| calculus for data analytics: Mathematical Foundations for Data Analysis Jeff M. Phillips, 2021-03-29 This textbook, suitable for an early undergraduate up to a graduate course, provides an overview of many basic principles and techniques needed for modern data analysis. In particular, this book was designed and written as preparation for students planning to take rigorous Machine Learning and Data Mining courses. It introduces key conceptual tools necessary for data analysis, including concentration of measure and PAC bounds, cross validation, gradient descent, and principal component analysis. It also surveys basic techniques in supervised (regression and classification) and unsupervised learning (dimensionality reduction and clustering) through an accessible, simplified presentation. Students are recommended to have some background in calculus, probability, and linear algebra. Some familiarity with programming and algorithms is useful to understand advanced topics on computational techniques. |
| calculus for data analytics: Foundations of Data Science Avrim Blum, John Hopcroft, Ravindran Kannan, 2020-01-23 This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data. |
| calculus for data analytics: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| calculus for data analytics: 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 data analytics: Probability and Statistics for Data Science Norman Matloff, 2019-06-21 Probability and Statistics for Data Science: Math + R + Data covers math stat—distributions, expected value, estimation etc.—but takes the phrase Data Science in the title quite seriously: * Real datasets are used extensively. * All data analysis is supported by R coding. * Includes many Data Science applications, such as PCA, mixture distributions, random graph models, Hidden Markov models, linear and logistic regression, and neural networks. * Leads the student to think critically about the how and why of statistics, and to see the big picture. * Not theorem/proof-oriented, but concepts and models are stated in a mathematically precise manner. Prerequisites are calculus, some matrix algebra, and some experience in programming. Norman Matloff is a professor of computer science at the University of California, Davis, and was formerly a statistics professor there. He is on the editorial boards of the Journal of Statistical Software and The R Journal. His book Statistical Regression and Classification: From Linear Models to Machine Learning was the recipient of the Ziegel Award for the best book reviewed in Technometrics in 2017. He is a recipient of his university's Distinguished Teaching Award. |
| calculus for data analytics: Data Science and Machine Learning Dirk P. Kroese, Zdravko Botev, Thomas Taimre, Radislav Vaisman, 2019-11-20 Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code |
| calculus for data analytics: Data Science Ivo D. Dinov, Milen Velchev Velev, 2021-12-06 The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the problems of time. The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public. |
| calculus for data analytics: Data Science from Scratch Joel Grus, 2015-04-14 Data science libraries, frameworks, modules, and toolkits are great for doing data science, but they’re also a good way to dive into the discipline without actually understanding data science. In this book, you’ll learn how many of the most fundamental data science tools and algorithms work by implementing them from scratch. If you have an aptitude for mathematics and some programming skills, author Joel Grus will help you get comfortable with the math and statistics at the core of data science, and with hacking skills you need to get started as a data scientist. Today’s messy glut of data holds answers to questions no one’s even thought to ask. This book provides you with the know-how to dig those answers out. Get a crash course in Python Learn the basics of linear algebra, statistics, and probability—and understand how and when they're used in data science Collect, explore, clean, munge, and manipulate data Dive into the fundamentals of machine learning Implement models such as k-nearest Neighbors, Naive Bayes, linear and logistic regression, decision trees, neural networks, and clustering Explore recommender systems, natural language processing, network analysis, MapReduce, and databases |
| calculus for data analytics: Statistics and Data Analysis for Financial Engineering David Ruppert, David S. Matteson, 2015-04-21 The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest. |
| calculus for data analytics: All of Statistics Larry Wasserman, 2013-12-11 Taken literally, the title All of Statistics is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data. |
| calculus for data analytics: 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. |
| calculus for data analytics: Mathematica Data Analysis Sergiy Suchok, 2015-12-24 Learn and explore the fundamentals of data analysis with power of Mathematica About This Book Use the power of Mathematica to analyze data in your applications Discover the capabilities of data classification and pattern recognition offered by Mathematica Use hundreds of algorithms for time series analysis to predict the future Who This Book Is For The book is for those who want to learn to use the power of Mathematica to analyze and process data. Perhaps you are already familiar with data analysis but have never used Mathematica, or you know Mathematica but you are new to data analysis. With the help of this book, you will be able to quickly catch up on the key points for a successful start. What You Will Learn Import data from different sources to Mathematica Link external libraries with programs written in