Mathematical Foundations For Data Analysis

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Mathematical Foundations for Data Analysis

Jeff M. Phillips
Mathematical Foundations for Data Analysis Book PDF

Author : Jeff M. Phillips
Publisher : Springer Nature
Page : 299 pages
File Size : 41,9 Mb
Release : 2021-03-29
Category : Mathematics
ISBN : 9783030623418

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Mathematical Foundations for Data Analysis by Jeff M. Phillips Pdf

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.

Foundations of Data Science

Avrim Blum,John Hopcroft,Ravindran Kannan
Foundations of Data Science Book PDF

Author : Avrim Blum,John Hopcroft,Ravindran Kannan
Publisher : Cambridge University Press
Page : 433 pages
File Size : 45,5 Mb
Release : 2020-01-23
Category : Computers
ISBN : 9781108485067

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Foundations of Data Science by Avrim Blum,John Hopcroft,Ravindran Kannan Pdf

Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.

Mathematical Foundations of Data Science Using R

Frank Emmert-Streib,Salissou Moutari,Matthias Dehmer
Mathematical Foundations of Data Science Using R Book PDF

Author : Frank Emmert-Streib,Salissou Moutari,Matthias Dehmer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 444 pages
File Size : 47,6 Mb
Release : 2022-10-24
Category : Computers
ISBN : 9783110796179

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Mathematical Foundations of Data Science Using R by Frank Emmert-Streib,Salissou Moutari,Matthias Dehmer Pdf

The aim of the book is to help students become data scientists. Since this requires a series of courses over a considerable period of time, the book intends to accompany students from the beginning to an advanced understanding of the knowledge and skills that define a modern data scientist. The book presents a comprehensive overview of the mathematical foundations of the programming language R and of its applications to data science.

Mathematical Foundations of Big Data Analytics

Vladimir Shikhman,David Müller
Mathematical Foundations of Big Data Analytics Book PDF

Author : Vladimir Shikhman,David Müller
Publisher : Springer Nature
Page : 273 pages
File Size : 52,5 Mb
Release : 2021-02-11
Category : Computers
ISBN : 9783662625217

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Mathematical Foundations of Big Data Analytics by Vladimir Shikhman,David Müller Pdf

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.

Statistical Foundations of Data Science

Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou
Statistical Foundations of Data Science Book PDF

Author : Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou
Publisher : CRC Press
Page : 752 pages
File Size : 47,8 Mb
Release : 2020-09-21
Category : Mathematics
ISBN : 9781466510852

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Statistical Foundations of Data Science by Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou Pdf

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.

Mathematical Foundations of Time Series Analysis

Jan Beran
Mathematical Foundations of Time Series Analysis Book PDF

Author : Jan Beran
Publisher : Springer
Page : 307 pages
File Size : 41,6 Mb
Release : 2018-03-23
Category : Mathematics
ISBN : 9783319743806

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Mathematical Foundations of Time Series Analysis by Jan Beran Pdf

This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.

Mathematical Foundations of Data Science Using R

Frank Emmert-Streib,Salissou Moutari,Matthias Dehmer
Mathematical Foundations of Data Science Using R Book PDF

Author : Frank Emmert-Streib,Salissou Moutari,Matthias Dehmer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 424 pages
File Size : 54,5 Mb
Release : 2022-10-24
Category : Computers
ISBN : 9783110796063

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Mathematical Foundations of Data Science Using R by Frank Emmert-Streib,Salissou Moutari,Matthias Dehmer Pdf

The aim of the book is to help students become data scientists. Since this requires a series of courses over a considerable period of time, the book intends to accompany students from the beginning to an advanced understanding of the knowledge and skills that define a modern data scientist. The book presents a comprehensive overview of the mathematical foundations of the programming language R and of its applications to data science.

Mathematical Foundations of Network Analysis

Paul Slepian
Mathematical Foundations of Network Analysis Book PDF

Author : Paul Slepian
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642874246

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Mathematical Foundations of Network Analysis by Paul Slepian Pdf

In this book we attempt to develop the fundamental results of resistive network analysis, based upon a sound mathematical structure. The axioms upon which our development is based are Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law. In order to state these axioms precisely, and use them in the development of our network analysis, an elaborate mathematical structure is introduced, involving concepts of graph theory, linear algebra, and one dimensional algebraic topology. The graph theory and one dimensional algebraic topology used are developed from first principles; the reader needs no background in these subjects. However, we do assume that the reader has some familiarity with elementary linear algebra. It is now stylish to teach elementary linear algebra at the sophomore college level, and we feel that the require ment that the reader should be familiar with elementary linear algebra is no more demanding than the usual requirement in most electrical engineering texts that the reader should be familiar with calculus. In this book, however, no calculus is needed. Although no formal training in circuit theory is needed for an understanding of the book, such experience would certainly help the reader by presenting him with familiar examples relevant to the mathematical abstractions introduced. It is our intention in this book to exhibit the effect of the topological properties of the network upon the branch voltages and branch currents, the objects of interest in network analysis.

