Statistical Inference From High Dimensional Data

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Statistical Inference from High Dimensional Data

Carlos Fernandez-Lozano
Statistical Inference from High Dimensional Data Book PDF

Author : Carlos Fernandez-Lozano
Publisher : MDPI
Page : 314 pages
File Size : 48,7 Mb
Release : 2021-04-28
Category : Science
ISBN : 9783036509440

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Statistical Inference from High Dimensional Data by Carlos Fernandez-Lozano Pdf

• Real-world problems can be high-dimensional, complex, and noisy • More data does not imply more information • Different approaches deal with the so-called curse of dimensionality to reduce irrelevant information • A process with multidimensional information is not necessarily easy to interpret nor process • In some real-world applications, the number of elements of a class is clearly lower than the other. The models tend to assume that the importance of the analysis belongs to the majority class and this is not usually the truth • The analysis of complex diseases such as cancer are focused on more-than-one dimensional omic data • The increasing amount of data thanks to the reduction of cost of the high-throughput experiments opens up a new era for integrative data-driven approaches • Entropy-based approaches are of interest to reduce the dimensionality of high-dimensional data

Statistics for High-Dimensional Data

Peter Bühlmann,Sara van de Geer
Statistics for High Dimensional Data Book PDF

Author : Peter Bühlmann,Sara van de Geer
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 45,7 Mb
Release : 2011-06-08
Category : Mathematics
ISBN : 9783642201929

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Statistics for High-Dimensional Data by Peter Bühlmann,Sara van de Geer Pdf

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.

Statistical Analysis for High-Dimensional Data

Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci
Statistical Analysis for High Dimensional Data Book PDF

Author : Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci
Publisher : Springer
Page : 306 pages
File Size : 46,9 Mb
Release : 2016-02-16
Category : Mathematics
ISBN : 9783319270999

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Statistical Analysis for High-Dimensional Data by Arnoldo Frigessi,Peter Bühlmann,Ingrid Glad,Mette Langaas,Sylvia Richardson,Marina Vannucci Pdf

This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvågar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in “big data” situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.

High-dimensional Data Analysis

Tianwen Tony Cai,Xiaotong Shen
High dimensional Data Analysis Book PDF

Author : Tianwen Tony Cai,Xiaotong Shen
Publisher : World Scientific Publishing Company Incorporated
Page : 307 pages
File Size : 48,8 Mb
Release : 2011
Category : Mathematics
ISBN : 981432485X

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High-dimensional Data Analysis by Tianwen Tony Cai,Xiaotong Shen Pdf

Over the last few years, significant developments have been taking place in high-dimensional 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 high-dimensional data analysis to explore key ideas for statistical inference and prediction. It is structured around topics on multiple hypothesis testing, feature selection, regression, classification, dimension reduction, as well as applications in survival analysis and biomedical research. The book will appeal to graduate students and new researchers interested in the plethora of opportunities available in high-dimensional data analysis.

High-Dimensional Statistics

Martin J. Wainwright
High Dimensional Statistics Book PDF

Author : Martin J. Wainwright
Publisher : Cambridge University Press
Page : 571 pages
File Size : 52,9 Mb
Release : 2019-02-21
Category : Business & Economics
ISBN : 9781108498029

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High-Dimensional Statistics by Martin J. Wainwright Pdf

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Fundamentals of High-Dimensional Statistics

Johannes Lederer
Fundamentals of High Dimensional Statistics Book PDF

Author : Johannes Lederer
Publisher : Springer Nature
Page : 355 pages
File Size : 42,5 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 9783030737924

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Fundamentals of High-Dimensional Statistics by Johannes Lederer Pdf

This textbook provides a step-by-step introduction to the tools and principles of high-dimensional statistics. Each chapter is complemented by numerous exercises, many of them with detailed solutions, and computer labs in R that convey valuable practical insights. The book covers the theory and practice of high-dimensional linear regression, graphical models, and inference, ensuring readers have a smooth start in the field. It also offers suggestions for further reading. Given its scope, the textbook is intended for beginning graduate and advanced undergraduate students in statistics, biostatistics, and bioinformatics, though it will be equally useful to a broader audience.

High-dimensional Data Analysis

Tony Cai;Xiaotong Shen,Tony Cai
High dimensional Data Analysis Book PDF

Author : Tony Cai;Xiaotong Shen,Tony Cai
Publisher : Unknown
Page : 318 pages
File Size : 55,7 Mb
Release : 2024-06-07
Category : Electronic
ISBN : 7894236322

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High-dimensional Data Analysis by Tony Cai;Xiaotong Shen,Tony Cai Pdf

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.

Introduction to High-Dimensional Statistics

Christophe Giraud
Introduction to High Dimensional Statistics Book PDF

Author : Christophe Giraud
Publisher : CRC Press
Page : 410 pages
File Size : 40,9 Mb
Release : 2021-08-25
Category : Computers
ISBN : 9781000408355

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Introduction to High-Dimensional Statistics by Christophe Giraud Pdf

Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.

Statistical Foundations of Data Science

Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou
Statistical Foundations of Data Science Book PDF

Author : Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou
Publisher : CRC Press
Page : 752 pages
File Size : 47,7 Mb
Release : 2020-09-21
Category : Mathematics
ISBN : 9781466510852

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Statistical Foundations of Data Science by Jianqing Fan,Runze Li,Cun-Hui Zhang,Hui Zou Pdf

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.

Analysis of Multivariate and High-Dimensional Data

Inge Koch
Analysis of Multivariate and High Dimensional Data Book PDF

Author : Inge Koch
Publisher : Cambridge University Press
Page : 531 pages
File Size : 43,8 Mb
Release : 2014
Category : Business & Economics
ISBN : 9780521887939

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Analysis of Multivariate and High-Dimensional Data by Inge Koch Pdf

This modern approach integrates classical and contemporary methods, fusing theory and practice and bridging the gap to statistical learning.