Mathematica Classify data and partition them into clusters Recognize faces, objects, text, and barcodes Use Mathematica functions for time series analysis Use algorithms for statistical data processing Predict the result based on the observations In Detail There are many algorithms for data analysis and it's not always possible to quickly choose the best one for each case. Implementation of the algorithms takes a lot of time. With the help of Mathematica, you can quickly get a result from the use of a particular method, because this system contains almost all the known algorithms for data analysis. If you are not a programmer but you need to analyze data, this book will show you the capabilities of Mathematica when just few strings of intelligible code help to solve huge tasks from statistical issues to pattern recognition. If you're a programmer, with the help of this book, you will learn how to use the library of algorithms implemented in Mathematica in your programs, as well as how to write algorithm testing procedure. With each chapter, you'll be more immersed in the special world of Mathematica. Along with intuitive queries for data processing, we will highlight the nuances and features of this system, allowing you to build effective analysis systems. With the help of this book, you will learn how to optimize the computations by combining your libraries with the Mathematica kernel. Style and approach This book takes a step-by-step approach, accompanied by examples, so you get a better understanding of the logic of writing algorithms for data analysis in Mathematica. We provide a detailed explanation of all the nuances of the Mathematica language, no matter what your level of experience is. |
| calculus for data analytics: 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 data analytics: Functional and Shape Data Analysis Anuj Srivastava, Eric P. Klassen, 2016-10-03 This textbook for courses on function data analysis and shape data analysis describes how to define, compare, and mathematically represent shapes, with a focus on statistical modeling and inference. It is aimed at graduate students in analysis in statistics, engineering, applied mathematics, neuroscience, biology, bioinformatics, and other related areas. The interdisciplinary nature of the broad range of ideas covered—from introductory theory to algorithmic implementations and some statistical case studies—is meant to familiarize graduate students with an array of tools that are relevant in developing computational solutions for shape and related analyses. These tools, gleaned from geometry, algebra, statistics, and computational science, are traditionally scattered across different courses, departments, and disciplines; Functional and Shape Data Analysis offers a unified, comprehensive solution by integrating the registration problem into shape analysis, better preparing graduate students for handling future scientific challenges. Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation. |
| calculus for data analytics: Data Science and Predictive Analytics Ivo D. Dinov, 2023-02-16 This textbook integrates important mathematical foundations, efficient computational algorithms, applied statistical inference techniques, and cutting-edge machine learning approaches to address a wide range of crucial biomedical informatics, health analytics applications, and decision science challenges. Each concept in the book includes a rigorous symbolic formulation coupled with computational algorithms and complete end-to-end pipeline protocols implemented as functional R electronic markdown notebooks. These workflows support active learning and demonstrate comprehensive data manipulations, interactive visualizations, and sophisticated analytics. The content includes open problems, state-of-the-art scientific knowledge, ethical integration of heterogeneous scientific tools, and procedures for systematic validation and dissemination of reproducible research findings. Complementary to the enormous challenges related to handling, interrogating, and understanding massive amounts of complex structured and unstructured data, there are unique opportunities that come with access to a wealth of feature-rich, high-dimensional, and time-varying information. The topics covered in Data Science and Predictive Analytics address specific knowledge gaps, resolve educational barriers, and mitigate workforce information-readiness and data science deficiencies. Specifically, it provides a transdisciplinary curriculum integrating core mathematical principles, modern computational methods, advanced data science techniques, model-based machine learning, model-free artificial intelligence, and innovative biomedical applications. The book’s fourteen chapters start with an introduction and progressively build foundational skills from visualization to linear modeling, dimensionality reduction, supervised classification, black-box machine learning techniques, qualitative learning methods, unsupervised clustering, model performance assessment, feature selection strategies, longitudinal data analytics, optimization, neural networks, and deep learning. The second edition of the book includes additional learning-based strategies utilizing generative adversarial networks, transfer learning, and synthetic data generation, as well as eight complementary electronic appendices. This textbook is suitable for formal didactic instructor-guided course education, as well as for individual or team-supported self-learning. The material is presented at the upper-division and graduate-level college courses and covers applied and interdisciplinary mathematics, contemporary learning-based data science techniques, computational algorithm development, optimization theory, statistical computing, and biomedical sciences. The analytical techniques and predictive scientific methods described in the book may be useful to a wide range of readers, formal and informal learners, college instructors, researchers, and engineers throughout the academy, industry, government, regulatory, funding, and policy agencies. The supporting book website provides many examples, datasets, functional scripts, complete electronic notebooks, extensive appendices, and additional materials. |