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators

Tailen Hsing,Randall Eubank
Theoretical Foundations of Functional Data Analysis with an Introduction to Linear Operators Book PDF

Author : Tailen Hsing,Randall Eubank
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 41,8 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9780470016916

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Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators by Tailen Hsing,Randall Eubank Pdf

Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.

Mathematics for Machine Learning

Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Mathematics for Machine Learning Book PDF

Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Publisher : Cambridge University Press
Page : 391 pages
File Size : 49,7 Mb
Release : 2020-04-23
Category : Computers
ISBN : 9781108470049

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Mathematics for Machine Learning by Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong Pdf

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

Mathematical Foundations of Infinite-Dimensional Statistical Models

Evarist Giné,Richard Nickl
Mathematical Foundations of Infinite Dimensional Statistical Models Book PDF

Author : Evarist Giné,Richard Nickl
Publisher : Cambridge University Press
Page : 705 pages
File Size : 51,9 Mb
Release : 2016
Category : Business & Economics
ISBN : 9781107043169

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Mathematical Foundations of Infinite-Dimensional Statistical Models by Evarist Giné,Richard Nickl Pdf

This book develops the theory of statistical inference in statistical models with an infinite-dimensional parameter space, including mathematical foundations and key decision-theoretic principles.

The Mathematics of Data

Michael W. Mahoney,John C. Duchi,Anna C. Gilbert
The Mathematics of Data Book PDF

Author : Michael W. Mahoney,John C. Duchi,Anna C. Gilbert
Publisher : American Mathematical Soc.
Page : 325 pages
File Size : 41,5 Mb
Release : 2018-11-15
Category : Big data
ISBN : 9781470435752

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The Mathematics of Data by Michael W. Mahoney,John C. Duchi,Anna C. Gilbert Pdf

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Foundations of Mathematical Analysis

Richard Johnsonbaugh,W.E. Pfaffenberger
Foundations of Mathematical Analysis Book PDF

Author : Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher : Courier Corporation
Page : 450 pages
File Size : 50,6 Mb
Release : 2012-09-11
Category : Mathematics
ISBN : 9780486134772

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Foundations of Mathematical Analysis by Richard Johnsonbaugh,W.E. Pfaffenberger Pdf

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Mathematical Foundations of Speech and Language Processing

Mark Johnson,Sanjeev P. Khudanpur,Mari Ostendorf,Roni Rosenfeld
Mathematical Foundations of Speech and Language Processing Book PDF

Author : Mark Johnson,Sanjeev P. Khudanpur,Mari Ostendorf,Roni Rosenfeld
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781441990174

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Mathematical Foundations of Speech and Language Processing by Mark Johnson,Sanjeev P. Khudanpur,Mari Ostendorf,Roni Rosenfeld Pdf

Speech and language technologies continue to grow in importance as they are used to create natural and efficient interfaces between people and machines, and to automatically transcribe, extract, analyze, and route information from high-volume streams of spoken and written information. The workshops on Mathematical Foundations of Speech Processing and Natural Language Modeling were held in the Fall of 2000 at the University of Minnesota's NSF-sponsored Institute for Mathematics and Its Applications, as part of a "Mathematics in Multimedia" year-long program. Each workshop brought together researchers in the respective technologies on the one hand, and mathematicians and statisticians on the other hand, for an intensive week of cross-fertilization. There is a long history of benefit from introducing mathematical techniques and ideas to speech and language technologies. Examples include the source-channel paradigm, hidden Markov models, decision trees, exponential models and formal languages theory. It is likely that new mathematical techniques, or novel applications of existing techniques, will once again prove pivotal for moving the field forward. This volume consists of original contributions presented by participants during the two workshops. Topics include language modeling, prosody, acoustic-phonetic modeling, and statistical methodology.

Formal Concept Analysis

Bernhard Ganter,Rudolf Wille
Formal Concept Analysis Book PDF

Author : Bernhard Ganter,Rudolf Wille
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642598302

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Formal Concept Analysis by Bernhard Ganter,Rudolf Wille Pdf

This first textbook on formal concept analysis gives a systematic presentation of the mathematical foundations and their relations to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. The mathematical foundations are treated thoroughly and are illuminated by means of numerous examples, making the basic theory readily accessible in compact form.