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| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Introduction to Deep Learning Sandro Skansi, 2018-02-04 This textbook presents a concise, accessible and engaging first introduction to deep learning, offering a wide range of connectionist models which represent the current state-of-the-art. The text explores the most popular algorithms and architectures in a simple and intuitive style, explaining the mathematical derivations in a step-by-step manner. The content coverage includes convolutional networks, LSTMs, Word2vec, RBMs, DBNs, neural Turing machines, memory networks and autoencoders. Numerous examples in working Python code are provided throughout the book, and the code is also supplied separately at an accompanying website. Topics and features: introduces the fundamentals of machine learning, and the mathematical and computational prerequisites for deep learning; discusses feed-forward neural networks, and explores the modifications to these which can be applied to any neural network; examines convolutional neural networks, and the recurrent connections to a feed-forward neural network; describes the notion of distributed representations, the concept of the autoencoder, and the ideas behind language processing with deep learning; presents a brief history of artificial intelligence and neural networks, and reviews interesting open research problems in deep learning and connectionism. This clearly written and lively primer on deep learning is essential reading for graduate and advanced undergraduate students of computer science, cognitive science and mathematics, as well as fields such as linguistics, logic, philosophy, and psychology. |
| calculus for artificial intelligence: 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 |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Probability Inequalities Zhengyan Lin, Zhidong Bai, 2011-05-30 Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. Probability Inequalities covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Mathematics and Programming for Machine Learning with R William Claster, 2020-10-26 Based on the author’s experience in teaching data science for more than 10 years, Mathematics and Programming for Machine Learning with R: From the Ground Up reveals how machine learning algorithms do their magic and explains how these algorithms can be implemented in code. It is designed to provide readers with an understanding of the reasoning behind machine learning algorithms as well as how to program them. Written for novice programmers, the book progresses step-by-step, providing the coding skills needed to implement machine learning algorithms in R. The book begins with simple implementations and fundamental concepts of logic, sets, and probability before moving to the coverage of powerful deep learning algorithms. The first eight chapters deal with probability-based machine learning algorithms, and the last eight chapters deal with machine learning based on artificial neural networks. The first half of the book does not require mathematical sophistication, although familiarity with probability and statistics would be helpful. The second half assumes the reader is familiar with at least one semester of calculus. The text guides novice R programmers through algorithms and their application and along the way; the reader gains programming confidence in tackling advanced R programming challenges. Highlights of the book include: More than 400 exercises A strong emphasis on improving programming skills and guiding beginners to the implementation of full-fledged algorithms Coverage of fundamental computer and mathematical concepts including logic, sets, and probability In-depth explanations of machine learning algorithms |
| calculus for artificial intelligence: Calculus for Machine Learning Jason Brownlee, Stefania Cristina, Mehreen Saeed, 2022-02-23 Calculus seems to be obscure, but it is everywhere. In machine learning, while we rarely write code on differentiation or integration, the algorithms we use have theoretical roots in calculus. If you ever wondered how to understand the calculus part when you listen to people explaining the theory behind a machine learning algorithm, this new Ebook, in the friendly Machine Learning Mastery style that you’re used to, is all you need. Using clear explanations and step-by-step tutorial lessons, you will understand the concept of calculus, how it is relates to machine learning, what it can help us on, and much more. |
