神经影像数据的贝叶斯张量回归
Bayesian Tensor Regression for Neuroimaging Data
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中文总结 AI 辅助
针对神经影像张量响应数据，提出贝叶斯张量包络回归模型，通过识别物质子空间实现降维，结合Gibbs采样算法，提升估计精度并应用于酒精使用与脑活动关联研究。
中文摘要 AI 辅助
多维数组数据（即张量）在神经影像学和其他高维应用中自然出现。我们针对脑图像为响应变量、预测变量为向量值协变量的研究，提出了一种简约的贝叶斯张量回归模型。该方法将贝叶斯包络降维扩展到张量响应，识别包含回归信息的物质子空间，同时去除与预测变量无关的变异。这一公式自然引出了Tucker张量分解，并允许空间依赖性和多种不确定性来源被联合建模。我们开发了一种基于Gibbs抽样的计算可行的马尔可夫链蒙特卡洛算法，并建立了所提出模型的后验一致性。模拟研究表明，当存在有意义的降维时，该方法在估计精度和不确定性量化方面有显著提升。我们将该方法应用于人类连接组计划（Human Connectome Project）的神经影像数据，以研究酒精使用与大脑活动之间的关联。结果展示了贝叶斯张量包络回归在高维、空间依赖性成像响应的推断中的价值。
英文摘要
Multidimensional array data, or tensors, arise naturally in neuroimaging and other high-dimensional applications. We propose a parsimonious Bayesian tensor regression model for studies in which a brain image is the response and predictors are vector-valued covariates. The method extends Bayesian envelope dimension reduction to tensor responses, identifying material subspaces that contain regression information while removing variation that is immaterial to the predictors. This formulation leads naturally to a Tucker tensor decomposition and allows spatial dependence and multiple sources of uncertainty to be modeled jointly. We develop a computationally feasible Markov chain Monte Carlo algorithm based on Gibbs sampling and establish posterior consistency for the proposed model. Simulation studies demonstrate substantial gains in estimation accuracy and uncertainty quantification when meaningful dimension reduction is present. We apply the method to Human Connectome Project neuroimaging data to investigate associations between alcohol use and brain activity. The results illustrate the value of Bayesian tensor envelope regression for inference with high-dimensional, spatially dependent imaging responses.
发表机构
- Sanford Health（桑福德健康）
- St. Edward’s University（圣爱德华大学）
- Virginia Commonwealth University（弗吉尼亚联邦大学）
- Bowling Green State University（鲍灵格林州立大学）
机构由 AI 辅助整理，请以论文原文为准。