| calculus for data analytics: Machine Learning Cookbook with Python Rehan Guha, 2020-11-12 A Cookbook that will help you implement Machine Learning algorithms and techniques by building real-world projects Ê KEY FEATURESÊ Learn how to handle an entire Machine Learning Pipeline supported with adequate mathematics. Create Predictive Models and choose the right model for various types of Datasets. Learn the art of tuning a model to improve accuracy as per Business requirements. Get familiar with concepts related to Data Analytics with Visualization, Data Science and Machine Learning. DESCRIPTION Machine Learning does not have to be intimidating at all. This book focuses on the concepts of Machine Learning and Data Analytics with mathematical explanations and programming examples. All the codes are written in Python as it is one of the most popular programming languages used for Data Science and Machine Learning. Here I have leveraged multiple libraries like NumPy, Pandas, scikit-learn, etc. to ease our task and not reinvent the wheel. There are five projects in total, each addressing a unique problem. With the recipes in this cookbook, one will learn how to solve Machine Learning problems for real-time data and perform Data Analysis and Analytics, Classification, and beyond. The datasets used are also unique and will help one to think, understand the problem and proceed towards the goal. The book is not saturated with Mathematics, but mostly all the Mathematical concepts are covered for the important topics. Every chapter typically starts with some theory and prerequisites, and then it gradually dives into the implementation of the same concept using Python, keeping a project in the background.Ê Ê WHAT WILL YOU LEARN Understand the working of the O.S.E.M.N. framework in Data Science.Ê Get familiar with the end-to-end implementation of Machine Learning Pipeline. Learn how to implement Machine Learning algorithms and concepts using Python. Learn how to build a Predictive Model for a Business case. WHO THIS BOOK IS FORÊ This cookbook is meant for anybody who is passionate enough to get into the World of Machine Learning and has a preliminary understanding of the Basics of Linear Algebra, Calculus, Probability, and Statistics. This book also serves as a reference guidebook for intermediate Machine Learning practitioners. Ê TABLE OF CONTENTS 1. Boston Crime 2. World Happiness Report 3. Iris Species 4. Credit Card Fraud Detection 5. Heart Disease UCI |
| calculus for data analytics: 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 data analytics: Data Science For Dummies Lillian Pierson, 2021-08-20 Monetize your company’s data and data science expertise without spending a fortune on hiring independent strategy consultants to help What if there was one simple, clear process for ensuring that all your company’s data science projects achieve a high a return on investment? What if you could validate your ideas for future data science projects, and select the one idea that’s most prime for achieving profitability while also moving your company closer to its business vision? There is. Industry-acclaimed data science consultant, Lillian Pierson, shares her proprietary STAR Framework – A simple, proven process for leading profit-forming data science projects. Not sure what data science is yet? Don’t worry! Parts 1 and 2 of Data Science For Dummies will get all the bases covered for you. And if you’re already a data science expert? Then you really won’t want to miss the data science strategy and data monetization gems that are shared in Part 3 onward throughout this book. Data Science For Dummies demonstrates: The only process you’ll ever need to lead profitable data science projects Secret, reverse-engineered data monetization tactics that no one’s talking about The shocking truth about how simple natural language processing can be How to beat the crowd of data professionals by cultivating your own unique blend of data science expertise Whether you’re new to the data science field or already a decade in, you’re sure to learn something new and incredibly valuable from Data Science For Dummies. Discover how to generate massive business wins from your company’s data by picking up your copy today. |
| calculus for data analytics: 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 data analytics: Statistical Foundations of Data Science Jianqing Fan, Runze Li, Cun-Hui Zhang, Hui Zou, 2020-09-21 Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning. |
| calculus for data analytics: Analysis I Terence Tao, 2016-08-29 This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory. |
| calculus for data analytics: Real Analysis and Probability R. M. Dudley, 2018-02-01 Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory. |