| calculus for artificial intelligence: Revolutionary Mathematics Justin Joque, 2022-01-18 Traces the revolution in statistics that gave rise to artificial intelligence and predictive algorithms refiguring contemporary capitalism. Our finances, politics, media, opportunities, information, shopping and knowledge production are mediated through algorithms and their statistical approaches to knowledge; increasingly, these methods form the organizational backbone of contemporary capitalism. Revolutionary Mathematics traces the revolution in statistics and probability that has quietly underwritten the explosion of machine learning, big data and predictive algorithms that now decide many aspects of our lives. Exploring shifts in the philosophical understanding of probability in the late twentieth century, Joque shows how this was not merely a technical change but a wholesale philosophical transformation in the production of knowledge and the extraction of value. This book provides a new and unique perspective on the dangers of allowing artificial intelligence and big data to manage society. It is essential reading for those who want to understand the underlying ideological and philosophical changes that have fueled the rise of algorithms and convinced so many to blindly trust their outputs, reshaping our current political and economic situation. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: The Statistics and Calculus with Python Workshop Peter Farrell, Alvaro Fuentes, Ajinkya Sudhir Kolhe, Quan Nguyen, Alexander Joseph Sarver, Marios Tsatsos, 2020-08-18 With examples and activities that help you achieve real results, applying calculus and statistical methods relevant to advanced data science has never been so easy Key FeaturesDiscover how most programmers use the main Python libraries when performing statistics with PythonUse descriptive statistics and visualizations to answer business and scientific questionsSolve complicated calculus problems, such as arc length and solids of revolution using derivatives and integralsBook Description Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you'll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges. What you will learnGet to grips with the fundamental mathematical functions in PythonPerform calculations on tabular datasets using pandasUnderstand the differences between polynomials, rational functions, exponential functions, and trigonometric functionsUse algebra techniques for solving systems of equationsSolve real-world problems with probabilitySolve optimization problems with derivatives and integralsWho this book is for If you are a Python programmer who wants to develop intelligent solutions that solve challenging business problems, then this book is for you. To better grasp the concepts explained in this book, you must have a thorough understanding of advanced mathematical concepts, such as Markov chains, Euler's formula, and Runge-Kutta methods as the book only explains how these techniques and concepts can be implemented in Python. |
| calculus for artificial intelligence: Optimization for Machine Learning Suvrit Sra, Sebastian Nowozin, Stephen J. Wright, 2012 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. |
| calculus for artificial intelligence: Bayesian Reasoning and Machine Learning David Barber, 2012-02-02 A practical introduction perfect for final-year undergraduate and graduate students without a solid background in linear algebra and calculus. |
| calculus for artificial intelligence: Visual Group Theory Nathan Carter, 2021-06-08 Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Calculus of Thought Daniel M Rice, 2013-10-15 Calculus of Thought: Neuromorphic Logistic Regression in Cognitive Machines is a must-read for all scientists about a very simple computation method designed to simulate big-data neural processing. This book is inspired by the Calculus Ratiocinator idea of Gottfried Leibniz, which is that machine computation should be developed to simulate human cognitive processes, thus avoiding problematic subjective bias in analytic solutions to practical and scientific problems. The reduced error logistic regression (RELR) method is proposed as such a Calculus of Thought. This book reviews how RELR's completely automated processing may parallel important aspects of explicit and implicit learning in neural processes. It emphasizes the fact that RELR is really just a simple adjustment to already widely used logistic regression, along with RELR's new applications that go well beyond standard logistic regression in prediction and explanation. Readers will learn how RELR solves some of the most basic problems in today's big and small data related to high dimensionality, multi-colinearity, and cognitive bias in capricious outcomes commonly involving human behavior. - Provides a high-level introduction and detailed reviews of the neural, statistical and machine learning knowledge base as a foundation for a new era of smarter machines - Argues that smarter machine learning to handle both explanation and prediction without cognitive bias must have a foundation in cognitive neuroscience and must embody similar explicit and implicit learning principles that occur in the brain |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Mathematical Methods in Artificial Intelligence Edward A. Bender, 1996-02-10 Mathematical Methods in Artificial Intelligence introduces the student to the important mathematical foundations and tools in AI and describes their applications to the design of AI algorithms. This useful text presents an introductory AI course based on the most important mathematics and its applications. It focuses on important topics that are proven useful in AI and involve the most broadly applicable mathematics. The book explores AI from three different viewpoints: goals, methods or