Download or read book Matrices Statistics and Big Data written by S. Ejaz Ahmed and published by Springer. This book was released on 2019-08-02 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features selected, refereed papers on various aspects of statistics, matrix theory and its applications to statistics, as well as related numerical linear algebra topics and numerical solution methods, which are relevant for problems arising in statistics and in big data. The contributions were originally presented at the 25th International Workshop on Matrices and Statistics (IWMS 2016), held in Funchal (Madeira), Portugal on June 6-9, 2016. The IWMS workshop series brings together statisticians, computer scientists, data scientists and mathematicians, helping them better understand each other’s tools, and fostering new collaborations at the interface of matrix theory and statistics.

Download or read book Mathematics of Big Data written by Jeremy Kepner and published by MIT Press. This book was released on 2018-08-07 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools—including spreadsheets, databases, matrices, and graphs—developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data.

Download or read book Spectral Analysis of Large Dimensional Random Matrices written by Zhidong Bai and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.

Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Smart Grid using Big Data Analytics written by Robert C. Qiu and published by John Wiley & Sons. This book was released on 2017-04-17 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.

Download or read book Probability and Statistics for Data Science written by Norman Matloff and published by CRC Press. This book was released on 2019-06-21 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Big Data Analytics written by Saumyadipta Pyne and published by Springer. This book was released on 2016-10-12 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has a collection of articles written by Big Data experts to describe some of the cutting-edge methods and applications from their respective areas of interest, and provides the reader with a detailed overview of the field of Big Data Analytics as it is practiced today. The chapters cover technical aspects of key areas that generate and use Big Data such as management and finance; medicine and healthcare; genome, cytome and microbiome; graphs and networks; Internet of Things; Big Data standards; bench-marking of systems; and others. In addition to different applications, key algorithmic approaches such as graph partitioning, clustering and finite mixture modelling of high-dimensional data are also covered. The varied collection of themes in this volume introduces the reader to the richness of the emerging field of Big Data Analytics.

Download or read book Statistical Data Analytics written by Walter W. Piegorsch and published by John Wiley & Sons. This book was released on 2015-08-21 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Data Analytics Statistical Data Analytics Foundations for Data Mining, Informatics, and Knowledge Discovery A comprehensive introduction to statistical methods for data mining and knowledge discovery Applications of data mining and ‘big data’ increasingly take center stage in our modern, knowledge-driven society, supported by advances in computing power, automated data acquisition, social media development and interactive, linkable internet software. This book presents a coherent, technical introduction to modern statistical learning and analytics, starting from the core foundations of statistics and probability. It includes an overview of probability and statistical distributions, basics of data manipulation and visualization, and the central components of standard statistical inferences. The majority of the text extends beyond these introductory topics, however, to supervised learning in linear regression, generalized linear models, and classification analytics. Finally, unsupervised learning via dimension reduction, cluster analysis, and market basket analysis are introduced. Extensive examples using actual data (with sample R programming code) are provided, illustrating diverse informatic sources in genomics, biomedicine, ecological remote sensing, astronomy, socioeconomics, marketing, advertising and finance, among many others. Statistical Data Analytics: Focuses on methods critically used in data mining and statistical informatics. Coherently describes the methods at an introductory level, with extensions to selected intermediate and advanced techniques. Provides informative, technical details for the highlighted methods. Employs the open-source R language as the computational vehicle – along with its burgeoning collection of online packages – to illustrate many of the analyses contained in the book. Concludes each chapter with a range of interesting and challenging homework exercises using actual data from a variety of informatic application areas. This book will appeal as a classroom or training text to intermediate and advanced undergraduates, and to beginning graduate students, with sufficient background in calculus and matrix algebra. It will also serve as a source-book on the foundations of statistical informatics and data analytics to practitioners who regularly apply statistical learning to their modern data.

Download or read book Large Sample Covariance Matrices and High Dimensional Data Analysis written by Jianfeng Yao and published by Cambridge University Press. This book was released on 2015-03-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional data appear in many fields, and their analysis has become increasingly important in modern statistics. However, it has long been observed that several well-known methods in multivariate analysis become inefficient, or even misleading, when the data dimension p is larger than, say, several tens. A seminal example is the well-known inefficiency of Hotelling's T2-test in such cases. This example shows that classical large sample limits may no longer hold for high-dimensional data; statisticians must seek new limiting theorems in these instances. Thus, the theory of random matrices (RMT) serves as a much-needed and welcome alternative framework. Based on the authors' own research, this book provides a first-hand introduction to new high-dimensional statistical methods derived from RMT. The book begins with a detailed introduction to useful tools from RMT, and then presents a series of high-dimensional problems with solutions provided by RMT methods.

Download or read book Statistical Foundations of Data Science written by Jianqing Fan and published by CRC Press. This book was released on 2020-09-21 with total page 942 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Fundamentals of Data Analytics written by Rudolf Mathar and published by Springer Nature. This book was released on 2020-09-15 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic methodologies for successful data analytics. Matrix optimization and approximation are explained in detail and extensively applied to dimensionality reduction by principal component analysis and multidimensional scaling. Diffusion maps and spectral clustering are derived as powerful tools. The methodological overlap between data science and machine learning is emphasized by demonstrating how data science is used for classification as well as supervised and unsupervised learning.

Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

Download or read book Data Science in Theory and Practice written by Maria Cristina Mariani and published by John Wiley & Sons. This book was released on 2021-10-12 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: DATA SCIENCE IN THEORY AND PRACTICE EXPLORE THE FOUNDATIONS OF DATA SCIENCE WITH THIS INSIGHTFUL NEW RESOURCE Data Science in Theory and Practice delivers a comprehensive treatment of the mathematical and statistical models useful for analyzing data sets arising in various disciplines, like banking, finance, health care, bioinformatics, security, education, and social services. Written in five parts, the book examines some of the most commonly used and fundamental mathematical and statistical concepts that form the basis of data science. The authors go on to analyze various data transformation techniques useful for extracting information from raw data, long memory behavior, and predictive modeling. The book offers readers a multitude of topics all relevant to the analysis of complex data sets. Along with a robust exploration of the theory underpinning data science, it contains numerous applications to specific and practical problems. The book also provides examples of code algorithms in R and Python and provides pseudo-algorithms to port the code to any other language. Ideal for students and practitioners without a strong background in data science, readers will also learn from topics like: Analyses of foundational theoretical subjects, including the history of data science, matrix algebra and random vectors, and multivariate analysis A comprehensive examination of time series forecasting, including the different components of time series and transformations to achieve stationarity Introductions to both the R and Python programming languages, including basic data types and sample manipulations for both languages An exploration of algorithms, including how to write one and how to perform an asymptotic analysis A comprehensive discussion of several techniques for analyzing and predicting complex data sets Perfect for advanced undergraduate and graduate students in Data Science, Business Analytics, and Statistics programs, Data Science in Theory and Practice will also earn a place in the libraries of practicing data scientists, data and business analysts, and statisticians in the private sector, government, and academia.

Download or read book Mathematical Foundations of Big Data Analytics written by Vladimir Shikhman and published by Springer Nature. This book was released on 2021-02-11 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this textbook, basic mathematical models used in Big Data Analytics are presented and application-oriented references to relevant practical issues are made. Necessary mathematical tools are examined and applied to current problems of data analysis, such as brand loyalty, portfolio selection, credit investigation, quality control, product clustering, asset pricing etc. – mainly in an economic context. In addition, we discuss interdisciplinary applications to biology, linguistics, sociology, electrical engineering, computer science and artificial intelligence. For the models, we make use of a wide range of mathematics – from basic disciplines of numerical linear algebra, statistics and optimization to more specialized game, graph and even complexity theories. By doing so, we cover all relevant techniques commonly used in Big Data Analytics.Each chapter starts with a concrete practical problem whose primary aim is to motivate the study of a particular Big Data Analytics technique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinary context. Exercises serve to improve understanding of the underlying theory. Complete solutions for exercises can be consulted by the interested reader at the end of the textbook; for some which have to be solved numerically, we provide descriptions of algorithms in Python code as supplementary material.This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.

Download or read book Computational Statistics in Data Science written by Richard A. Levine and published by John Wiley & Sons. This book was released on 2022-03-23 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ein unverzichtbarer Leitfaden bei der Anwendung computergestützter Statistik in der modernen Datenwissenschaft In Computational Statistics in Data Science präsentiert ein Team aus bekannten Mathematikern und Statistikern eine fundierte Zusammenstellung von Konzepten, Theorien, Techniken und Praktiken der computergestützten Statistik für ein Publikum, das auf der Suche nach einem einzigen, umfassenden Referenzwerk für Statistik in der modernen Datenwissenschaft ist. Das Buch enthält etliche Kapitel zu den wesentlichen konkreten Bereichen der computergestützten Statistik, in denen modernste Techniken zeitgemäß und verständlich dargestellt werden. Darüber hinaus bietet Computational Statistics in Data Science einen kostenlosen Zugang zu den fertigen Einträgen im Online-Nachschlagewerk Wiley StatsRef: Statistics Reference Online. Außerdem erhalten die Leserinnen und Leser: * Eine gründliche Einführung in die computergestützte Statistik mit relevanten und verständlichen Informationen für Anwender und Forscher in verschiedenen datenintensiven Bereichen * Umfassende Erläuterungen zu aktuellen Themen in der Statistik, darunter Big Data, Datenstromverarbeitung, quantitative Visualisierung und Deep Learning Das Werk eignet sich perfekt für Forscher und Wissenschaftler sämtlicher Fachbereiche, die Techniken der computergestützten Statistik auf einem gehobenen oder fortgeschrittenen Niveau anwenden müssen. Zudem gehört Computational Statistics in Data Science in das Bücherregal von Wissenschaftlern, die sich mit der Erforschung und Entwicklung von Techniken der computergestützten Statistik und statistischen Grafiken beschäftigen.

Download or read book Data Science and Machine Learning written by Dirk P. Kroese and published by CRC Press. This book was released on 2019-11-20 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Advanced Statistical Methods in Data Science written by Ding-Geng Chen and published by Springer. This book was released on 2016-11-30 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers invited presentations from the 2nd Symposium of the ICSA- CANADA Chapter held at the University of Calgary from August 4-6, 2015. The aim of this Symposium was to promote advanced statistical methods in big-data sciences and to allow researchers to exchange ideas on statistics and data science and to embraces the challenges and opportunities of statistics and data science in the modern world. It addresses diverse themes in advanced statistical analysis in big-data sciences, including methods for administrative data analysis, survival data analysis, missing data analysis, high-dimensional and genetic data analysis, longitudinal and functional data analysis, the design and analysis of studies with response-dependent and multi-phase designs, time series and robust statistics, statistical inference based on likelihood, empirical likelihood and estimating functions. The editorial group selected 14 high-quality presentations from this successful symposium and invited the presenters to prepare a full chapter for this book in order to disseminate the findings and promote further research collaborations in this area. This timely book offers new methods that impact advanced statistical model development in big-data sciences.