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Homogeneity Pursuit.

ABSTRACT: This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of homogeneity with a large cluster of known atom zero. In this article, we propose a new method called clustering algorithm in regression via data-driven segmentation (CARDS) to explore homogeneity. New mathematics are provided on the gain that can be achieved by exploring homogeneity. Statistical properties of two versions of CARDS are analyzed. In particular, the asymptotic normality of our proposed CARDS estimator is established, which reveals better estimation accuracy for homogeneous parameters than that without homogeneity exploration. When our methods are combined with sparsity exploration, further efficiency can be achieved beyond the exploration of sparsity alone. This provides additional insights into the power of exploring low-dimensional structures in high-dimensional regression: homogeneity and sparsity. Our results also shed lights on the properties of the fussed Lasso. The newly developed method is further illustrated by simulation studies and applications to real data. Supplementary materials for this article are available online.

SUBMITTER: Ke T

PROVIDER: S-EPMC4465377 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Homogeneity Pursuit.

Ke Tracy T Fan Jianqing J Wu Yichao Y

Journal of the American Statistical Association 20150101 509

This paper explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of homogeneity with a large cluster of known atom zero. In this article, we propose a new method called cluste ...[more]

PMID: 26085701

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Project description:The aim of this study is to determine whether regional homogeneity (ReHo) of resting-state blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (rsfMRI) data based on Kendall's coefficient of concordance (KCC-ReHo) and coherence (Cohe-ReHo) metrics may allow detection of brain tumor-induced neurovascular uncoupling (NVU) in the sensorimotor network similar to findings in standard motor task-based BOLD fMRI (tbfMRI) activation. Twelve de novo brain tumor patients undergoing clinical fMRI exams (tbfMRI and rsfMRI) were included in this Institutional Review Board (IRB)-approved study. Each patient displayed decreased/absent tbfMRI activation in the primary ipsilesional sensorimotor cortex in the absence of corresponding motor deficit or suboptimal task performance, consistent with NVU. Z-score maps for motor tasks were obtained from the general linear model (GLM) analysis (reflecting motor activation vs. rest). KCC-ReHo and Cohe-ReHo maps were calculated from rsfMRI data. Precentral and postcentral gyri in contralesional (CL) and ipsilesional (IL) hemispheres were parcellated using an automated anatomical labeling (AAL) template for each patient. Similar region of interest (ROI) analysis was performed on tbfMRI, KCC-ReHo, and Cohe-ReHo maps to allow direct comparison of results. Voxel values in CL and IL ROIs of each map were divided by the corresponding global mean of KCC-ReHo and Cohe-ReHo in bihemispheric cortical brain tissue. Group analysis revealed significantly decreased IL mean KCC-ReHo (p?=?0.02) and Cohe-ReHo (p?=?0.04) metrics compared with respective values in the CL ROIs, consistent with similar findings of significantly decreased ipsilesional BOLD signal for tbfMRI (p?=?0.0005). Ipsilesional abnormalities in ReHo derived from rsfMRI may serve as potential indicators of NVU in patients with brain tumors and other resectable brain lesions; as such, ReHo findings may complement findings on tbfMRI used for presurgical planning.

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Homogeneity Pursuit.

Publications

Homogeneity Pursuit.

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