Ultra High Dimension Variable Selection With Threshold Partial Correlations
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Ultra High Dimension Variable Selection with Threshold Partial Correlations
With respect to variable selection in linear regression, partial correlation for normal models (Buhlmann, Kalisch and Maathuis, 2010), was a powerful alternative method to penalized least squares approaches (LASSO, SCAD, etc.). The method was improved by Li, Liu, Lou (2015) with the concept of threshold partial correlation (TPC) and extension to elliptical contoured dis- tributions. The TPC procedure is endowed with its dominant advantages over the simple partial correlation in high or ultrahigh dimensional cases (where the dimension of predictors increases in an exponential rate of the sample size). However, the convergence rate for TPC is not very satis- fying since it usually takes substantial amount of time for the procedure to reach the final solution, especially in high or even ultrahigh dimensional scenarios. Besides, the model assumptions on the TPC are too strong, which suggest the approach might not be conveniently used in practice. To address these two important issues, this dissertation puts forward an innovative model selection al- gorithm. It starts with an alternative definition of elliptical contoured distributions, which restricts the impact of the marginal kurtosis. This posts a relatively weaker condition for the validity of the model selection algorithm. Based on the simulation results, the new approach demonstrates not only competitive outcomes with established methods such as LASSO and SCAD, but also advan- tages in terms of computing efficiency. The idea of the algorithm is extended to survival data and nonparametric inference by exploring various measurements on correlations between the response variable and predictors.
Analysis of Variance for High-Dimensional Data
Overview of methods for analyzing high-dimensional experimental data, including theory, methodologies, and applications Analysis of Variance for High-Dimensional Data summarizes all the methods to analyze high-dimensional data that are obtained through applying an experimental design in the life, food, and chemical sciences, especially those developed in recent years. Written by international experts who lead development in the field, Analysis of Variance for High-Dimensional Data includes information on: Basic and established theories on linear models from a mathematical and statistical perspective Available methods and their mutual relationships, including coverage of ASCA, APCA, PC-ANOVA, ASCA+, LiMM-PCA and RM-ASCA+, and PERMANOVA, as well as various alternative methods and extensions Applications in metabolomics, microbiome, gene expression, proteomics, food science, sensory science, and chemistry Commercially available and open-source software for application of these methods Analysis of Variance for High-Dimensional Data is an essential reference for practitioners involved in data analysis in the natural sciences, including professionals working in chemometrics, bioinformatics, data science, statistics, and machine learning. The book is valuable for developers of new methods in high dimensional data analysis.
Robust Correlation
Author: Georgy L. Shevlyakov
language: en
Publisher: John Wiley & Sons
Release Date: 2016-09-19
This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data. Key features: Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields. Focuses on implementation of methodology and application of robust correlation with R. Introduces the main approaches in robust statistics, such as Huber’s minimax approach and Hampel’s approach based on influence functions. Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates. Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data. Includes an accompanying website featuring computer code and datasets Features exercises and examples throughout the text using both small and large data sets. Theoretical and applied statisticians, specialists in multivariate statistics, robust statistics, robust time series analysis, data analysis and signal processing will benefit from this book. Practitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful.