成分树的正则化回归及其在MRI分析中的应用
Regularized regression on compositional trees with application to MRI analysis
摘要：
合成树是指一组随机变量上的树结构，其中每个随机变量是一个节点，并且合成发生在树的每个非叶节点处。作为组成数据的概括，组成树处理随机变量之间更复杂的关系，出现在许多学科中，例如脑成像、基因组学和金融学。我们考虑与组合树相关的数据的稀疏回归问题，并提出了一种基于无变换树的正则化回归方法用于组件选择。正则化惩罚是基于树结构设计的，并鼓励稀疏树表示。我们证明了我们所提出的回归系数的估计是相容的和模型选择相容的。在仿真研究中，我们的方法显示出更高的精度比竞争的方法在不同的情况下。通过分析来自阿尔茨海默病研究的脑成像数据集，我们的方法确定了记忆衰退与大脑区域体积之间的有意义的关联，这与目前的理解是一致的。
英文摘要：
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees handle more complex relationships among random variables and appear in many disciplines, such as brain imaging, genomics and finance. We consider the problem of sparse regression on data that are associated with a compositional tree and propose a transformation-free tree-based regularized regression method for component selection. The regularization penalty is designed based on the tree structure and encourages a sparse tree representation. We prove that our proposed estimator for regression coefficients is both consistent and model selection consistent. In the simulation study, our method shows higher accuracy than competing methods under different scenarios. By analyzing a brain imaging data set from studies of Alzheimer's disease, our method identifies meaningful associations between memory declination and volume of brain regions that are consistent with current understanding.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
