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Foundations of Statistical Algorithms

Author : Claus Weihs

Publisher : CRC Press

Page : 495 pages

File Size : 50,48 MB

Release : 2013-12-09

Category : Mathematics

ISBN : 1439878870

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Book Description

A new and refreshingly different approach to presenting the foundations of statistical algorithms, Foundations of Statistical Algorithms: With References to R Packages reviews the historical development of basic algorithms to illuminate the evolution of today’s more powerful statistical algorithms. It emphasizes recurring themes in all statistical algorithms, including computation, assessment and verification, iteration, intuition, randomness, repetition and parallelization, and scalability. Unique in scope, the book reviews the upcoming challenge of scaling many of the established techniques to very large data sets and delves into systematic verification by demonstrating how to derive general classes of worst case inputs and emphasizing the importance of testing over a large number of different inputs. Broadly accessible, the book offers examples, exercises, and selected solutions in each chapter as well as access to a supplementary website. After working through the material covered in the book, readers should not only understand current algorithms but also gain a deeper understanding of how algorithms are constructed, how to evaluate new algorithms, which recurring principles are used to tackle some of the tough problems statistical programmers face, and how to take an idea for a new method and turn it into something practically useful.



Foundations of Statistical Natural Language Processing

Author : Christopher Manning

Publisher : MIT Press

Page : 719 pages

File Size : 30,84 MB

Release : 1999-05-28

Category : Language Arts & Disciplines

ISBN : 0262303795

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Book Description

Statistical approaches to processing natural language text have become dominant in recent years. This foundational text is the first comprehensive introduction to statistical natural language processing (NLP) to appear. The book contains all the theory and algorithms needed for building NLP tools. It provides broad but rigorous coverage of mathematical and linguistic foundations, as well as detailed discussion of statistical methods, allowing students and researchers to construct their own implementations. The book covers collocation finding, word sense disambiguation, probabilistic parsing, information retrieval, and other applications.



Statistical Foundations of Data Science

Author : Jianqing Fan

Publisher : CRC Press

Page : 942 pages

File Size : 50,68 MB

Release : 2020-09-21

Category : Mathematics

ISBN : 0429527616

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Book Description

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.



Foundations of Statistical Algorithms

Author : Claus Weihs

Publisher : CRC Press

Page : 502 pages

File Size : 32,41 MB

Release : 2013-12-09

Category : Mathematics

ISBN : 1439878854

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Book Description

A new and refreshingly different approach to presenting the foundations of statistical algorithms, Foundations of Statistical Algorithms: With References to R Packages reviews the historical development of basic algorithms to illuminate the evolution of today’s more powerful statistical algorithms. It emphasizes recurring themes in all statistical algorithms, including computation, assessment and verification, iteration, intuition, randomness, repetition and parallelization, and scalability. Unique in scope, the book reviews the upcoming challenge of scaling many of the established techniques to very large data sets and delves into systematic verification by demonstrating how to derive general classes of worst case inputs and emphasizing the importance of testing over a large number of different inputs. Broadly accessible, the book offers examples, exercises, and selected solutions in each chapter as well as access to a supplementary website. After working through the material covered in the book, readers should not only understand current algorithms but also gain a deeper understanding of how algorithms are constructed, how to evaluate new algorithms, which recurring principles are used to tackle some of the tough problems statistical programmers face, and how to take an idea for a new method and turn it into something practically useful.



Foundations of Data Science

Author : Avrim Blum

Publisher : Cambridge University Press

Page : 433 pages

File Size : 21,81 MB

Release : 2020-01-23

Category : Computers

ISBN : 1108617360

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Book Description

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.



