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| artificial intelligence linear algebra: Linear Algebra and Optimization for Machine Learning Charu C. Aggarwal, 2020-05-13 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. |
| artificial intelligence linear algebra: Basics of Linear Algebra for Machine Learning Jason Brownlee, 2018-01-24 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. |
| artificial intelligence linear algebra: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 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. |
| artificial intelligence linear algebra: A Matrix Algebra Approach to Artificial Intelligence Xian-Da Zhang, 2021-05-23 Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective. The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering. |
| artificial intelligence linear algebra: A Matrix Algebra Approach to Artificial Intelligence Xian-Da Zhang, 2020-05-23 Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective. The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering. |
| artificial intelligence linear algebra: Introduction to Applied Linear Algebra Stephen Boyd, Lieven Vandenberghe, 2018-06-07 A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples. |
| artificial intelligence linear algebra: Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning Jean H Gallier, Jocelyn Quaintance, 2020-01-22 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. |
| artificial intelligence linear algebra: Linear Algebra and Learning from Data Gilbert Strang, 2019-01-31 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. |
| artificial intelligence linear algebra: Deep Learning for Natural Language Processing Stephan Raaijmakers, 2022-12-20 Explore the most challenging issues of natural language processing, and learn how to solve them with cutting-edge deep learning! Inside Deep Learning for Natural Language Processing you’ll find a wealth of NLP insights, including: An overview of NLP and deep learning One-hot text representations Word embeddings Models for textual similarity Sequential NLP Semantic role labeling Deep memory-based NLP Linguistic structure Hyperparameters for deep NLP Deep learning has advanced natural language processing to exciting new levels and powerful new applications! For the first time, computer systems can achieve human levels of summarizing, making connections, and other tasks that require comprehension and context. Deep Learning for Natural Language Processing reveals the groundbreaking techniques that make these innovations possible. Stephan Raaijmakers distills his extensive knowledge into useful best practices, real-world applications, and the inner workings of top NLP algorithms. About the technology Deep learning has transformed the field of natural language processing. Neural networks recognize not just words and phrases, but also patterns. Models infer meaning from context, and determine emotional tone. Powerful deep learning-based NLP models open up a goldmine of potential uses. About the book Deep Learning for Natural Language Processing teaches you how to create advanced NLP applications using Python and the Keras deep learning library. You’ll learn to use state-of the-art tools and techniques including BERT and XLNET, multitask learning, and deep memory-based NLP. Fascinating examples give you hands-on experience with a variety of real world NLP applications. Plus, the detailed code discussions show you exactly how to adapt each example to your own uses! What's inside Improve question answering with sequential NLP Boost performance with linguistic multitask learning Accurately interpret linguistic structure Master multiple word embedding techniques About the reader For readers with intermediate Python skills and a general knowledge of NLP. No experience with deep learning is required. About the author Stephan Raaijmakers is professor of Communicative AI at Leiden University and a senior scientist at The Netherlands Organization for Applied Scientific Research (TNO). Table of Contents PART 1 INTRODUCTION 1 Deep learning for NLP 2 Deep learning and language: The basics 3 Text embeddings PART 2 DEEP NLP 4 Textual similarity 5 Sequential NLP 6 Episodic memory for NLP PART 3 ADVANCED TOPICS 7 Attention 8 Multitask learning 9 Transformers 10 Applications of Transformers: Hands-on with BERT |
| artificial intelligence linear algebra: Linear Algebra Problem Book Paul R. Halmos, 1995-12-31 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. |
| artificial intelligence linear algebra: Introduction to Linear Algebra Gilbert Strang, 2016-08-11 Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions, while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB®, Julia, and Python. |
| artificial intelligence linear algebra: Linear Algebra for Data Science, Machine Learning, and Signal Processing Jeffrey A. Fessler, Raj Rao Nadakuditi, 2024-04-30 Master matrix methods via engaging data-driven applications, aided by classroom-tested quizzes, homework exercises and online Julia demos. |
| artificial intelligence linear algebra: Deep Learning Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016-11-10 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. |
| artificial intelligence linear algebra: Hands-On Mathematics for Deep Learning Jay Dawani, 2020-06-12 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. |
| artificial intelligence linear algebra: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 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 |
| artificial intelligence linear algebra: Deep Learning Illustrated Jon Krohn, Grant Beyleveld, Aglaé Bassens, 2019-08-05 The authors’ clear visual style provides a comprehensive look at what’s currently possible with artificial neural networks as well as a glimpse of the magic that’s to come. – Tim Urban, author of Wait But Why Fully Practical, Insightful Guide to Modern Deep Learning Deep learning is transforming software, facilitating powerful new artificial intelligence capabilities, and driving unprecedented algorithm performance. Deep Learning Illustrated is uniquely intuitive and offers a complete introduction to the discipline’s techniques. Packed with full-color figures and easy-to-follow code, it sweeps away the complexity of building deep learning models, making the subject approachable and fun to learn. World-class instructor and practitioner Jon Krohn–with visionary content from Grant Beyleveld and beautiful illustrations by Aglaé Bassens–presents straightforward analogies to explain what deep learning is, why it has become so popular, and how it relates to other machine learning approaches. Krohn has created a practical reference and tutorial for developers, data scientists, researchers, analysts, and students who want to start applying it. He illuminates theory with hands-on Python code in accompanying Jupyter notebooks. To help you progress quickly, he focuses on the versatile deep learning library Keras to nimbly construct efficient TensorFlow models; PyTorch, the leading alternative library, is also covered. You’ll gain a pragmatic understanding of all major deep learning approaches and their uses in applications ranging from machine vision and natural language processing to image generation and game-playing algorithms. Discover what makes deep learning systems unique, and the implications for practitioners Explore new tools that make deep learning models easier to build, use, and improve Master essential theory: artificial neurons, training, optimization, convolutional nets, recurrent nets, generative adversarial networks (GANs), deep reinforcement learning, and more Walk through building interactive deep learning applications, and move forward with your own artificial intelligence projects Register your book for convenient access to downloads, updates, and/or corrections as they become available. See inside book for details. |
| artificial intelligence linear algebra: Practical Linear Algebra for Machine Learning Amirsina Torfi, 2019-12-26 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. |
| artificial intelligence linear algebra: Linear Algebra For Dummies Mary Jane Sterling, 2009-06-05 Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants |
| artificial intelligence linear algebra: Linear Algebra Tools for Data Mining Dan A. Simovici, 2012 This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications. Key Features Integrates the mathematical developments to their applications in data mining without sacrificing the mathematical rigor Presented applications with full mathematical justifications and are often accompanied by MATLAB code Highlights strong links between linear algebra, topology and graph theory because these links are essentially important for applications A self-contained book that deals with mathematics that is immediately relevant for data mining Book jacket. |
| artificial intelligence linear algebra: A Matrix Handbook for Statisticians George A. F. Seber, 2008-01-28 A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: Complex matrices A wide range of special matrices and their properties Special products and operators, such as the Kronecker product Partitioned and patterned matrices Matrix analysis and approximation Matrix optimization Majorization Random vectors and matrices Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers. |
| artificial intelligence linear algebra: Coding the Matrix Philip N. Klein, 2013-07 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. |
| artificial intelligence linear algebra: Neural Networks and Deep Learning Charu C. Aggarwal, 2018-08-25 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. |
| artificial intelligence linear algebra: Math for Deep Learning Ronald T. Kneusel, 2021-12-07 Math for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits. With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network. In addition you’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta. |
| artificial intelligence linear algebra: Linear Algebra for the 21st Century Anthony Roberts, 2020 Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places SVD as central to the text early on to empower the students in these disciplines to learn and use the best techniques. |
| artificial intelligence linear algebra: Matrix Algebra From a Statistician's Perspective David A. Harville, 2008-06-27 A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's Matrix Algebra: Exercises and Solutions. |
| artificial intelligence linear algebra: Math for Machine Learning Richard Han, 2018-07-12 This book explains the math behind machine learning using simple but concrete examples. This book will get you started in machine learning in a smooth and natural way, preparing you for more advanced topics and dispelling the belief that machine learning is complicated, difficult, and intimidating. |
| artificial intelligence linear algebra: Foundations of Machine Learning, second edition Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar, 2018-12-25 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. |
| artificial intelligence linear algebra: Introduction to Lattice Algebra Gerhard X. Ritter, Gonzalo Urcid, 2021-08-23 Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and – depending on the student’s major – can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Contains numerous exercises. |
