Regularized regression on compositional trees with application to MRI analysis

Bingkai Wang, Brian S. Caffo, Xi Luo, Chin‐Fu Liu, Andreia V. Faria, Michael I. Miller, Yi Zhao and for the Alzheimer's Disease Neuroimaging Initiative*

Journal of the Royal Statistical Society Series C, 2022, vol. 71, issue 3, 541-561

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 analysing 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.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/rssc.12545

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssc:v:71:y:2022:i:3:p:541-561

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9876

Access Statistics for this article

Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith

More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().