Regularized regression on compositional trees with application to MRI analysis

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 appe...

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Published inJournal of the Royal Statistical Society Series C: Applied Statistics Vol. 71; no. 3; pp. 541 - 561
Main Authors Wang, Bingkai, Caffo, Brian S., Luo, Xi, Liu, Chin‐Fu, Faria, Andreia V., Miller, Michael I., Zhao, Yi
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.06.2022
Subjects
Alzheimer's disease
Brain
Complex variables
composition
Finance
Genomics
hierarchical tree
Magnetic resonance imaging
Medical imaging
Neuroimaging
Random variables
Regression coefficients
Regularization
regularized regression
Simulation
Transformation
Trees
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Summary: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.
Bibliography:Funding information
NIH,P30AG072976;U54AG065181;R01EB029977;P41EB031771;U54DA049110
http://adni.loni.usc.edu/wpcontent/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf
Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at
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Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete list of ADNI investigators can be found at: http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf
ISSN:0035-9254
1467-9876
DOI:10.1111/rssc.12545