| artificial intelligence linear algebra: Linear Algebra for Beginners: Open Doors to Great Careers Richard Han, 2018-10-16 From machine learning and data science to engineering and finance, linear algebra is an important prerequisite for the careers of today and of the future. There aren't many resources out there that give simple detailed examples and that walk you through the topics step by step. Many resources out there are either too dry or too difficult. This book aims to teach linear algebra step-by-step with examples that are simple but concrete. |
| artificial intelligence linear algebra: Linear Algebra: Theory, Intuition, Code Mike X. Cohen, 2021-02 Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on.The way linear algebra is presented in traditional textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the determinant of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you!If you are interested in learning the mathematical concepts linear algebra and matrix analysis, but also want to apply those concepts to data analyses on computers (e.g., statistics or signal processing), then this book is for you. You'll see all the math concepts implemented in MATLAB and in Python.Unique aspects of this book: - Clear and comprehensible explanations of concepts and theories in linear algebra. - Several distinct explanations of the same ideas, which is a proven technique for learning. - Visualization using graphs, which strengthens the geometric intuition of linear algebra. - Implementations in MATLAB and Python. Com'on, in the real world, you never solve math problems by hand! You need to know how to implement math in software! - Beginner to intermediate topics, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition. - Strong focus on modern applications-oriented aspects of linear algebra and matrix analysis. - Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition. - Codes (MATLAB and Python) are provided to help you understand and apply linear algebra concepts on computers. - A combination of hand-solved exercises and more advanced code challenges. Math is not a spectator sport! |
| artificial intelligence linear algebra: Machine Learning for Text Charu C. Aggarwal, 2018-03-19 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. |
| artificial intelligence linear algebra: The Data Science Design Manual Steven S. Skiena, 2017-07-01 This engaging and clearly written textbook/reference provides a must-have introduction to the rapidly emerging interdisciplinary field of data science. It focuses on the principles fundamental to becoming a good data scientist and the key skills needed to build systems for collecting, analyzing, and interpreting data. The Data Science Design Manual is a source of practical insights that highlights what really matters in analyzing data, and provides an intuitive understanding of how these core concepts can be used. The book does not emphasize any particular programming language or suite of data-analysis tools, focusing instead on high-level discussion of important design principles. This easy-to-read text ideally serves the needs of undergraduate and early graduate students embarking on an “Introduction to Data Science” course. It reveals how this discipline sits at the intersection of statistics, computer science, and machine learning, with a distinct heft and character of its own. Practitioners in these and related fields will find this book perfect for self-study as well. Additional learning tools: Contains “War Stories,” offering perspectives on how data science applies in the real world Includes “Homework Problems,” providing a wide range of exercises and projects for self-study Provides a complete set of lecture slides and online video lectures at www.data-manual.com Provides “Take-Home Lessons,” emphasizing the big-picture concepts to learn from each chapter Recommends exciting “Kaggle Challenges” from the online platform Kaggle Highlights “False Starts,” revealing the subtle reasons why certain approaches fail Offers examples taken from the data science television show “The Quant Shop” (www.quant-shop.com) |
| artificial intelligence linear algebra: Understanding Machine Learning Shai Shalev-Shwartz, Shai Ben-David, 2014-05-19 Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage. |
| artificial intelligence linear algebra: Mathematics of Big Data Jeremy Kepner, Hayden Jananthan, 2018-08-07 The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data. |
| artificial intelligence linear algebra: Statistical Machine Learning Richard Golden, 2020-06-24 The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing, analyzing, evaluating, and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students, engineers, and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular, the material in this text directly supports the mathematical analysis and design of old, new, and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised, unsupervised, and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive, batch, minibatch, MCEM, and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics, computer science, electrical engineering, and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students, professional engineers, and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph.D., M.S.E.E., B.S.E.E.) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models. |
