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Sufficient Dimension Reduction

Author : Bing Li
Publisher : CRC Press
ISBN 13 : 1351645730
Total Pages : 362 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Sufficient Dimension Reduction by : Bing Li

Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.

Dimension Reduction

Author : Christopher J. C. Burges
Publisher : Now Publishers Inc
ISBN 13 : 1601983786
Total Pages : 104 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Dimension Reduction by : Christopher J. C. Burges

Download or read book Dimension Reduction written by Christopher J. C. Burges and published by Now Publishers Inc. This book was released on 2010 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give a tutorial overview of several foundational methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis (CCA), kernel CCA, Fisher discriminant analysis, oriented PCA, and several techniques for sufficient dimension reduction. For the manifold methods, we review multidimensional scaling (MDS), landmark MDS, Isomap, locally linear embedding, Laplacian eigenmaps, and spectral clustering. Although the review focuses on foundations, we also provide pointers to some more modern techniques. We also describe the correlation dimension as one method for estimating the intrinsic dimension, and we point out that the notion of dimension can be a scale-dependent quantity. The Nystr m method, which links several of the manifold algorithms, is also reviewed. We use a publicly available dataset to illustrate some of the methods. The goal is to provide a self-contained overview of key concepts underlying many of these algorithms, and to give pointers for further reading.

Regression Graphics

Author : R. Dennis Cook
Publisher : John Wiley & Sons
ISBN 13 : 9780471193654
Total Pages : 380 pages
Book Rating : 4.1/5 (936 download)

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Book Synopsis Regression Graphics by : R. Dennis Cook

Download or read book Regression Graphics written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 1998-09-30 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zur graphischen Präsentation von Regressionsdaten gibt es seit dem Vormarsch der Computertechnik vielfältige neue Möglichkeiten, die über die klassischen Ansätze hinausgehen. Der Autor betritt mit seinen Ideen häufig Neuland; er illustriert sie mit zahlreichen Beispielen, Diagrammen und Abbildungen (die entsprechenden 3D- und Farbversionen sind über Internet abrufbar). (11/98)

Robust Statistics

Author : Ricardo A. Maronna
Publisher : John Wiley & Sons
ISBN 13 : 1119214688
Total Pages : 466 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis Robust Statistics by : Ricardo A. Maronna

Download or read book Robust Statistics written by Ricardo A. Maronna and published by John Wiley & Sons. This book was released on 2019-01-04 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.

Partially Linear Models

Author : Wolfgang Härdle
Publisher : Springer Science & Business Media
ISBN 13 : 3642577008
Total Pages : 210 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Partially Linear Models by : Wolfgang Härdle

Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.

Advances in Data Science

Author : Edwin Diday
Publisher : John Wiley & Sons
ISBN 13 : 1119694965
Total Pages : 232 pages
Book Rating : 4.1/5 (196 download)

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Book Synopsis Advances in Data Science by : Edwin Diday

Download or read book Advances in Data Science written by Edwin Diday and published by John Wiley & Sons. This book was released on 2020-01-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data science unifies statistics, data analysis and machine learning to achieve a better understanding of the masses of data which are produced today, and to improve prediction. Special kinds of data (symbolic, network, complex, compositional) are increasingly frequent in data science. These data require specific methodologies, but there is a lack of reference work in this field. Advances in Data Science fills this gap. It presents a collection of up-to-date contributions by eminent scholars following two international workshops held in Beijing and Paris. The 10 chapters are organized into four parts: Symbolic Data, Complex Data, Network Data and Clustering. They include fundamental contributions, as well as applications to several domains, including business and the social sciences.

A Survey of Statistical Network Models

Author : Anna Goldenberg
Publisher : Now Publishers Inc
ISBN 13 : 1601983204
Total Pages : 118 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis A Survey of Statistical Network Models by : Anna Goldenberg

Download or read book A Survey of Statistical Network Models written by Anna Goldenberg and published by Now Publishers Inc. This book was released on 2010 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

Active Subspaces

Author : Paul G. Constantine
Publisher : SIAM
ISBN 13 : 1611973864
Total Pages : 105 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Active Subspaces by : Paul G. Constantine

Download or read book Active Subspaces written by Paul G. Constantine and published by SIAM. This book was released on 2015-03-17 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.

Modern Dimension Reduction

Author : Philip D. Waggoner
Publisher : Cambridge University Press
ISBN 13 : 1108991645
Total Pages : 98 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Modern Dimension Reduction by : Philip D. Waggoner

Download or read book Modern Dimension Reduction written by Philip D. Waggoner and published by Cambridge University Press. This book was released on 2021-08-05 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern society. All code is publicly accessible on Github.