tools, and achievements and failures. Its goals of reasoning, planning, learning, or language understanding and use are centered around the expert system idea. The tools of AI are presented in terms of what can be incorporated in the data structures. The book looks into the concepts and tools of limited structure, mathematical logic, logic-like representation, numerical information, and nonsymbolic structures. The text emphasizes the main mathematical tools for representing and manipulating knowledge symbolically. These are various forms of logic for qualitative knowledge, and probability and related concepts for quantitative knowledge. The main tools for manipulating knowledge nonsymbolically, as neural nets, are optimization methods and statistics. This material is covered in the text by topics such as trees and search, classical mathematical logic, and uncertainty and reasoning. A solutions diskette is available, please call for more information. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Introduction to Artificial Intelligence Philip C. Jackson, 2019-08-14 Can computers think? Can they use reason to develop their own concepts, solve complex problems, understand our languages? This updated edition of a comprehensive survey includes extensive new text on Artificial Intelligence in the 21st Century, introducing deep neural networks, conceptual graphs, languages of thought, mental models, metacognition, economic prospects, and research toward human-level AI. Ideal for both lay readers and students of computer science, the original text features abundant illustrations, diagrams, and photographs as well as challenging exercises. Lucid, easy-to-read discussions examine problem-solving methods and representations, game playing, automated understanding of natural languages, heuristic search theory, robot systems, heuristic scene analysis, predicate-calculus theorem proving, automatic programming, and many other topics. |
| calculus for artificial intelligence: Deep Learning and the Game of Go Kevin Ferguson, Max Pumperla, 2019-01-06 Summary Deep Learning and the Game of Go teaches you how to apply the power of deep learning to complex reasoning tasks by building a Go-playing AI. After exposing you to the foundations of machine and deep learning, you'll use Python to build a bot and then teach it the rules of the game. Foreword by Thore Graepel, DeepMind Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology The ancient strategy game of Go is an incredible case study for AI. In 2016, a deep learning-based system shocked the Go world by defeating a world champion. Shortly after that, the upgraded AlphaGo Zero crushed the original bot by using deep reinforcement learning to master the game. Now, you can learn those same deep learning techniques by building your own Go bot! About the Book Deep Learning and the Game of Go introduces deep learning by teaching you to build a Go-winning bot. As you progress, you'll apply increasingly complex training techniques and strategies using the Python deep learning library Keras. You'll enjoy watching your bot master the game of Go, and along the way, you'll discover how to apply your new deep learning skills to a wide range of other scenarios! What's inside Build and teach a self-improving game AI Enhance classical game AI systems with deep learning Implement neural networks for deep learning About the Reader All you need are basic Python skills and high school-level math. No deep learning experience required. About the Author Max Pumperla and Kevin Ferguson are experienced deep learning specialists skilled in distributed systems and data science. Together, Max and Kevin built the open source bot BetaGo. Table of Contents PART 1 - FOUNDATIONS Toward deep learning: a machine-learning introduction Go as a machine-learning problem Implementing your first Go bot PART 2 - MACHINE LEARNING AND GAME AI Playing games with tree search Getting started with neural networks Designing a neural network for Go data Learning from data: a deep-learning bot Deploying bots in the wild Learning by practice: reinforcement learning Reinforcement learning with policy gradients Reinforcement learning with value methods Reinforcement learning with actor-critic methods PART 3 - GREATER THAN THE SUM OF ITS PARTS AlphaGo: Bringing it all together AlphaGo Zero: Integrating tree search with reinforcement learning |
| calculus for artificial intelligence: Thomas' Calculus Weir, Joel Hass, 2008 |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Linear Algebra Done Right Sheldon Axler, 1997-07-18 This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text. |