Algorithms for Data Science

Author : Brian Steele

Publisher : Springer

Page : 438 pages

File Size : 41,86 MB

Release : 2016-12-25

Category : Computers

ISBN : 3319457977

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Book Description

This textbook on practical data analytics unites fundamental principles, algorithms, and data. Algorithms are the keystone of data analytics and the focal point of this textbook. Clear and intuitive explanations of the mathematical and statistical foundations make the algorithms transparent. But practical data analytics requires more than just the foundations. Problems and data are enormously variable and only the most elementary of algorithms can be used without modification. Programming fluency and experience with real and challenging data is indispensable and so the reader is immersed in Python and R and real data analysis. By the end of the book, the reader will have gained the ability to adapt algorithms to new problems and carry out innovative analyses. This book has three parts:(a) Data Reduction: Begins with the concepts of data reduction, data maps, and information extraction. The second chapter introduces associative statistics, the mathematical foundation of scalable algorithms and distributed computing. Practical aspects of distributed computing is the subject of the Hadoop and MapReduce chapter.(b) Extracting Information from Data: Linear regression and data visualization are the principal topics of Part II. The authors dedicate a chapter to the critical domain of Healthcare Analytics for an extended example of practical data analytics. The algorithms and analytics will be of much interest to practitioners interested in utilizing the large and unwieldly data sets of the Centers for Disease Control and Prevention's Behavioral Risk Factor Surveillance System.(c) Predictive Analytics Two foundational and widely used algorithms, k-nearest neighbors and naive Bayes, are developed in detail. A chapter is dedicated to forecasting. The last chapter focuses on streaming data and uses publicly accessible data streams originating from the Twitter API and the NASDAQ stock market in the tutorials. This book is intended for a one- or two-semester course in data analytics for upper-division undergraduate and graduate students in mathematics, statistics, and computer science. The prerequisites are kept low, and students with one or two courses in probability or statistics, an exposure to vectors and matrices, and a programming course will have no difficulty. The core material of every chapter is accessible to all with these prerequisites. The chapters often expand at the close with innovations of interest to practitioners of data science. Each chapter includes exercises of varying levels of difficulty. The text is eminently suitable for self-study and an exceptional resource for practitioners.



An Introduction to Statistical Learning

Author : Gareth James

Publisher : Springer Nature

Page : 617 pages

File Size : 38,31 MB

Release : 2023-08-01

Category : Mathematics

ISBN : 3031387473

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Book Description

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance, marketing, and astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. This book is targeted at statisticians and non-statisticians alike, who wish to use cutting-edge statistical learning techniques to analyze their data. Four of the authors co-wrote An Introduction to Statistical Learning, With Applications in R (ISLR), which has become a mainstay of undergraduate and graduate classrooms worldwide, as well as an important reference book for data scientists. One of the keys to its success was that each chapter contains a tutorial on implementing the analyses and methods presented in the R scientific computing environment. However, in recent years Python has become a popular language for data science, and there has been increasing demand for a Python-based alternative to ISLR. Hence, this book (ISLP) covers the same materials as ISLR but with labs implemented in Python. These labs will be useful both for Python novices, as well as experienced users.



Introduction to Data Science

Author : Rafael A. Irizarry

Publisher : CRC Press

Page : 836 pages

File Size : 39,31 MB

Release : 2019-11-20

Category : Mathematics

ISBN : 1000708039

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Book Description

Introduction to Data Science: Data Analysis and Prediction Algorithms with R introduces concepts and skills that can help you tackle real-world data analysis challenges. It covers concepts from probability, statistical inference, linear regression, and machine learning. It also helps you develop skills such as R programming, data wrangling, data visualization, predictive algorithm building, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation. This book is a textbook for a first course in data science. No previous knowledge of R is necessary, although some experience with programming may be helpful. The book is divided into six parts: R, data visualization, statistics with R, data wrangling, machine learning, and productivity tools. Each part has several chapters meant to be presented as one lecture. The author uses motivating case studies that realistically mimic a data scientist’s experience. He starts by asking specific questions and answers these through data analysis so concepts are learned as a means to answering the questions. Examples of the case studies included are: US murder rates by state, self-reported student heights, trends in world health and economics, the impact of vaccines on infectious disease rates, the financial crisis of 2007-2008, election forecasting, building a baseball team, image processing of hand-written digits, and movie recommendation systems. The statistical concepts used to answer the case study questions are only briefly introduced, so complementing with a probability and statistics textbook is highly recommended for in-depth understanding of these concepts. If you read and understand the chapters and complete the exercises, you will be prepared to learn the more advanced concepts and skills needed to become an expert.



Ensemble Methods

Author : Zhi-Hua Zhou

Publisher : CRC Press

Page : 238 pages

File Size : 15,56 MB

Release : 2012-06-06

Category : Business & Economics

ISBN : 1439830037

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Book Description

An up-to-date, self-contained introduction to a state-of-the-art machine learning approach, Ensemble Methods: Foundations and Algorithms shows how these accurate methods are used in real-world tasks. It gives you the necessary groundwork to carry out further research in this evolving field. After presenting background and terminology, the book covers the main algorithms and theories, including Boosting, Bagging, Random Forest, averaging and voting schemes, the Stacking method, mixture of experts, and diversity measures. It also discusses multiclass extension, noise tolerance, error-ambiguity and bias-variance decompositions, and recent progress in information theoretic diversity. Moving on to more advanced topics, the author explains how to achieve better performance through ensemble pruning and how to generate better clustering results by combining multiple clusterings. In addition, he describes developments of ensemble methods in semi-supervised learning, active learning, cost-sensitive learning, class-imbalance learning, and comprehensibility enhancement.



Computer Age Statistical Inference

Author : Bradley Efron

Publisher : Cambridge University Press

Page : 496 pages

File Size : 38,54 MB

Release : 2016-07-21

Category : Mathematics

ISBN : 1108107958

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Book Description

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.