| calculus for data analytics: Principles of Data Science Sinan Ozdemir, 2016-12-16 Learn the techniques and math you need to start making sense of your data About This Book Enhance your knowledge of coding with data science theory for practical insight into data science and analysis More than just a math class, learn how to perform real-world data science tasks with R and Python Create actionable insights and transform raw data into tangible value Who This Book Is For You should be fairly well acquainted with basic algebra and should feel comfortable reading snippets of R/Python as well as pseudo code. You should have the urge to learn and apply the techniques put forth in this book on either your own data sets or those provided to you. If you have the basic math skills but want to apply them in data science or you have good programming skills but lack math, then this book is for you. What You Will Learn Get to know the five most important steps of data science Use your data intelligently and learn how to handle it with care Bridge the gap between mathematics and programming Learn about probability, calculus, and how to use statistical models to control and clean your data and drive actionable results Build and evaluate baseline machine learning models Explore the most effective metrics to determine the success of your machine learning models Create data visualizations that communicate actionable insights Read and apply machine learning concepts to your problems and make actual predictions In Detail Need to turn your skills at programming into effective data science skills? Principles of Data Science is created to help you join the dots between mathematics, programming, and business analysis. With this book, you'll feel confident about asking—and answering—complex and sophisticated questions of your data to move from abstract and raw statistics to actionable ideas. With a unique approach that bridges the gap between mathematics and computer science, this books takes you through the entire data science pipeline. Beginning with cleaning and preparing data, and effective data mining strategies and techniques, you'll move on to build a comprehensive picture of how every piece of the data science puzzle fits together. Learn the fundamentals of computational mathematics and statistics, as well as some pseudocode being used today by data scientists and analysts. You'll get to grips with machine learning, discover the statistical models that help you take control and navigate even the densest datasets, and find out how to create powerful visualizations that communicate what your data means. Style and approach This is an easy-to-understand and accessible tutorial. It is a step-by-step guide with use cases, examples, and illustrations to get you well-versed with the concepts of data science. Along with explaining the fundamentals, the book will also introduce you to slightly advanced concepts later on and will help you implement these techniques in the real world. |
| calculus for data analytics: 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. |
| calculus for data analytics: Data Science for Undergraduates National Academies of Sciences, Engineering, and Medicine, Division of Behavioral and Social Sciences and Education, Board on Science Education, Division on Engineering and Physical Sciences, Committee on Applied and Theoretical Statistics, Board on Mathematical Sciences and Analytics, Computer Science and Telecommunications Board, Committee on Envisioning the Data Science Discipline: The Undergraduate Perspective, 2018-11-11 Data science is emerging as a field that is revolutionizing science and industries alike. Work across nearly all domains is becoming more data driven, affecting both the jobs that are available and the skills that are required. As more data and ways of analyzing them become available, more aspects of the economy, society, and daily life will become dependent on data. It is imperative that educators, administrators, and students begin today to consider how to best prepare for and keep pace with this data-driven era of tomorrow. Undergraduate teaching, in particular, offers a critical link in offering more data science exposure to students and expanding the supply of data science talent. Data Science for Undergraduates: Opportunities and Options offers a vision for the emerging discipline of data science at the undergraduate level. This report outlines some considerations and approaches for academic institutions and others in the broader data science communities to help guide the ongoing transformation of this field. |
| calculus for data analytics: Data Science for Mathematicians Nathan Carter, 2020-09-15 Mathematicians have skills that, if deepened in the right ways, would enable them to use data to answer questions important to them and others, and report those answers in compelling ways. Data science combines parts of mathematics, statistics, computer science. Gaining such power and the ability to teach has reinvigorated the careers of mathematicians. This handbook will assist mathematicians to better understand the opportunities presented by data science. As it applies to the curriculum, research, and career opportunities, data science is a fast-growing field. Contributors from both academics and industry present their views on these opportunities and how to advantage them. |
| calculus for data analytics: The Statistical Analysis of Experimental Data John Mandel, 2012-06-08 First half of book presents fundamental mathematical definitions, concepts, and facts while remaining half deals with statistics primarily as an interpretive tool. Well-written text, numerous worked examples with step-by-step presentation. Includes 116 tables. |
| calculus for data analytics: A Modern Introduction to Probability and Statistics F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester, 2006-03-30 Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books |
