Download or read book Dimension Reduction in Statistical Modeling written by Linquan Ma (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the data object is described by a large number of features, it is often beneficial to reduce the dimension of the data, so that the statistical analysis can have better efficiencies. Recently, a new dimension reduction method called the envelope method by Cook, Li, and Chiaromonte (2010) has been proposed in multivariate regressions. It has the potential to gain substantial efficiency over the standard least squares estimator. Chapter 2 proposes an approach to use the envelope method when the predictors and/or the responses are missing at random. When there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. We incorporate the envelope structure in the expectation-maximization (EM) algorithm. Our method is guaranteed to be more efficient, or at least as efficient as, the standard EM algorithm. We give asymptotic properties of our method under both normal and non-normal cases. Chapter 3 extends the envelope model to the mixed effects model for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Chapter 4 proposes a semiparametric variant of the inner envelope model (Su and Cook, 2012) that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. The instrumental variables (IV) are frequently used in observational studies to recover the effect of exposure in the presence of unmeasured confounding. A key fact is that the strength of IV matters: an IV with a stronger association with the exposure results in a more accurate estimation of a causal effect. While it is hard to find a stronger IV, we generalize a sufficient dimension method to remove immaterial IVs. Chapter 5 investigates two different ways of incorporating the envelope method into IV regression. We show that the first stage envelope method does not yield any efficiency gain on the standard IV estimator, however, it may reduce the finite sample bias. The second stage envelope can achieve substantial efficiency gain under certain conditions.
Download or read book Dimension Reduction in Statistical Modeling written by Linquan Ma (Ph.D.) and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When the data object is described by a large number of features, it is often beneficial to reduce the dimension of the data, so that the statistical analysis can have better efficiencies. Recently, a new dimension reduction method called the envelope method by Cook, Li, and Chiaromonte (2010) has been proposed in multivariate regressions. It has the potential to gain substantial efficiency over the standard least squares estimator. Chapter 2 proposes an approach to use the envelope method when the predictors and/or the responses are missing at random. When there exists missing data, the envelope method using the complete case observations may lead to biased and inefficient results. We incorporate the envelope structure in the expectation-maximization (EM) algorithm. Our method is guaranteed to be more efficient, or at least as efficient as, the standard EM algorithm. We give asymptotic properties of our method under both normal and non-normal cases. Chapter 3 extends the envelope model to the mixed effects model for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Chapter 4 proposes a semiparametric variant of the inner envelope model (Su and Cook, 2012) that does not rely on the linear model nor the normality assumption. We show that our proposal leads to globally and locally efficient estimators of the inner envelope spaces. We also present a computationally tractable algorithm to estimate the inner envelope. The instrumental variables (IV) are frequently used in observational studies to recover the effect of exposure in the presence of unmeasured confounding. A key fact is that the strength of IV matters: an IV with a stronger association with the exposure results in a more accurate estimation of a causal effect. While it is hard to find a stronger IV, we generalize a sufficient dimension method to remove immaterial IVs. Chapter 5 investigates two different ways of incorporating the envelope method into IV regression. We show that the first stage envelope method does not yield any efficiency gain on the standard IV estimator, however, it may reduce the finite sample bias. The second stage envelope can achieve substantial efficiency gain under certain conditions.
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 307 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.
Download or read book Machine Learning Techniques for Multimedia written by Matthieu Cord and published by Springer Science & Business Media. This book was released on 2008-02-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processing multimedia content has emerged as a key area for the application of machine learning techniques, where the objectives are to provide insight into the domain from which the data is drawn, and to organize that data and improve the performance of the processes manipulating it. Arising from the EU MUSCLE network, this multidisciplinary book provides a comprehensive coverage of the most important machine learning techniques used and their application in this domain.
Download or read book Feature Engineering and Selection written by Max Kuhn and published by CRC Press. This book was released on 2019-07-25 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.
Download or read book Principal Manifolds for Data Visualization and Dimension Reduction written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2007-09-11 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.
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.
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.
Download or read book Dimensionality Reduction with Unsupervised Nearest Neighbors written by Oliver Kramer and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a novel approach for dimensionality reduction based on the famous nearest neighbor method that is a powerful classification and regression approach. It starts with an introduction to machine learning concepts and a real-world application from the energy domain. Then, unsupervised nearest neighbors (UNN) is introduced as efficient iterative method for dimensionality reduction. Various UNN models are developed step by step, reaching from a simple iterative strategy for discrete latent spaces to a stochastic kernel-based algorithm for learning submanifolds with independent parameterizations. Extensions that allow the embedding of incomplete and noisy patterns are introduced. Various optimization approaches are compared, from evolutionary to swarm-based heuristics. Experimental comparisons to related methodologies taking into account artificial test data sets and also real-world data demonstrate the behavior of UNN in practical scenarios. The book contains numerous color figures to illustrate the introduced concepts and to highlight the experimental results.