Theory of Spatial Statistics

Author : M.N.M. van Lieshout
Publisher : CRC Press
ISBN 13 : 0429627033
Total Pages : 221 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Theory of Spatial Statistics by : M.N.M. van Lieshout

Download or read book Theory of Spatial Statistics written by M.N.M. van Lieshout and published by CRC Press. This book was released on 2019-03-19 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

Nonlinear Dimensionality Reduction

Author : John A. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 038739351X
Total Pages : 316 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Nonlinear Dimensionality Reduction by : John A. Lee

Download or read book Nonlinear Dimensionality Reduction written by John A. Lee and published by Springer Science & Business Media. This book was released on 2007-10-31 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes established and advanced methods for reducing the dimensionality of numerical databases. Each description starts from intuitive ideas, develops the necessary mathematical details, and ends by outlining the algorithmic implementation. The text provides a lucid summary of facts and concepts relating to well-known methods as well as recent developments in nonlinear dimensionality reduction. Methods are all described from a unifying point of view, which helps to highlight their respective strengths and shortcomings. The presentation will appeal to statisticians, computer scientists and data analysts, and other practitioners having a basic background in statistics or computational learning.

High-dimensional Data Analysis

Author : Tony Cai;Xiaotong Shen
Publisher :
ISBN 13 : 9787894236326
Total Pages : 318 pages
Book Rating : 4.2/5 (363 download)

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Book Synopsis High-dimensional Data Analysis by : Tony Cai;Xiaotong Shen

Download or read book High-dimensional Data Analysis written by Tony Cai;Xiaotong Shen and published by . This book was released on with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few years, significant developments have been taking place in highdimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics and signal processing. In particular, substantial advances have been made in the areas of feature selection, covariance estimation, classification and regression. This book intends to examine important issues arising from highdimensional data analysis to explore key ideas for statistical inference and prediction. It is structured around topics on multiple hypothesis testing, feature selection, regression, cla.

Density Ratio Estimation in Machine Learning

Author : Masashi Sugiyama
Publisher : Cambridge University Press
ISBN 13 : 0521190177
Total Pages : 343 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis Density Ratio Estimation in Machine Learning by : Masashi Sugiyama

Download or read book Density Ratio Estimation in Machine Learning written by Masashi Sugiyama and published by Cambridge University Press. This book was released on 2012-02-20 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces theories, methods and applications of density ratio estimation, a newly emerging paradigm in the machine learning community.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Handbook of Approximate Bayesian Computation

Author : Scott A. Sisson
Publisher : CRC Press
ISBN 13 : 1439881510
Total Pages : 679 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Handbook of Approximate Bayesian Computation by : Scott A. Sisson

Download or read book Handbook of Approximate Bayesian Computation written by Scott A. Sisson and published by CRC Press. This book was released on 2018-09-03 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement. The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.

Frontiers in Massive Data Analysis

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309287812
Total Pages : 191 pages
Book Rating : 4.3/5 (92 download)

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Book Synopsis Frontiers in Massive Data Analysis by : National Research Council

Download or read book Frontiers in Massive Data Analysis written by National Research Council and published by National Academies Press. This book was released on 2013-09-03 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data mining of massive data sets is transforming the way we think about crisis response, marketing, entertainment, cybersecurity and national intelligence. Collections of documents, images, videos, and networks are being thought of not merely as bit strings to be stored, indexed, and retrieved, but as potential sources of discovery and knowledge, requiring sophisticated analysis techniques that go far beyond classical indexing and keyword counting, aiming to find relational and semantic interpretations of the phenomena underlying the data. Frontiers in Massive Data Analysis examines the frontier of analyzing massive amounts of data, whether in a static database or streaming through a system. Data at that scale-terabytes and petabytes-is increasingly common in science (e.g., particle physics, remote sensing, genomics), Internet commerce, business analytics, national security, communications, and elsewhere. The tools that work to infer knowledge from data at smaller scales do not necessarily work, or work well, at such massive scale. New tools, skills, and approaches are necessary, and this report identifies many of them, plus promising research directions to explore. Frontiers in Massive Data Analysis discusses pitfalls in trying to infer knowledge from massive data, and it characterizes seven major classes of computation that are common in the analysis of massive data. Overall, this report illustrates the cross-disciplinary knowledge-from computer science, statistics, machine learning, and application disciplines-that must be brought to bear to make useful inferences from massive data.

Proceedings of the Second Seattle Symposium in Biostatistics

Author : Danyu Lin
Publisher : Springer Science & Business Media
ISBN 13 : 1441990763
Total Pages : 332 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Proceedings of the Second Seattle Symposium in Biostatistics by : Danyu Lin

Download or read book Proceedings of the Second Seattle Symposium in Biostatistics written by Danyu Lin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers presented at the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data. The symposium was held in 2000 to celebrate the 30th anniversary of the University of Washington School of Public Health and Community Medicine. It featured keynote lectures by Norman Breslow, David Cox and Ross Prentice and 16 invited presentations by other prominent researchers. The papers contained in this volume encompass recent methodological advances in several important areas, such as longitudinal data, multivariate failure time data and genetic data, as well as innovative applications of the existing theory and methods. This volume is a valuable reference for researchers and practitioners in the field of correlated data analysis.