| artificial intelligence linear algebra: Kernel Methods and Machine Learning S. Y. Kung, 2014-04-17 Offering a fundamental basis in kernel-based learning theory, this book covers both statistical and algebraic principles. It provides over 30 major theorems for kernel-based supervised and unsupervised learning models. The first of the theorems establishes a condition, arguably necessary and sufficient, for the kernelization of learning models. In addition, several other theorems are devoted to proving mathematical equivalence between seemingly unrelated models. With over 25 closed-form and iterative algorithms, the book provides a step-by-step guide to algorithmic procedures and analysing which factors to consider in tackling a given problem, enabling readers to improve specifically designed learning algorithms, build models for new applications and develop efficient techniques suitable for green machine learning technologies. Numerous real-world examples and over 200 problems, several of which are Matlab-based simulation exercises, make this an essential resource for graduate students and professionals in computer science, electrical and biomedical engineering. Solutions to problems are provided online for instructors. |
| artificial intelligence linear algebra: Groups, Matrices, and Vector Spaces James B. Carrell, 2017-09-02 This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable. |
| artificial intelligence linear algebra: Hands-On Genetic Algorithms with Python Eyal Wirsansky, 2020-01-31 Explore the ever-growing world of genetic algorithms to solve search, optimization, and AI-related tasks, and improve machine learning models using Python libraries such as DEAP, scikit-learn, and NumPy Key Features Explore the ins and outs of genetic algorithms with this fast-paced guide Implement tasks such as feature selection, search optimization, and cluster analysis using Python Solve combinatorial problems, optimize functions, and enhance the performance of artificial intelligence applications Book DescriptionGenetic algorithms are a family of search, optimization, and learning algorithms inspired by the principles of natural evolution. By imitating the evolutionary process, genetic algorithms can overcome hurdles encountered in traditional search algorithms and provide high-quality solutions for a variety of problems. This book will help you get to grips with a powerful yet simple approach to applying genetic algorithms to a wide range of tasks using Python, covering the latest developments in artificial intelligence. After introducing you to genetic algorithms and their principles of operation, you'll understand how they differ from traditional algorithms and what types of problems they can solve. You'll then discover how they can be applied to search and optimization problems, such as planning, scheduling, gaming, and analytics. As you advance, you'll also learn how to use genetic algorithms to improve your machine learning and deep learning models, solve reinforcement learning tasks, and perform image reconstruction. Finally, you'll cover several related technologies that can open up new possibilities for future applications. By the end of this book, you'll have hands-on experience of applying genetic algorithms in artificial intelligence as well as in numerous other domains.What you will learn Understand how to use state-of-the-art Python tools to create genetic algorithm-based applications Use genetic algorithms to optimize functions and solve planning and scheduling problems Enhance the performance of machine learning models and optimize deep learning network architecture Apply genetic algorithms to reinforcement learning tasks using OpenAI Gym Explore how images can be reconstructed using a set of semi-transparent shapes Discover other bio-inspired techniques, such as genetic programming and particle swarm optimization Who this book is for This book is for software developers, data scientists, and AI enthusiasts who want to use genetic algorithms to carry out intelligent tasks in their applications. Working knowledge of Python and basic knowledge of mathematics and computer science will help you get the most out of this book. |
| artificial intelligence linear algebra: Probability for Machine Learning Jason Brownlee, 2019-09-24 Probability is the bedrock of machine learning. You cannot develop a deep understanding and application of machine learning without it. Cut through the equations, Greek letters, and confusion, and discover the topics in probability that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover the importance of probability to machine learning, Bayesian probability, entropy, density estimation, maximum likelihood, and much more. |
| artificial intelligence linear algebra: Learning How to Learn Barbara Oakley, PhD, Terrence Sejnowski, PhD, Alistair McConville, 2018-08-07 A surprisingly simple way for students to master any subject--based on one of the world's most popular online courses and the bestselling book A Mind for Numbers A Mind for Numbers and its wildly popular online companion course Learning How to Learn have empowered more than two million learners of all ages from around the world to master subjects that they once struggled with. Fans often wish they'd discovered these learning strategies earlier and ask how they can help their kids master these skills as well. Now in this new book for kids and teens, the authors reveal how to make the most of time spent studying. We all have the tools to learn what might not seem to come naturally to us at first--the secret is to understand how the brain works so we can unlock its power. This book explains: Why sometimes letting your mind wander is an important part of the learning process How to avoid rut think in order to think outside the box Why having a poor memory can be a good thing The value of metaphors in developing understanding A simple, yet powerful, way to stop procrastinating Filled with illustrations, application questions, and exercises, this book makes learning easy and fun. |
ARTIFICIAL Definition & Meaning - Merriam-Webster
The meaning of ARTIFICIAL is made, produced, or done by humans especially to seem like something natural : man-made. How to use artificial in a sentence.
