High Dimensional Dependent Data Analysis for Neuroimaging.

High dimensional dependent data;Neuroimaging;Multiple testing;Hidden Markov random field;Covariance/precision matrix estimation;Polynomial-decay-dominated temporal dependence;Statistics and Numeric Data;Science;Biostatistics

Shu, HaiBerrocal, Veronica ;

University of Michigan

关键词: High dimensional dependent data;    Neuroimaging;    Multiple testing;    Hidden Markov random field;    Covariance/precision matrix estimation;    Polynomial-decay-dominated temporal dependence;    Statistics and Numeric Data;    Science;    Biostatistics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/133198/haishu_1.pdf?sequence=1&isAllowed=y

瑞士|英语

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

【 摘 要 】

This dissertation contains three projects focusing on two major high-dimensional problems for dependent data, particularly neuroimaging data: multiple testing and estimation of large covariance/precision matrices. Project 1 focuses on the multiple testing problem. Traditional voxel-level false discovery rate (FDR) controlling procedures for neuroimaging data often ignore the spatial correlations among neighboring voxels, thus suffer from substantial loss of efficiency in reducing the false non-discovery rate. We extend the one-dimensional hidden Markov chain based local-significance-index procedure to three-dimensional hidden Markov random field (HMRF). To estimate model parameters, a generalized EM algorithm is proposed for maximizing the penalized likelihood. Simulations show increased efficiency of the proposed approach over commonly used FDR controlling procedures. We apply the method to the comparison between patients with mild cognitive impairment and normal controls in the ADNI FDG-PET imaging study. Project 2 considers estimating large covariance and precision matrices from temporally dependent observations, in particular, the resting-state functional MRI (rfMRI) data in brain functional connectivity studies. Existing work on large covariance and precision matrices is primarily for i.i.d. observations. The rfMRI data from the Human Connectome Project, however, are shown to have long-range memory. Assuming a polynomial-decay-dominated temporal dependence, we obtain convergence rates for the generalized thresholding estimation of covariance and correlation matrices, and for the constrained $ell_1$ minimization and the $ell_1$ penalized likelihood estimation of precision matrix. Properties of sparsistency and sign-consistency are also established. We apply the considered methods to estimating the functional connectivity from single-subject rfMRI data. Project 3 extends Project 2 to multiple independent samples of temporally dependent observations. This is motivated by the group-level functional connectivity analysis using rfMRI data, where each subject has a sample of temporally dependent image observations. We use different concentration inequalities to obtain faster convergence rates than those in Project 2 of the considered estimators for multi-sample data. The new proof allows more general within-sample temporal dependence. We also discuss a potential way of improving the convergence rates by using a weighted sample covariance matrix. We apply the considered methods to the functional connectivity estimation for the ADHD-200 rfMRI data.