Faculty, Staff and Student Publications
Publication Date
6-1-2022
Journal
Journal of the Royal Statistical Society: Series C
Abstract
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 decline and volume of brain regions that are consistent with current understanding.
Keywords
composition, hierarchical tree, regularized regression
DOI
10.1111/rssc.12545
PMID
35991528
PMCID
PMC9387759
PubMedCentral® Posted Date
8-18-2022
PubMedCentral® Full Text Version
Author MSS
Published Open-Access
yes
