Sparse Learning and Structure Identification for Ultrahigh-Dimensional Image-on-Scalar Regression
Sparse Learning and Structure Identification for Ultrahigh-Dimensional Image-on-Scalar Regression
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DOI：
10.1080/01621459.2020.1753523
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发表时间：
2020-05-26
影响因子：
3.7
通讯作者：
Wang, Huixia Judy
中科院分区：
文献类型：
--
作者：
Li, Xinyi;Wang, Li;Wang, Huixia Judy
本文考虑高维图像-标量回归，其中协变量效应对成像响应的空间异质性通过一个灵活的部分线性空间变系数模型进行了研究。为了解决由感兴趣区域组成的成像响应复杂域的空间平滑问题，我们通过三角剖分上的二元样条函数来近似空间变化系数函数。首先研究了常系数函数和变系数函数事先已知时的估计问题。然后，我们进一步开发了一种统一的方法，用于在超高维协变量存在下同时进行稀疏学习和模型结构识别。该方法能准确有效地识别零、非零常数和空间变化分量。常系数函数和变系数函数的估计量是一致的，对于常系数估计量是渐近正态的。该方法通过蒙特卡罗模拟研究进行评估，并应用于阿尔茨海默病神经成像倡议提供的数据集。这篇文章可以在网上找到。
This article considers high-dimensional image-on-scalar regression, where the spatial heterogeneity of covariate effects on imaging responses is investigated via a flexible partially linear spatially varying coefficient model. To tackle the challenges of spatial smoothing over the imaging response's complex domain consisting of regions of interest, we approximate the spatially varying coefficient functions via bivariate spline functions over triangulation. We first study estimation when the active constant coefficients and varying coefficient functions are known in advance. We then further develop a unified approach for simultaneous sparse learning and model structure identification in the presence of ultrahigh-dimensional covariates. Our method can identify zero, nonzero constant, and spatially varying components correctly and efficiently. The estimators of constant coefficients and varying coefficient functions are consistent and asymptotically normal for constant coefficient estimators. The method is evaluated by Monte Carlo simulation studies and applied to a dataset provided by the Alzheimer's Disease Neuroimaging Initiative.for this article are available online.