| calculus for data analytics: Outliers in Control Engineering Paweł D. Domański, YangQuan Chen, Maciej Ławryńczuk, 2022-03-07 Outliers play an important, though underestimated, role in control engineering. Traditionally they are unseen and neglected. In opposition, industrial practice gives frequent examples of their existence and their mostly negative impacts on the control quality. The origin of outliers is never fully known. Some of them are generated externally to the process (exogenous), like for instance erroneous observations, data corrupted by control systems or the effect of human intervention. Such outliers appear occasionally with some unknow probability shifting real value often to some strange and nonsense value. They are frequently called deviants, anomalies or contaminants. In most cases we are interested in their detection and removal. However, there exists the second kind of outliers. Quite often strange looking data observations are not artificial data occurrences. They may be just representatives of the underlying generation mechanism being inseparable internal part of the process (endogenous outliers). In such a case they are not wrong and should be treated with cautiousness, as they may include important information about the dynamic nature of the process. As such they cannot be neglected nor simply removed. The Outlier should be detected, labelled and suitably treated. These activities cannot be performed without proper analytical tools and modeling approaches. There are dozens of methods proposed by scientists, starting from Gaussian-based statistical scoring up to data mining artificial intelligence tools. The research presented in this book presents novel approach incorporating non-Gaussian statistical tools and fractional calculus approach revealing new data analytics applied to this important and challenging task. The proposed book includes a collection of contributions addressing different yet cohesive subjects, like dynamic modelling, classical control, advanced control, fractional calculus, statistical analytics focused on an ultimate goal: robust and outlier-proof analysis. All studied problems show that outliers play an important role and classical methods, in which outlier are not taken into account, do not give good results. Applications from different engineering areas are considered such as semiconductor process control and monitoring, MIMO peltier temperature control and health monitoring, networked control systems, and etc. |
| calculus for data analytics: Data Science for Business Foster Provost, Tom Fawcett, 2013-07-27 Written by renowned data science experts Foster Provost and Tom Fawcett, Data Science for Business introduces the fundamental principles of data science, and walks you through the data-analytic thinking necessary for extracting useful knowledge and business value from the data you collect. This guide also helps you understand the many data-mining techniques in use today. Based on an MBA course Provost has taught at New York University over the past ten years, Data Science for Business provides examples of real-world business problems to illustrate these principles. You’ll not only learn how to improve communication between business stakeholders and data scientists, but also how participate intelligently in your company’s data science projects. You’ll also discover how to think data-analytically, and fully appreciate how data science methods can support business decision-making. Understand how data science fits in your organization—and how you can use it for competitive advantage Treat data as a business asset that requires careful investment if you’re to gain real value Approach business problems data-analytically, using the data-mining process to gather good data in the most appropriate way Learn general concepts for actually extracting knowledge from data Apply data science principles when interviewing data science job candidates |
| calculus for data analytics: Doing Math with Python Amit Saha, 2015-08-01 Doing Math with Python shows you how to use Python to delve into high school–level math topics like statistics, geometry, probability, and calculus. You’ll start with simple projects, like a factoring program and a quadratic-equation solver, and then create more complex projects once you’ve gotten the hang of things. Along the way, you’ll discover new ways to explore math and gain valuable programming skills that you’ll use throughout your study of math and computer science. Learn how to: –Describe your data with statistics, and visualize it with line graphs, bar charts, and scatter plots –Explore set theory and probability with programs for coin flips, dicing, and other games of chance –Solve algebra problems using Python’s symbolic math functions –Draw geometric shapes and explore fractals like the Barnsley fern, the Sierpinski triangle, and the Mandelbrot set –Write programs to find derivatives and integrate functions Creative coding challenges and applied examples help you see how you can put your new math and coding skills into practice. You’ll write an inequality solver, plot gravity’s effect on how far a bullet will travel, shuffle a deck of cards, estimate the area of a circle by throwing 100,000 darts at a board, explore the relationship between the Fibonacci sequence and the golden ratio, and more. Whether you’re interested in math but have yet to dip into programming or you’re a teacher looking to bring programming into the classroom, you’ll find that Python makes programming easy and practical. Let Python handle the grunt work while you focus on the math. Uses Python 3 |
| calculus for data analytics: Bayesian Data Analysis, Third Edition Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, Donald B. Rubin, 2013-11-01 Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page. |
| calculus for data analytics: 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) |
