Alzheimer's disease can be diagnosed by analyzing brain images (eg, magnetic resonance imaging, MRI) and neuropsychological tests (eg, mini-mental state examination, MMSE). A partially linear mean shift model (PLMSM) is here proposed to investigate the relationship between MMSE score and high-dimensional regions of interest in MRI, and detect the outliers. In the presence of high-dimensional data, existing Bayesian approaches (eg, Markov chain Monte Carlo) to analyze a PLMSM take intensive computational cost and require huge memory, and have low convergence rate. To address these issues, a variational Bayesian inference is developed to simultaneously estimate parameters and nonparametric functions and identify outliers in a PLMSM. A Bayesian P-splines method is presented to approximate nonparametric functions, a Bayesian adaptive Lasso approach is employed to select predictors, and outliers are detected by the classification variable. Two simulation studies are conducted to assess the finite sample performance of the proposed method. An MRI dataset with elderly cognitive ability is provided to corroborate the proposed method.

中文翻译：

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高维阿尔茨海默病神经影像数据的变分贝叶斯部分线性均值漂移模型

阿尔茨海默病可以通过分析大脑图像（例如，磁共振成像，MRI）和神经心理学测试（例如，微型精神状态检查，MMSE）来诊断。这里提出了一种部分线性均值漂移模型（PLMSM）来研究 MMSE 分数与 MRI 中高维感兴趣区域之间的关系，并检测异常值。在存在高维数据的情况下，现有的用于分析PLMSM 的贝叶斯方法（例如，马尔可夫链蒙特卡罗）需要大量的计算成本并且需要巨大的内存，并且收敛速度低。为了解决这些问题，开发了变分贝叶斯推理以同时估计参数和非参数函数并识别 PLMSM 中的异常值。提出了一种贝叶斯 P 样条方法来逼近非参数函数，采用贝叶斯自适应套索方法选择预测变量，并通过分类变量检测异常值。进行了两次模拟研究以评估所提出方法的有限样本性能。提供了具有老年人认知能力的 MRI 数据集来证实所提出的方法。