High-Dimensional Probability

Roman Vershynin
High Dimensional Probability Book PDF

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 43,6 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194

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High-Dimensional Probability by Roman Vershynin Pdf

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Principles and Methods for Data Science

Anonim
Principles and Methods for Data Science Book PDF

Author : Anonim
Publisher : Elsevier
Page : 498 pages
File Size : 42,5 Mb
Release : 2020-05-28
Category : Mathematics
ISBN : 9780444642127

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Principles and Methods for Data Science by Anonim Pdf

Principles and Methods for Data Science, Volume 43 in the Handbook of Statistics series, highlights new advances in the field, with this updated volume presenting interesting and timely topics, including Competing risks, aims and methods, Data analysis and mining of microbial community dynamics, Support Vector Machines, a robust prediction method with applications in bioinformatics, Bayesian Model Selection for Data with High Dimension, High dimensional statistical inference: theoretical development to data analytics, Big data challenges in genomics, Analysis of microarray gene expression data using information theory and stochastic algorithm, Hybrid Models, Markov Chain Monte Carlo Methods: Theory and Practice, and more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Principles and Methods for Data Science

Statistical Inference Via Convex Optimization

Anatoli Juditsky,Arkadi Nemirovski
Statistical Inference Via Convex Optimization Book PDF

Author : Anatoli Juditsky,Arkadi Nemirovski
Publisher : Princeton University Press
Page : 655 pages
File Size : 55,8 Mb
Release : 2020-04-07
Category : Mathematics
ISBN : 9780691197296

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Statistical Inference Via Convex Optimization by Anatoli Juditsky,Arkadi Nemirovski Pdf

This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences. Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems—sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals—demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems. Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.

Sparse Graphical Modeling for High Dimensional Data

Faming Liang,Bochao Jia
Sparse Graphical Modeling for High Dimensional Data Book PDF

Author : Faming Liang,Bochao Jia
Publisher : CRC Press
Page : 150 pages
File Size : 44,5 Mb
Release : 2023-08-02
Category : Mathematics
ISBN : 9780429582905

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Sparse Graphical Modeling for High Dimensional Data by Faming Liang,Bochao Jia Pdf

This book provides a general framework for learning sparse graphical models with conditional independence tests. It includes complete treatments for Gaussian, Poisson, multinomial, and mixed data; unified treatments for covariate adjustments, data integration, and network comparison; unified treatments for missing data and heterogeneous data; efficient methods for joint estimation of multiple graphical models; effective methods of high-dimensional variable selection; and effective methods of high-dimensional inference. The methods possess an embarrassingly parallel structure in performing conditional independence tests, and the computation can be significantly accelerated by running in parallel on a multi-core computer or a parallel architecture. This book is intended to serve researchers and scientists interested in high-dimensional statistics, and graduate students in broad data science disciplines. Key Features: A general framework for learning sparse graphical models with conditional independence tests Complete treatments for different types of data, Gaussian, Poisson, multinomial, and mixed data Unified treatments for data integration, network comparison, and covariate adjustment Unified treatments for missing data and heterogeneous data Efficient methods for joint estimation of multiple graphical models Effective methods of high-dimensional variable selection Effective methods of high-dimensional inference

Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data

Syed Ejaz Ahmed,Feryaal Ahmed,Bahadir Yüzbaşı
Post Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data Book PDF

Author : Syed Ejaz Ahmed,Feryaal Ahmed,Bahadir Yüzbaşı
Publisher : CRC Press
Page : 409 pages
File Size : 44,5 Mb
Release : 2023-05-25
Category : Business & Economics
ISBN : 9781000876659

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Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data by Syed Ejaz Ahmed,Feryaal Ahmed,Bahadir Yüzbaşı Pdf

This book presents some post-estimation and predictions strategies for the host of useful statistical models with applications in data science. It combines statistical learning and machine learning techniques in a unique and optimal way. It is well-known that machine learning methods are subject to many issues relating to bias, and consequently the mean squared error and prediction error may explode. For this reason, we suggest shrinkage strategies to control the bias by combining a submodel selected by a penalized method with a model with many features. Further, the suggested shrinkage methodology can be successfully implemented for high dimensional data analysis. Many researchers in statistics and medical sciences work with big data. They need to analyse this data through statistical modelling. Estimating the model parameters accurately is an important part of the data analysis. This book may be a repository for developing improve estimation strategies for statisticians. This book will help researchers and practitioners for their teaching and advanced research, and is an excellent textbook for advanced undergraduate and graduate courses involving shrinkage, statistical, and machine learning. The book succinctly reveals the bias inherited in machine learning method and successfully provides tools, tricks and tips to deal with the bias issue. Expertly sheds light on the fundamental reasoning for model selection and post estimation using shrinkage and related strategies. This presentation is fundamental, because shrinkage and other methods appropriate for model selection and estimation problems and there is a growing interest in this area to fill the gap between competitive strategies. Application of these strategies to real life data set from many walks of life. Analytical results are fully corroborated by numerical work and numerous worked examples are included in each chapter with numerous graphs for data visualization. The presentation and style of the book clearly makes it accessible to a broad audience. It offers rich, concise expositions of each strategy and clearly describes how to use each estimation strategy for the problem at hand. This book emphasizes that statistics/statisticians can play a dominant role in solving Big Data problems, and will put them on the precipice of scientific discovery. The book contributes novel methodologies for HDDA and will open a door for continued research in this hot area. The practical impact of the proposed work stems from wide applications. The developed computational packages will aid in analyzing a broad range of applications in many walks of life.