machine learning, and natural language processing, and this textbook carefully covers a coherently organized framework drawn from these intersecting topics. The chapters of this textbook is organized into three categories: - Basic algorithms: Chapters 1 through 7 discuss the classical algorithms for machine learning from text such as preprocessing, similarity computation, topic modeling, matrix factorization, clustering, classification, regression, and ensemble analysis. - Domain-sensitive mining: Chapters 8 and 9 discuss the learning methods from text when combined with different domains such as multimedia and the Web. The problem of information retrieval and Web search is also discussed in the context of its relationship with ranking and machine learning methods. - Sequence-centric mining: Chapters 10 through 14 discuss various sequence-centric and natural language applications, such as feature engineering, neural language models, deep learning, text summarization, information extraction, opinion mining, text segmentation, and event detection. This textbook covers machine learning topics for text in detail. Since the coverage is extensive,multiple courses can be offered from the same book, depending on course level. Even though the presentation is text-centric, Chapters 3 to 7 cover machine learning algorithms that are often used indomains beyond text data. Therefore, the book can be used to offer courses not just in text analytics but also from the broader perspective of machine learning (with text as a backdrop). This textbook targets graduate students in computer science, as well as researchers, professors, and industrial practitioners working in these related fields. This textbook is accompanied with a solution manual for classroom teaching.