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Connectivity-Informed Adaptive Regularization for Generalized Outcomes

Damian Brzyski, Marta Karas, Beau Ances, Mario Dzemidzic, Joaquin Goni, Timothy W Randolph, Jaroslaw Harezlak
doi: https://doi.org/10.1101/322420
Damian Brzyski
aDepartment of Epidemiology and Biostatistics, Indiana University, Bloomington, IN, USA
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Marta Karas
bJohns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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Beau Ances
cJohns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
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Mario Dzemidzic
dIndiana University School of Medicine, Indianapolis, IN, USA
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Joaquin Goni
ePurdue University, West Lafayette, IN, USA
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Timothy W Randolph
fFred Hutchinson Cancer Research Center, Seattle, WA, USA
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Jaroslaw Harezlak
aDepartment of Epidemiology and Biostatistics, Indiana University, Bloomington, IN, USA
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Abstract

One of the challenging problems in the brain imaging research is a principled incorporation of information from different imaging modalities in association studies. Frequently, data from each modality is analyzed separately using, for instance, dimensionality reduction techniques, which result in a loss of mutual information. We propose a novel regularization method, griPEER (generalized ridgified Partially Empirical Eigenvectors for Regression) to estimate the association between the brain structure features and a scalar outcome within the generalized linear regression framework. griPEER provides a principled approach to use external information from the structural brain connectivity to improve the regression coefficient estimation. Our proposal incorporates a penalty term, derived from the structural connectivity Laplacian matrix, in the penalized generalized linear regression. We address both theoretical and computational issues and show that our method is robust to the incomplete information about the structural brain connectivity. We also provide a significance testing procedure for performing inference on the estimated coefficients in this model. griPEER is evaluated in extensive simulation studies and it is applied in classification of the HIV+ and HIV- individuals.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted May 15, 2018.
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Connectivity-Informed Adaptive Regularization for Generalized Outcomes
Damian Brzyski, Marta Karas, Beau Ances, Mario Dzemidzic, Joaquin Goni, Timothy W Randolph, Jaroslaw Harezlak
bioRxiv 322420; doi: https://doi.org/10.1101/322420
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Connectivity-Informed Adaptive Regularization for Generalized Outcomes
Damian Brzyski, Marta Karas, Beau Ances, Mario Dzemidzic, Joaquin Goni, Timothy W Randolph, Jaroslaw Harezlak
bioRxiv 322420; doi: https://doi.org/10.1101/322420

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