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.

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:

Download or read book Sufficient Dimension Reduction in High dimensional Data written by Lexin Li and published by . This book was released on 2003 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Dimensional Methodologies for Sufficient Dimension Reduction Discriminant Analysis and Tensor Data written by Jing Zeng and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thanks to the advancement of data-collecting technology in brain imaging, genomics, financial econometrics, and machine learning, scientific data tend to grow in both size and structural complexity, which are not amenable to traditional statistical analysis. In this dissertation, we developed novel high-dimensional methodologies for dimension reduction, discriminant analysis, and tensor data. In the first chapter, we proposed a unified framework, called subspace estimation with automatic dimension and variable selection (SEAS), to extend many existing low-dimensional sufficient dimension reduction (SDR) methods to the high-dimensional setting. The flexibility of SEAS considerably widens the application scope of many SDR methods. Our proposal only relies on a double-penalized convex formulation, which can be solved efficiently. From the theoretical perspective, we established a satisfactory convergence rate for our proposal, which is optimal in a minimax sense. In the second chapter, we established a population model for the reduced-rank linear discriminant analysis (LDA) problem, which arises naturally in many scenarios. We also developed an efficient algorithm and derived the non-asymptotic results in the high-dimensional setting. In the last chapter, we studied how two data modalities associate and interact with each other given a third modality, which is a crucial problem in multimodal integrative analysis but has no available statistical solution. We formulated this problem as a tensor decomposition problem and proposed a novel generalized liquid association analysis (GLAA) method. A high-order orthogonal iteration algorithm is provided accordingly. Furthermore, we established the non-asymptotic results for the proposed estimators.

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.

Download or read book Advances in Forward Sufficient Dimension Reduction Methods for Statistical Learning written by Harris Quach and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern information collection methods continue to generate an abundance of data from which practitioners, in fields ranging from the social sciences and humanities to the natural and biomedical sciences, attempt to draw new insights and discoveries through statistical analyses. Against this backdrop, dimension reduction methods have come to prominence as a tool for extracting important or informative features from high dimensional data sets. In particular, Sufficient Dimension Reduction (SDR) methods have become a popular and effective tool for supervised dimension reduction. Since the seminal paper by K.-C. Li (1991), Sufficient Dimension Reduction has developed at a rapid pace, with inverse regression methods having undergone substantial development and becoming widely applicable. Alternative approaches to sufficient dimension reduction have received relatively less attention, despite being less restrictive and more effective in many scenarios. The objective of this thesis is to advance the forward regression approach for sufficient dimension reduction by developing methods that are more effective for categorical and ordinal responses, and methods that apply to functional data.

Download or read book Statistical Methods in Molecular Biology written by Heejung Bang and published by Humana. This book was released on 2016-08-23 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This progressive book presents the basic principles of proper statistical analyses. It progresses to more advanced statistical methods in response to rapidly developing technologies and methodologies in the field of molecular biology.

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 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.

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.

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.

Download or read book On Sufficient Dimension Reduction Via Asymmetric Least Squares written by Abdul-Nasah Soale and published by . This book was released on 2021 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying the advances in computer technology is an increase collection of high dimensional data in many scientific and social studies. Sufficient dimension reduction (SDR) is a statistical method that enable us to reduce the dimension ofpredictors without loss of regression information. In this dissertation, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) often do not perform well in the presence of heteroscedastic error, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function. PALS is not designed to handle symmetric link function between the response and the predictors. As a remedy, we develop expectile-assisted inverse regression estimation (EA-IRE) as a unified framework for moment-based inverse regression. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature including slice inverse regression, slice average variance estimation, and directional regression are extended under this general framework. The proposed expectile-assisted methods outperform existing moment-based dimension reduction methods in both numerical studies and an analysis of the Big Mac data.

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.

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.

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.

Download or read book Efficient Estimation and Order Determination for Sufficient Dimension Reduction written by Wei Luo and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction (SDR) has driven intense interest in the recent decades as a solution to deal with high-dimensional data. The goal of SDR is to construct, usually by a linear transformation of the original predictor, a lower-dimensional sufficient statistic that serves as the new predictor in subsequent modeling. An important problem in SDR, is to determine the reduced dimension of the new predictor. In this dissertation, we first propose two order-determination methods that are applicable to a large class of SDR methods, with both of them proved consistent and shown efficient via simulation study and real data examples.Another part of the dissertation focuses on the development of a new class of efficient estimators of the linear transformation under various SDR assumptions, in a unifying semi-parametric approach. These estimators are expected to outperform their competitors in the literature, which were developed without consideration of semi-parametric efficiency. We derive the efficient score functions that generate these estimators, together with a computationally efficient algorithm. We also conduct the corresponding simulation studies and real data analysis to further show the effectiveness of the estimators in application.

Download or read book Dimension Reduction for Clustered High dimensional Data written by Enikö Melinda Székely and published by . This book was released on 2011 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: