High Dimensional Covariance Estimation
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| Author | : Mohsen Pourahmadi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 204 |
| Release | : 2013-06-24 |
| Genre | : Mathematics |
| ISBN | : 1118034295 |
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.
| Author | : Aygul Zagidullina |
| Publisher | : Springer Nature |
| Total Pages | : 123 |
| Release | : 2021-10-29 |
| Genre | : Business & Economics |
| ISBN | : 3030800652 |
This book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.
| Author | : Roman Vershynin |
| Publisher | : Cambridge University Press |
| Total Pages | : 299 |
| Release | : 2018-09-27 |
| Genre | : Business & Economics |
| ISBN | : 1108415199 |
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
| Author | : Mohsen Pourahmadi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 204 |
| Release | : 2013-05-28 |
| Genre | : Mathematics |
| ISBN | : 1118573668 |
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.
| Author | : Jianfeng Yao |
| Publisher | : Cambridge University Press |
| Total Pages | : 0 |
| Release | : 2015-03-26 |
| Genre | : Mathematics |
| ISBN | : 9781107065178 |
High-dimensional data appear in many fields, and their analysis has become increasingly important in modern statistics. However, it has long been observed that several well-known methods in multivariate analysis become inefficient, or even misleading, when the data dimension p is larger than, say, several tens. A seminal example is the well-known inefficiency of Hotelling's T2-test in such cases. This example shows that classical large sample limits may no longer hold for high-dimensional data; statisticians must seek new limiting theorems in these instances. Thus, the theory of random matrices (RMT) serves as a much-needed and welcome alternative framework. Based on the authors' own research, this book provides a first-hand introduction to new high-dimensional statistical methods derived from RMT. The book begins with a detailed introduction to useful tools from RMT, and then presents a series of high-dimensional problems with solutions provided by RMT methods.
| Author | : Sumeet Dua |
| Publisher | : CRC Press |
| Total Pages | : 351 |
| Release | : 2012-11-06 |
| Genre | : Computers |
| ISBN | : 0849328012 |
Covering theory, algorithms, and methodologies, as well as data mining technologies, Data Mining for Bioinformatics provides a comprehensive discussion of data-intensive computations used in data mining with applications in bioinformatics. It supplies a broad, yet in-depth, overview of the application domains of data mining for bioinformatics to help readers from both biology and computer science backgrounds gain an enhanced understanding of this cross-disciplinary field. The book offers authoritative coverage of data mining techniques, technologies, and frameworks used for storing, analyzing, and extracting knowledge from large databases in the bioinformatics domains, including genomics and proteomics. It begins by describing the evolution of bioinformatics and highlighting the challenges that can be addressed using data mining techniques. Introducing the various data mining techniques that can be employed in biological databases, the text is organized into four sections: Supplies a complete overview of the evolution of the field and its intersection with computational learning Describes the role of data mining in analyzing large biological databases—explaining the breath of the various feature selection and feature extraction techniques that data mining has to offer Focuses on concepts of unsupervised learning using clustering techniques and its application to large biological data Covers supervised learning using classification techniques most commonly used in bioinformatics—addressing the need for validation and benchmarking of inferences derived using either clustering or classification The book describes the various biological databases prominently referred to in bioinformatics and includes a detailed list of the applications of advanced clustering algorithms used in bioinformatics. Highlighting the challenges encountered during the application of classification on biological databases, it considers systems of both single and ensemble classifiers and shares effort-saving tips for model selection and performance estimation strategies.
| Author | : Martin J. Wainwright |
| Publisher | : Cambridge University Press |
| Total Pages | : 571 |
| Release | : 2019-02-21 |
| Genre | : Business & Economics |
| ISBN | : 1108498027 |
A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.
| Author | : P. Hall |
| Publisher | : Academic Press |
| Total Pages | : 321 |
| Release | : 2014-07-10 |
| Genre | : Mathematics |
| ISBN | : 1483263223 |
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
| Author | : Mohsen Pourahmadi |
| Publisher | : John Wiley & Sons |
| Total Pages | : 446 |
| Release | : 2001-06-01 |
| Genre | : Mathematics |
| ISBN | : 9780471394341 |
Foundations of time series for researchers and students This volume provides a mathematical foundation for time seriesanalysis and prediction theory using the idea of regression and thegeometry of Hilbert spaces. It presents an overview of the tools oftime series data analysis, a detailed structural analysis ofstationary processes through various reparameterizations employingtechniques from prediction theory, digital signal processing, andlinear algebra. The author emphasizes the foundation and structureof time series and backs up this coverage with theory andapplication. End-of-chapter exercises provide reinforcement for self-study andappendices covering multivariate distributions and Bayesianforecasting add useful reference material. Further coveragefeatures: * Similarities between time series analysis and longitudinal dataanalysis * Parsimonious modeling of covariance matrices through ARMA-likemodels * Fundamental roles of the Wold decomposition andorthogonalization * Applications in digital signal processing and Kalmanfiltering * Review of functional and harmonic analysis and predictiontheory Foundations of Time Series Analysis and Prediction Theory guidesreaders from the very applied principles of time series analysisthrough the most theoretical underpinnings of prediction theory. Itprovides a firm foundation for a widely applicable subject forstudents, researchers, and professionals in diverse scientificfields.
| Author | : Jianqing Fan |
| Publisher | : CRC Press |
| Total Pages | : 974 |
| Release | : 2020-09-21 |
| Genre | : Mathematics |
| ISBN | : 0429527616 |
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
