稳定和可预测的功能域选择及其在脑图像中的应用
Stable and predictive functional domain selection with application to brain images
摘要：
出于越来越多的相关脑图像的临床结果感兴趣的趋势，我们提出了一个功能域选择（FuDoS）的方法，有效地选择与结果相关的大脑的子区域。将每个人的大脑视为一个三维功能对象，统计的目的是区分回归系数$β(t)=0$与$β(t)\neq0$的区域，其中$t$表示空间位置。FuDoS由两个估计阶段组成。我们首先根据相关结构将大脑分割成几个小部分。然后，潜在的子集建立使用所获得的段和它们的预测性能进行评估，以选择最佳的子集，增强的稳定性选择标准。我们进行了广泛的模拟1D和3D的功能数据，并评估其有效性，在选择真正的子区域。我们还研究了选定的稳定区域的预测能力。为了找到与认知能力相关的大脑区域，将FuDoS应用于ADNI的PET数据。由于诱导的稀疏性，结果自然提供了更多关于区域和结果之间关系的可解释信息。此外，从我们的分析中选择的区域显示出与已知具有记忆相关功能的预期解剖大脑区域的高度关联。
英文摘要：
Motivated by increasing trends of relating brain images to a clinical outcome of interest, we propose a functional domain selection (FuDoS) method that effectively selects subregions of the brain associated with the outcome. View each individual's brain as a 3D functional object, the statistical aim is to distinguish the region where a regression coefficient $β(t)=0$ from $β(t)\neq0$, where $t$ denotes spatial location. FuDoS is composed of two stages of estimation. We first segment the brain into several small parts based on the correlation structure. Then, potential subsets are built using the obtained segments and their predictive performance are evaluated to select the best subset, augmented by a stability selection criterion. We conduct extensive simulations both for 1D and 3D functional data, and evaluate its effectiveness in selecting the true subregion. We also investigate predictive ability of the selected stable regions. To find the brain regions related to cognitive ability, FuDoS is applied to the ADNI's PET data. Due to the induced sparseness, the results naturally provide more interpretable information about the relations between the regions and the outcome. Moreover, the selected regions from our analysis show high associations with the expected anatomical brain areas known to have memory-related functions.
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