Download or read book Bayesian Assessment of Dimensionality in Multivariate Reduced Rank Regression written by Jukka Corander and published by . This book was released on 2001 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sparse Bayesian Inference Using Reduced rank Regression Approaches written by Dunfu Yang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In multivariate regression analysis, reduced-rank regression (RRR) has received considerable attention as a powerful way of improving estimation and prediction performances. In this dissertation, we aim to address challenges of dimension reduction associated with rank selection and variable selection in RRR. Our proposed methods are developed in a Bayesian framework so that the uncertainties of rank selection and variable selection can be integrated out via marginalization. We pay special attention to high-dimensional problems in which the number of potential predictors is greater than the sample size. We propose new posterior computation schemes to tackle high-dimensional data challenges under the RRR framework. A great merit of our proposed methods is that they are applicable to a variety of statistical models and machine learning methods including generalized linear models and support vector machines. In addition, various posterior sampling strategies are proposed for handling a variety of rank selection and variable selection problems. To investigate the performance of our proposed methods, simulation study and real data analysis are extensively implemented. This dissertation consists of five chapters. In Chapter 1, we discuss the background and motivation of our study. In Chapter 2, we develop a fully Bayesian approach for high-dimensional RRR problems. In Chapter 3, we propose a multivariate extension of generalized linear models using the sparse RRR idea to handle various data types, including binary, count, and continuous responses. In Chapter 4, we develop a new support vector machine approach for multivariate binary outcomes by incorporating the RRR scheme into the Bayesian support vector machine framework. In Chapter 5, we discuss some remarks and future directions.
Download or read book Bayesian Reduced Rank Regression with Fixed Dimensionality written by Mattias Villani and published by . This book was released on 1998 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivariate Reduced Rank Regression written by Gregory C. Reinsel and published by Springer Nature. This book was released on 2022-11-30 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.
Download or read book Multivariate Reduced Rank Regression written by Raja Velu and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the area of multivariate analysis, there are two broad themes that have emerged over time. The analysis typically involves exploring the variations in a set of interrelated variables or investigating the simultaneous relation ships between two or more sets of variables. In either case, the themes involve explicit modeling of the relationships or dimension-reduction of the sets of variables. The multivariate regression methodology and its variants are the preferred tools for the parametric modeling and descriptive tools such as principal components or canonical correlations are the tools used for addressing the dimension-reduction issues. Both act as complementary to each other and data analysts typically want to make use of these tools for a thorough analysis of multivariate data. A technique that combines the two broad themes in a natural fashion is the method of reduced-rank regres sion. This method starts with the classical multivariate regression model framework but recognizes the possibility for the reduction in the number of parameters through a restrietion on the rank of the regression coefficient matrix. This feature is attractive because regression methods, whether they are in the context of a single response variable or in the context of several response variables, are popular statistical tools. The technique of reduced rank regression and its encompassing features are the primary focus of this book. The book develops the method of reduced-rank regression starting from the classical multivariate linear regression model.
Download or read book The Oxford Handbook of Economic Forecasting written by Michael P. Clements and published by OUP USA. This book was released on 2011-07-08 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greater data availability has been coupled with developments in statistical theory and economic theory to allow more elaborate and complicated models to be entertained. These include factor models, DSGE models, restricted vector autoregressions, and non-linear models.
Download or read book Modern Multivariate Statistical Techniques written by Alan J. Izenman and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.
Download or read book Reduced Rank Regression written by Heinz Schmidli and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reduced rank regression is widely used in statistics to model multivariate data. In this monograph, theoretical and data analytical approaches are developed for the application of reduced rank regression in multivariate prediction problems. For the first time, both classical and Bayesian inference is discussed, using recently proposed procedures such as the ECM-algorithm and the Gibbs sampler. All methods are motivated and illustrated by examples taken from the area of quantitative structure-activity relationships (QSAR).
Download or read book Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models written by Andrea Carriero and published by . This book was released on 2009 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Analysis of Reduced Rank Regression Models Using Post processing written by Christian Aßmann and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Envelopes written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2018-09-07 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading expert in the field, this text reviews the major new developments in envelope models and methods An Introduction to Envelopes provides an overview of the theory and methods of envelopes, a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives. The author offers a balance between foundations and methodology by integrating illustrative examples that show how envelopes can be used in practice. He discusses how to use envelopes to target selected coefficients and explores predictor envelopes and their connection with partial least squares regression. The book reveals the potential for envelope methodology to improve estimation of a multivariate mean. The text also includes information on how envelopes can be used in generalized linear models, regressions with a matrix-valued response, and reviews work on sparse and Bayesian response envelopes. In addition, the text explores relationships between envelopes and other dimension reduction methods, including canonical correlations, reduced-rank regression, supervised singular value decomposition, sufficient dimension reduction, principal components, and principal fitted components. This important resource: • Offers a text written by the leading expert in this field • Describes groundbreaking work that puts the focus on this burgeoning area of study • Covers the important new developments in the field and highlights the most important directions • Discusses the underlying mathematics and linear algebra • Includes an online companion site with both R and Matlab support Written for researchers and graduate students in multivariate analysis and dimension reduction, as well as practitioners interested in statistical methodology, An Introduction to Envelopes offers the first book on the theory and methods of envelopes.
