论文标题
多组标量的双软阈值模型在矢量值图像回归上
Double soft-thresholded model for multi-group scalar on vector-valued image regression
论文作者
论文摘要
在本文中，我们开发了一种新型的空间变量选择方法，用于在多组设置中对矢量值图像回归的标量。在这里，“矢量值映像”是指在每个像素/体素位置中包含矢量值信息的成像数据集，例如在RGB颜色图像，多模式医学图像，DTI成像等中。此工作的重点是识别图像中的空间位置对标量结果的重要效果。具体而言，每个体素的总体效果是感兴趣的。因此，我们通过软阈值\ ell_2的\ ell_2标准进行了潜在的多元高斯过程的\ ell_2规范，因此我们开发了一种新颖的收缩。这将使我们能够估计稀疏和分段平滑的空间变化的矢量值回归系数函数。对于后推断，开发了有效的MCMC算法。假设真实的回归系数是平稳的，我们为参数估计的后验收缩率和一致性的一致性。最后，我们证明了所提出的方法在仿真研究中的优势，并在ADNI数据集中进一步说明了基于基于DTI的矢量值值成像标记的MMSE分数进行建模。
In this paper, we develop a novel spatial variable selection method for scalar on vector-valued image regression in a multi-group setting. Here, 'vector-valued image' refers to the imaging datasets that contain vector-valued information at each pixel/voxel location, such as in RGB color images, multimodal medical images, DTI imaging, etc. The focus of this work is to identify the spatial locations in the image having an important effect on the scalar outcome measure. Specifically, the overall effect of each voxel is of interest. We thus develop a novel shrinkage prior by soft-thresholding the \ell_2 norm of a latent multivariate Gaussian process. It will allow us to estimate sparse and piecewise-smooth spatially varying vector-valued regression coefficient functions. For posterior inference, an efficient MCMC algorithm is developed. We establish the posterior contraction rate for parameter estimation and consistency for variable selection of the proposed Bayesian model, assuming that the true regression coefficients are Holder smooth. Finally, we demonstrate the advantages of the proposed method in simulation studies and further illustrate in an ADNI dataset for modeling MMSE scores based on DTI-based vector-valued imaging markers.