| calculus for data analytics: Machine Learning Kevin P. Murphy, 2012-08-24 A comprehensive introduction to machine learning that uses probabilistic models and inference as a unifying approach. Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students. |
| calculus for data analytics: Principles of Statistics M. G. Bulmer, 2012-04-26 Concise description of classical statistics, from basic dice probabilities to modern regression analysis. Equal stress on theory and applications. Moderate difficulty; only basic calculus required. Includes problems with answers. |
| calculus for data analytics: Guide to Intelligent Data Science Michael R. Berthold, Christian Borgelt, Frank Höppner, Frank Klawonn, Rosaria Silipo, 2020-08-06 Making use of data is not anymore a niche project but central to almost every project. With access to massive compute resources and vast amounts of data, it seems at least in principle possible to solve any problem. However, successful data science projects result from the intelligent application of: human intuition in combination with computational power; sound background knowledge with computer-aided modelling; and critical reflection of the obtained insights and results. Substantially updating the previous edition, then entitled Guide to Intelligent Data Analysis, this core textbook continues to provide a hands-on instructional approach to many data science techniques, and explains how these are used to solve real world problems. The work balances the practical aspects of applying and using data science techniques with the theoretical and algorithmic underpinnings from mathematics and statistics. Major updates on techniques and subject coverage (including deep learning) are included. Topics and features: guides the reader through the process of data science, following the interdependent steps of project understanding, data understanding, data blending and transformation, modeling, as well as deployment and monitoring; includes numerous examples using the open source KNIME Analytics Platform, together with an introductory appendix; provides a review of the basics of classical statistics that support and justify many data analysis methods, and a glossary of statistical terms; integrates illustrations and case-study-style examples to support pedagogical exposition; supplies further tools and information at an associated website. This practical and systematic textbook/reference is a “need-to-have” tool for graduate and advanced undergraduate students and essential reading for all professionals who face data science problems. Moreover, it is a “need to use, need to keep” resource following one's exploration of the subject. |
| calculus for data analytics: Statistics Robin H. Lock, Patti Frazer Lock, Kari Lock Morgan, Eric F. Lock, Dennis F. Lock, 2020-10-13 Statistics: Unlocking the Power of Data, 3rd Edition is designed for an introductory statistics course focusing on data analysis with real-world applications. Students use simulation methods to effectively collect, analyze, and interpret data to draw conclusions. Randomization and bootstrap interval methods introduce the fundamentals of statistical inference, bringing concepts to life through authentically relevant examples. More traditional methods like t-tests, chi-square tests, etc. are introduced after students have developed a strong intuitive understanding of inference through randomization methods. While any popular statistical software package may be used, the authors have created StatKey to perform simulations using data sets and examples from the text. A variety of videos, activities, and a modular chapter on probability are adaptable to many classroom formats and approaches. |
| calculus for data analytics: Statistics Manual United States. Naval Ordnance Test Station, Inyokern, Calif. Research Department, Edwin L. Crow, Naval Ordnance Test Station (Inyokern, Calif.). Research Dept, Francis A. Davis, Margaret W. Maxfield, Frances R. A. Davis, 1960-01-01 A thorough collection of methods of making statistical inferences, this text covers sign tests, linear multiple, and nonlinear regression, correlation, reliability, quality control fiducial limits, Chi-Square runs, more. Includes 32 tables and charts. |
| calculus for data analytics: The Mathematics of Data Michael W. Mahoney, John C. Duchi, Anna C. Gilbert, 2018-11-15 Nothing provided |
| calculus for data analytics: The Design of Everyday Things Don Norman, 2013-11-05 Even the smartest among us can feel inept as we fail to figure out which light switch or oven burner to turn on, or whether to push, pull, or slide a door. The fault, argues this ingenious—even liberating—book, lies not in ourselves, but in product design that ignores the needs of users and the principles of cognitive psychology. The problems range from ambiguous and hidden controls to arbitrary relationships between controls and functions, coupled with a lack of feedback or other assistance and unreasonable demands on memorization. The Design of Everyday Things shows that good, usable design is possible. The rules are simple: make things visible, exploit natural relationships that couple function and control, and make intelligent use of constraints. The goal: guide the user effortlessly to the right action on the right control at the right time. In this entertaining and insightful analysis, cognitive scientist Don Norman hails excellence of design as the most important key to regaining the competitive edge in influencing consumer behavior. Now fully expanded and updated, with a new introduction by the author, The Design of Everyday Things is a powerful primer on how—and why—some products satisfy customers while others only frustrate them. |
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