Download or read book Factor Analysis and Dimension Reduction in R written by G. David Garson and published by Taylor & Francis. This book was released on 2022-12-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factor Analysis and Dimension Reduction in R provides coverage, with worked examples, of a large number of dimension reduction procedures along with model performance metrics to compare them. Factor analysis in the form of principal components analysis (PCA) or principal factor analysis (PFA) is familiar to most social scientists. However, what is less familiar is understanding that factor analysis is a subset of the more general statistical family of dimension reduction methods. The social scientist's toolkit for factor analysis problems can be expanded to include the range of solutions this book presents. In addition to covering FA and PCA with orthogonal and oblique rotation, this book’s coverage includes higher-order factor models, bifactor models, models based on binary and ordinal data, models based on mixed data, generalized low-rank models, cluster analysis with GLRM, models involving supplemental variables or observations, Bayesian factor analysis, regularized factor analysis, testing for unidimensionality, and prediction with factor scores. The second half of the book deals with other procedures for dimension reduction. These include coverage of kernel PCA, factor analysis with multidimensional scaling, locally linear embedding models, Laplacian eigenmaps, diffusion maps, force directed methods, t-distributed stochastic neighbor embedding, independent component analysis (ICA), dimensionality reduction via regression (DRR), non-negative matrix factorization (NNMF), Isomap, Autoencoder, uniform manifold approximation and projection (UMAP) models, neural network models, and longitudinal factor analysis models. In addition, a special chapter covers metrics for comparing model performance. Features of this book include: Numerous worked examples with replicable R code Explicit comprehensive coverage of data assumptions Adaptation of factor methods to binary, ordinal, and categorical data Residual and outlier analysis Visualization of factor results Final chapters that treat integration of factor analysis with neural network and time series methods Presented in color with R code and introduction to R and RStudio, this book will be suitable for graduate-level and optional module courses for social scientists, and on quantitative methods and multivariate statistics courses.
Download or read book Multi Label Dimensionality Reduction written by Liang Sun and published by CRC Press. This book was released on 2016-04-19 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Similar to other data mining and machine learning tasks, multi-label learning suffers from dimensionality. An effective way to mitigate this problem is through dimensionality reduction, which extracts a small number of features by removing irrelevant, redundant, and noisy information. The data mining and machine learning literature currently lacks
Download or read book Functional Statistics and Related Fields written by Germán Aneiros and published by Springer. This book was released on 2017-04-25 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the Fourth International Workshop on Functional and Operatorial Statistics (IWFOS 2017) held in A Coruña, Spain, from 15 to 17 June 2017. The series of IWFOS workshops was initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008. Since then, many of the major advances in functional statistics and related fields have been periodically presented and discussed at the IWFOS workshops.
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.
Download or read book An Introduction to Multivariate Statistical Analysis written by T. W. Anderson and published by Wiley-Interscience. This book was released on 2003-07-25 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perfected over three editions and more than forty years, this field- and classroom-tested reference: * Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures. * Treats all the basic and important topics in multivariate statistics. * Adds two new chapters, along with a number of new sections. * Provides the most methodical, up-to-date information on MV statistics available.
Download or read book Segmentation and Dimension Reduction written by Joost van Rosmalen. and published by . This book was released on 2009 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dimension Reduction of Large Scale Systems written by Peter Benner and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.
Download or read book Advances in Statistical Modeling and Inference written by Vijay Nair and published by World Scientific. This book was released on 2007 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been major developments in the field of statistics over the last quarter century, spurred by the rapid advances in computing and data-measurement technologies. These developments have revolutionized the field and have greatly influenced research directions in theory and methodology. Increased computing power has spawned entirely new areas of research in computationally-intensive methods, allowing us to move away from narrowly applicable parametric techniques based on restrictive assumptions to much more flexible and realistic models and methods. These computational advances have also led to the extensive use of simulation and Monte Carlo techniques in statistical inference. All of these developments have, in turn, stimulated new research in theoretical statistics. This volume provides an up-to-date overview of recent advances in statistical modeling and inference. Written by renowned researchers from across the world, it discusses flexible models, semi-parametric methods and transformation models, nonparametric regression and mixture models, survival and reliability analysis, and re-sampling techniques. With its coverage of methodology and theory as well as applications, the book is an essential reference for researchers, graduate students, and practitioners.
