Название: Sufficient Dimension Reduction: Methods and Applications with R
Автор: Bing Li
Издательство: Chapman and Hall/CRC
ISBN: 1498704476
Год: 2018
Страниц: 304
Язык: английский
Формат: pdf (true)
Размер: 42.8 MB

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.

Sufficient Dimension Reduction is a powerful tool to extract the core information hidden in the high-dimensional data, for the purpose of classifying or predicting one or several response variables. The extraction of information is based on the notion of sufficiency, which means a set of functions of the predictors provides all the information needed to understand the response, so that the rest of the predictors can be ignored without loss of information. Sufficiency is derived from conditional independence, a statistical concept that plays the central role in this theory.

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.