ARTIFICIAL | English meaning - Cambridge Dictionary
ARTIFICIAL definition: 1. made by people, often as a copy of something natural: 2. not sincere: 3. made by people, often…. Learn more.
Artificial - definition of artificial by The Free Dictionary
1. produced by man; not occurring naturally: artificial materials of great strength. 2. made in imitation of a natural product, esp as a substitute; not genuine: artificial cream. 3. pretended; …
ARTIFICIAL Definition & Meaning | Dictionary.com
Artificial is used to describe things that are made or manufactured as opposed to occurring naturally. Artificial is often used as the opposite of natural. A close synonym of artificial is …
ARTIFICIAL definition and meaning | Collins English Dictionary
Artificial objects, materials, or processes do not occur naturally and are created by human beings, for example using science or technology.
artificial adjective - Definition, pictures, pronunciation and usage ...
Definition of artificial adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Artificial - Definition, Meaning & Synonyms - Vocabulary.com
While artificial can simply mean “made by humans,” it’s often used in a negative sense, conveying the idea that an artificial product is inferior to the real thing. If you remark that your friend’s new …
artificial - Wiktionary, the free dictionary
6 days ago · artificial (comparative more artificial, superlative most artificial) Man-made; made by humans; of artifice. The flowers were artificial, and he thought them rather tacky. An artificial …
What does artificial mean? - Definitions.net
Artificial refers to something that is made or produced by human beings rather than occurring naturally or in the environment. It often implies an imitation of something natural or a real …
Artificial Intelligence Is Not Intelligent - The Atlantic
Jun 6, 2025 · The good news is that nothing about this is inevitable: According to a study released in April by the Pew Research Center, although 56 percent of “AI experts” think artificial …
ARTIFICIAL Definition & Meaning - Merriam-Webster
The meaning of ARTIFICIAL is made, produced, or done by humans especially to seem like something natural : man-made. How to use artificial in a sentence.
ARTIFICIAL | English meaning - Cambridge Dictionary
ARTIFICIAL definition: 1. made by people, often as a copy of something natural: 2. not sincere: 3. made by people, often…. Learn more.
Artificial - definition of artificial by The Free Dictionary
1. produced by man; not occurring naturally: artificial materials of great strength. 2. made in imitation of a natural product, esp as a substitute; not genuine: artificial cream. 3. pretended; …
ARTIFICIAL Definition & Meaning | Dictionary.com
Artificial is used to describe things that are made or manufactured as opposed to occurring naturally. Artificial is often used as the opposite of natural. A close synonym of artificial is …
ARTIFICIAL definition and meaning | Collins English Dictionary
Artificial objects, materials, or processes do not occur naturally and are created by human beings, for example using science or technology.
artificial adjective - Definition, pictures, pronunciation and usage ...
Definition of artificial adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Artificial - Definition, Meaning & Synonyms - Vocabulary.com
While artificial can simply mean “made by humans,” it’s often used in a negative sense, conveying the idea that an artificial product is inferior to the real thing. If you remark that your friend’s new …
artificial - Wiktionary, the free dictionary
6 days ago · artificial (comparative more artificial, superlative most artificial) Man-made; made by humans; of artifice. The flowers were artificial, and he thought them rather tacky. An artificial …
What does artificial mean? - Definitions.net
Artificial refers to something that is made or produced by human beings rather than occurring naturally or in the environment. It often implies an imitation of something natural or a real …
Artificial Intelligence Is Not Intelligent - The Atlantic
Jun 6, 2025 · The good news is that nothing about this is inevitable: According to a study released in April by the Pew Research Center, although 56 percent of “AI experts” think artificial …