| calculus for artificial intelligence: Artificial Intelligence Engines James V Stone, 2019-04 The brain has always had a fundamental advantage over conventional computers: it can learn. However, a new generation of artificial intelligence algorithms, in the form of deep neural networks, is rapidly eliminating that advantage. Deep neural networks rely on adaptive algorithms to master a wide variety of tasks, including cancer diagnosis, object recognition, speech recognition, robotic control, chess, poker, backgammon and Go, at super-human levels of performance. In this richly illustrated book, key neural network learning algorithms are explained informally first, followed by detailed mathematical analyses. Topics include both historically important neural networks (e.g. perceptrons), and modern deep neural networks (e.g. generative adversarial networks). Online computer programs, collated from open source repositories, give hands-on experience of neural networks, and PowerPoint slides provide support for teaching. Written in an informal style, with a comprehensive glossary, tutorial appendices (e.g. Bayes' theorem), and a list of further readings, this is an ideal introduction to the algorithmic engines of modern artificial intelligence. |
| calculus for artificial intelligence: Behavioral Mathematics for Game AI Dave Mark, 2009 Human behavior is never an exact science, making the design and programming of artificial intelligence that seeks to replicate human behavior difficult. Usually, the answers cannot be found in sterile algorithms that are often the focus of artificial intelligence programming. However, by analyzing why people behave the way we do, we can break down the process into increasingly smaller components. We can model many of those individual components in the language of logic and mathematics and then reassemble them into larger, more involved decision-making processes. Drawing from classical game theory, Behavioral Mathematics for Game AI covers both the psychological foundations of human decisions and the mathematical modeling techniques that AI designers and programmers can use to replicate them. With examples from both real life and game situations, you'll explore topics such as utility, the fallacy of rational behavior, and the inconsistencies and contradictions that human behavior often exhibits. You'll examine various ways of using statistics, formulas, and algorithms to create believable simulations and to model these dynamic, realistic, and interesting behaviors in video games. Finally, you'll be introduced to a number of tools you can use in conjunction with standard AI algorithms to make it easier to utilize the mathematical models. |
| calculus for artificial intelligence: Advanced Calculus (Revised Edition) Lynn Harold Loomis, Shlomo Zvi Sternberg, 2014-02-26 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| calculus for artificial intelligence: Machine Learning Paul Wilmott, 2019-05-20 Machine Learning: An Applied Mathematics Introduction covers the essential mathematics behind all of the following topics - K Nearest Neighbours; K Means Clustering; Naïve Bayes Classifier; Regression Methods; Support Vector Machines; Self-Organizing Maps; Decision Trees; Neural Networks; Reinforcement Learning |
| calculus for artificial intelligence: A Thousand Brains Jeff Hawkins, 2021-03-02 A bestselling author, neuroscientist, and computer engineer unveils a theory of intelligence that will revolutionize our understanding of the brain and the future of AI. For all of neuroscience's advances, we've made little progress on its biggest question: How do simple cells in the brain create intelligence? Jeff Hawkins and his team discovered that the brain uses maplike structures to build a model of the world—not just one model, but hundreds of thousands of models of everything we know. This discovery allows Hawkins to answer important questions about how we perceive the world, why we have a sense of self, and the origin of high-level thought. A Thousand Brains heralds a revolution in the understanding of intelligence. It is a big-think book, in every sense of the word. One of the Financial Times' Best Books of 2021 One of Bill Gates' Five Favorite Books of 2021 |
| calculus for artificial intelligence: Artificial and Mathematical Theory of Computation Vladimir Lifschitz, 2012-12-02 Artificial and Mathematical Theory of Computation is a collection of papers that discusses the technical, historical, and philosophical problems related to artificial intelligence and the mathematical theory of computation. Papers cover the logical approach to artificial intelligence; knowledge representation and common sense reasoning; automated deduction; logic programming; nonmonotonic reasoning and circumscription. One paper suggests that the design of parallel programming languages will invariably become more sophisticated as human skill in programming and software developments improves to attain faster running programs. An example of metaprogramming to systems concerns the design and control of operations of factory devices, such as robots and numerically controlled machine tools. Metaprogramming involves two design aspects: that of the activity of a single device and that of the interaction with other devices. One paper cites the application of artificial intelligence pertaining to the project proof checker for first-order logic at the Stanford Artificial Intelligence Laboratory. Another paper explains why the bisection algorithm widely used in computer science does not work. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering, as well as, for computer programmers and designers of industrial processes. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Intelligent Mathematics: Computational Analysis George A. Anastassiou, 2011-03-19 Knowledge can be modeled and computed using computational mathematical methods, then lead to real world conclusions. The strongly related to that Computational Analysis is a very large area with lots of applications. This monograph includes a great variety of topics of Computational Analysis. We present: probabilistic wavelet approximations, constrained abstract approximation theory, shape preserving weighted approximation, non positive approximations to definite integrals, discrete best approximation, approximation theory of general Picard singular operators including global smoothness preservation property, fractional singular operators. We also deal with non-isotropic general Picard singular multivariate operators and q-Gauss-Weierstrass singular q-integral operators. We talk about quantitative approximations by shift-invariant univariate and multivariate integral operators, nonlinear neural networks approximation, convergence with rates of positive linear operators, quantitative approximation by bounded linear operators, univariate and multivariate quantitative approximation by stochastic positive linear operators on univariate and multivariate stochastic processes. We further present right fractional calculus and give quantitative fractional Korovkin theory of positive linear operators. We also give analytical inequalities, fractional Opial inequalities, fractional identities and inequalities regarding fractional integrals. We further deal with semi group operator approximation, simultaneous Feller probabilistic approximation. We also present Fuzzy singular operator approximations. We give transfers from real to fuzzy approximation and talk about fuzzy wavelet and fuzzy neural networks approximations, fuzzy fractional calculus and fuzzy Ostrowski inequality. We talk about discrete fractional calculus, nabla discrete fractional calculus and inequalities. We study the q-inequalities, and q-fractional inequalities. We further study time scales: delta and nabla approaches, duality principle and inequalities. We introduce delta and nabla time scales fractional calculus and inequalities. We finally study convergence with rates of approximate solutions to exact solution of multivariate Dirichlet problem and multivariate heat equation, and discuss the uniqueness of solution of general evolution partial differential equation \ in multivariate time. The exposed results are expected to find applications to: applied and computational mathematics, stochastics, engineering, artificial intelligence, vision, complexity and machine learning. This monograph is suitable for graduate students and researchers. |
| calculus for artificial intelligence: 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. |
| calculus for artificial intelligence: Machine Learning Mathematics Samuel Hack, 2021-01-08 |
| calculus for artificial intelligence: The First 100 Days of Your Book Joel Stafford, 2019-09-04 Today having an excellent book with an great idea isn't enough for success. Over 2,000,000 books published every year, don't expect the crowd to pick up your book and say it is a masterwork even if it is. I swear you won't find any marketing bullshit in this book: No social media is the king crap No just order a gold marketing package and problem is solved No do a giveaway or kindle free promotion and everybody will buy your book I collected all the working marketing steps for those who want to make an impact with their books. You won't find any of the words strategy or planning in this book. I'm a practical guy and so I try to keep the bullshit and time-wasting things away from you, but I deeply believe that there are methods that should be shared with the new authors who have limited resources to do marketing. I'm focusing mainly on KDP authors, since it is the best platform to publish indie books in 2019. You will find small steps (not time-consuming), and some bigger steps in this short book which will be effective in long term. I tried to keep these steps in a linear timeline as it may happen even in real life. I hope you will enjoy reading this book, and you will find some useful resources and unique tactics that will raise your book out from the crowd. |
| calculus for artificial intelligence: Machine Intelligence in Design Automation Rohit Sharma, 2018-03-13 This book presents a hands-on approach for solving electronic design automation problems with modern machine intelligence techniques by including step-by-step development of commercial grade design applications including resistance estimation, capacitance estimation, cell classification and others using dataset extracted from designs at 20nm. It walks the reader step by step in building solution flow for EDA problems with Python and Tensorflow.Intended audience includes design automation engineers, managers, executives, research professionals, graduate students, Machine learning enthusiasts, EDA and CAD developers, mentors, and the merely inquisitive. It is organized to serve as a compendium to a beginner, a ready reference to intermediate and source for an expert. |
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