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Author : Chong Wang
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.:/5 (995 download)
Download or read book A Study of Sufficient Dimension Reduction Methods written by Chong Wang and published by . This book was released on 2017 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bing Li
Publisher : CRC Press
ISBN 13 : 1351645730
Total Pages : 362 pages
Book Rating : 4.3/5 (516 download)
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.
Author : QI XIA
Publisher :
ISBN 13 :
Total Pages : 143 pages
Book Rating : 4.:/5 (128 download)
Download or read book Sufficient Dimension Reduction with Missing Data written by QI XIA and published by . This book was released on 2017 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Existing sufficient dimension reduction (SDR) methods typically consider cases with no missing data. The dissertation aims to propose methods to facilitate the SDR methods when the response can be missing. The first part of the dissertation focuses on the seminal sliced inverse regression (SIR) approach proposed by Li (1991). We show that missing responses generally affect the validity of the inverse regressions under the mechanism of missing at random. We then propose a simple and effective adjustment with inverse probability weighting that guarantees the validity of SIR. Furthermore, a marginal coordinate test is introduced for this adjusted estimator. The proposed method share the simplicity of SIR and requires the linear conditional mean assumption. The second part of the dissertation proposes two new estimating equation procedures: the complete case estimating equation approach and the inverse probability weighted estimating equation approach. The two approaches are applied to a family of dimension reduction methods, which includes ordinary least squares, principal Hessian directions, and SIR. By solving the estimating equations, the two approaches are able to avoid the common assumptions in the SDR literature, the linear conditional mean assumption, and the constant conditional variance assumption. For all the aforementioned methods, the asymptotic properties are established, and their superb finite sample performances are demonstrated through extensive numerical studies as well as a real data analysis. In addition, existing estimators of the central mean space have uneven performances across different types of link functions. To address this limitation, a new hybrid SDR estimator is proposed that successfully recovers the central mean space for a wide range of link functions. Based on the new hybrid estimator, we further study the order determination procedure and the marginal coordinate test. The superior performance of the hybrid estimator over existing methods is demonstrated in simulation studies. Note that the proposed procedures dealing with the missing response at random can be simply adapted to this hybrid method.
Author : Jingyue Lu
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (144 download)
Download or read book Sufficient Dimension Reduction written by Jingyue Lu and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In regression analysis, it is difficult to uncover the dependence relationship between a response variable and a covariate vector when the dimension of the covariate vector is high. To reduce the dimension of the covariate vector, one approach is sufficient dimension reduction. Sufficient dimension reduction is based on the assumption that the response variable relates to only a few linear combinations of the covariate vector. Thus, by replacing the covariate vector with these linear combinations, sufficient dimension reduction achieves dimension reduction. The goal of sufficient dimension reduction is to estimate the space spanned by these linear combinations of the covariate vector. We denote this space by S. In this thesis, we give an introductory review on three important sufficient dimension reduction methods. They are Sliced Inverse Regression (SIR), Sliced Average Variance Estimate (SAVE) and Principle Hessian Directions (pHd). Li proposed SIR in 1991. SIR is a method that exploits the simplicity of the inverse regression. Given the univariate response variable and the high dimensional covariate, it is much easier to regress the covariate against the response variable than the other way around. Motivated by a theorem that connects forward regression and inverse regression, SIR estimates S using inverse regression lines. Since SIR uses first moments only, it fails when there exists symmetry dependence between the response variable and the covariate. To make up for this defect, Cook proposed SAVE in a comment on SIR in 1991. SAVE follows the general lines of SIR but uses second moments as well as first moments to estimate S. pHd is also a second moment method. Li developed pHd in 1992 based on the observation that the eigenvectors for the Hessian matrices of the regression function are closely related to the basis vectors of S. Therefore pHd provides an estimate of S by using these eigenvectors. To compare these methods, a simulation study is presented at the end. From the simulation results, SIR is the most efficient method and SAVE is the most time consuming method. Since SIR fails when symmetry dependence exists, we recommend pHd when symmetry dependence presents and SIR in other cases.
Author : Christopher J. C. Burges
Publisher : Now Publishers Inc
ISBN 13 : 1601983786
Total Pages : 104 pages
Book Rating : 4.6/5 (19 download)
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.
Author : R. Dennis Cook
Publisher : John Wiley & Sons
ISBN 13 : 0470317779
Total Pages : 378 pages
Book Rating : 4.4/5 (73 download)
Download or read book Regression Graphics written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of regression graphics through computer graphics. Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory. Other important features of this book include: * Extensive coverage of a relatively new regression context based on dimension-reduction subspaces and sufficient summary plots * Graphical regression, an iterative visualization process for constructing sufficient regression views * Graphics for regressions with a binary response * Graphics for model assessment, including residual plots * Net-effects plots for assessing predictor contributions * Graphics for predictor and response transformations * Inverse regression methods * Access to a Web site of supplemental plots, data sets, and 3D color displays. An ideal text for students in graduate-level courses on statistical analysis, Regression Graphics is also an excellent reference for professional statisticians.
