High Dimensional Correlation Networks And Their Applications.

Big Data;High Dimensional Data;Correlation Analysis;Time Series Analysis;Covariance Estimation;Dimensionality Reduction;Electrical Engineering;Engineering;Electrical Engineering: Systems

Firouzi, HamedVershynin, Roman ;

University of Michigan

关键词: Big Data;    High Dimensional Data;    Correlation Analysis;    Time Series Analysis;    Covariance Estimation;    Dimensionality Reduction;    Electrical Engineering;    Engineering;    Electrical Engineering: Systems;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/113492/firouzi_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Analysis of interactions between variables in a large data set has recently attracted special attention in the context of high dimensional multivariate statistical analysis. Variable interactions play a role in many inference tasks, such as, classification, clustering, estimation, and prediction. This thesis focuses on the discovery of correlation and partial correlation structures as well as their applications in high dimensional data analysis and inference. The thesis considers problems of screening correlationand partial correlation networks by thresholding the sample correlation or the sample partial correlation matrix. The selection of the threshold is guided by our high dimensional asymptotic theory for screening such networks. Scalable methods of edge and hub screening are developed for applications in spatio-temporal analysis of time series, variable selection for linear prediction, and support recovery. The proposed methods are specifically designed for very high dimensional data with limited number of samples. Moreover, the correlation screening theory developed in this thesis provides high dimensional family-wise error rates on false discoveries.