Download or read book Case Studies in Bayesian Statistics written by Constantine Gatsonis and published by Springer. This book was released on 2018-08-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited case studies with the accompanying discussion as well as contributed papers selected by a refereeing process of 6th Workshop on Case Studies in Bayesian Statistics was held at the Carnegie Mellon University in October, 2001.
Download or read book Bayesian Multilevel Models for Repeated Measures Data written by Santiago Barreda and published by Taylor & Francis. This book was released on 2023-05-18 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is an introduction to multilevel Bayesian models in R using brms and the Stan programming language. Featuring a series of fully worked analyses of repeated measures data, the focus is placed on active learning through the analyses of the progressively more complicated models presented throughout the book. In this book, the authors offer an introduction to statistics entirely focused on repeated measures data beginning with very simple two-group comparisons and ending with multinomial regression models with many ‘random effects’. Across 13 well-structured chapters, readers are provided with all the code necessary to run all the analyses and make all the plots in the book, as well as useful examples of how to interpret and write up their own analyses. This book provides an accessible introduction for readers in any field, with any level of statistical background. Senior undergraduate students, graduate students, and experienced researchers looking to ‘translate’ their skills with more traditional models to a Bayesian framework will benefit greatly from the lessons in this text.
Download or read book Multidimensional Stationary Time Series written by Marianna Bolla and published by CRC Press. This book was released on 2021-04-29 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix. Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.
Download or read book Information Processing and Management of Uncertainty in Knowledge Based Systems written by Marie-Jeanne Lesot and published by Springer Nature. This book was released on 2020-06-05 with total page 839 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three volume set (CCIS 1237-1239) constitutes the proceedings of the 18th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2020, in June 2020. The conference was scheduled to take place in Lisbon, Portugal, at University of Lisbon, but due to COVID-19 pandemic it was held virtually. The 173 papers were carefully reviewed and selected from 213 submissions. The papers are organized in topical sections: homage to Enrique Ruspini; invited talks; foundations and mathematics; decision making, preferences and votes; optimization and uncertainty; games; real world applications; knowledge processing and creation; machine learning I; machine learning II; XAI; image processing; temporal data processing; text analysis and processing; fuzzy interval analysis; theoretical and applied aspects of imprecise probabilities; similarities in artificial intelligence; belief function theory and its applications; aggregation: theory and practice; aggregation: pre-aggregation functions and other generalizations of monotonicity; aggregation: aggregation of different data structures; fuzzy methods in data mining and knowledge discovery; computational intelligence for logistics and transportation problems; fuzzy implication functions; soft methods in statistics and data analysis; image understanding and explainable AI; fuzzy and generalized quantifier theory; mathematical methods towards dealing with uncertainty in applied sciences; statistical image processing and analysis, with applications in neuroimaging; interval uncertainty; discrete models and computational intelligence; current techniques to model, process and describe time series; mathematical fuzzy logic and graded reasoning models; formal concept analysis, rough sets, general operators and related topics; computational intelligence methods in information modelling, representation and processing.
Download or read book High Dimensional Covariance Estimation written by Mohsen Pourahmadi and published by John Wiley & Sons. This book was released on 2013-06-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction, and mean-variance portfolio management. The book relies heavily on regression-based ideas and interpretations to connect and unify many existing methods and algorithms for the task. High-Dimensional Covariance Estimation features chapters on: Data, Sparsity, and Regularization Regularizing the Eigenstructure Banding, Tapering, and Thresholding Covariance Matrices Sparse Gaussian Graphical Models Multivariate Regression The book is an ideal resource for researchers in statistics, mathematics, business and economics, computer sciences, and engineering, as well as a useful text or supplement for graduate-level courses in multivariate analysis, covariance estimation, statistical learning, and high-dimensional data analysis.
Download or read book Bayesian Trace Statistics for the Reduced Rank Regression Model written by Rodney W. Strachan and published by . This book was released on 1999 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