Author : Efstathia Bura
Publisher : Springer Nature
ISBN 13 : 3030690091
Total Pages : 200 pages
Book Rating : 4.0/5 (36 download)
Download or read book Festschrift in Honor of R. Dennis Cook written by Efstathia Bura and published by Springer Nature. This book was released on 2021-04-27 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of professor and renowned statistician R. Dennis Cook, this festschrift explores his influential contributions to an array of statistical disciplines ranging from experimental design and population genetics, to statistical diagnostics and all areas of regression-related inference and analysis. Since the early 1990s, Prof. Cook has led the development of dimension reduction methodology in three distinct but related regression contexts: envelopes, sufficient dimension reduction (SDR), and regression graphics. In particular, he has made fundamental and pioneering contributions to SDR, inventing or co-inventing many popular dimension reduction methods, such as sliced average variance estimation, the minimum discrepancy approach, model-free variable selection, and sufficient dimension reduction subspaces. A prolific researcher and mentor, Prof. Cook is known for his ability to identify research problems in statistics that are both challenging and important, as well as his deep appreciation for the applied side of statistics. This collection of Prof. Cook's collaborators, colleagues, friends, and former students reflects the broad array of his contributions to the research and instructional arenas of statistics.
Author : Lipu Tian
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (794 download)
Download or read book A Simulation Study on Using Moment Functions for Sufficient Dimension Reduction written by Lipu Tian and published by . This book was released on 2012 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Edwin Diday
Publisher : John Wiley & Sons
ISBN 13 : 1119694965
Total Pages : 225 pages
Book Rating : 4.1/5 (196 download)
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 225 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.
Author : Philip D. Waggoner
Publisher : Cambridge University Press
ISBN 13 : 1108991645
Total Pages : 98 pages
Book Rating : 4.1/5 (89 download)
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.
Author : Yeshan Withanage
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Analysis of Sparse Sufficient Dimension Reduction Models written by Yeshan Withanage and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction (SDR) in regression analysis with response variable y and predictor vector x is focused on reducing the dimension of x to a small number of linear combinations of the components in x. Since the introduction of the inverse regression method, SDR became a very active topic in the literature. When the dimension p of x is increasing with the number of observations n, the traditional SDR methods may not perform well. The purpose of this study is two fold, theoretical and empirical. In the theoretical analysis, I provide a proof for the consistency of a variable selection procedure in sparse single-index models (a special SDR model) through an inverse regression method called CUME. And for the case of multiple linear regression, I obtain the influence functions for estimators of the parameter vector with SCAD and MCP penalties by extending the idea of LASSO influence function. In the empirical aspect, I combine the LASSO-SIR algorithm with the influence function of LASSO to construct a new metric for choosing the penalty parameter for variable selection as an alternative approach to the usual cross-validation method. From the empirical analysis, it was found that the newly proposed influence function-based measure outperforms the traditional cross-validation method in a wide range of settings. Finally, I also propose an algorithm to estimate the structural dimension d of SDR models with large dimension p
Author : Kyongwon Kim
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (119 download)
Download or read book Dimension Reduction and Sufficient Graphical Models written by Kyongwon Kim and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods I develop in my thesis are based on linear or nonlinear sufficient dimension reduction. The basic principle of linear sufficient dimension reduction is to extract a small number of linear combinations of predictor variables, which can represent original predictor variables without loss of information on the conditional distribution of response variable given predictor variables. Nonlinear sufficient dimension reduction is a more generalized version of linear sufficient dimension reduction to the nonlinear context. I am focusing on applying sufficient dimension reduction methods into two areas, regression modeling and graphical models. The first project is about statistical inference in regression context after sufficient dimension reduction. Second, I apply nonlinear sufficient dimension reduction method to the well known statistical graphical models in machine learning. These projects have consistency in a context that discovering areas that sufficient dimension reduction can be applied and establishing statistical theory behind their applications. My first project is about post sufficient dimension reduction statistical inference. The methodologies of sufficient dimension reduction have undergone extensive developments in the past three decades. However, there has been a lack of systematic and rigorous development of post dimension reduction inference, which has seriously hindered its applications. The current common practice is to treat the estimated sufficient predictors as the true predictors and use them as the starting point of the downstream statistical inference. However, this naive inference approach would grossly overestimate the confidence level of an interval, or the power of a test, leading to the distorted results. In this project, we develop a general and comprehensive framework of post dimension reduction inference, which can accommodate any dimension reduction method and model building method, as long as their corresponding influence functions are available. Within this general framework, we derive the influence functions and present the explicit post reduction formulas for the combinations of numerous dimension reduction and model building methods. We then develop post reduction inference methods for both confidence interval and hypothesis testing. We investigate the finite-sample performance of our procedures by simulations and a real data analysis. My second project is about applying nonlinear dimension reduction technique to graphical models. We introduce the Sufficient Graphical Model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. Graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike fully nonparametric graphical model, which relies on the high-dimensional kernel to characterize a conditional independence, our graphical model is based on a conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way, we avoid the curse of dimensionality that comes with a high-dimensional kernel. We develop the population-level properties, convergence rate, and consistency of our estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, we demonstrate that our method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.
Author : Jiaying Weng
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (126 download)
Download or read book Transforms in Sufficient Dimension Reduction and Their Applications in High Dimensional Data written by Jiaying Weng and published by . This book was released on 2019 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Xin Chen
Publisher :
ISBN 13 :
Total Pages : 69 pages
Book Rating : 4.:/5 (71 download)
Download or read book Sufficient Dimension Reduction and Variable Selection written by Xin Chen and published by . This book was released on 2010 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John A. Lee
Publisher : Springer Science & Business Media
ISBN 13 : 038739351X
Total Pages : 316 pages
Book Rating : 4.3/5 (873 download)
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.
Author : Danyu Lin
Publisher : Springer Science & Business Media
ISBN 13 : 1441990763
Total Pages : 332 pages
Book Rating : 4.4/5 (419 download)
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.
Author : Anna Goldenberg
Publisher : Now Publishers Inc
ISBN 13 : 1601983204
Total Pages : 118 pages
Book Rating : 4.6/5 (19 download)
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.
