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Brain connectivity-informed regularization methods for regression

Marta Karas, Damian Brzyski, Mario Dzemidzic, Joaquin Goni, David A. Kareken, Timothy W. Randolph, Jaroslaw Harezlak
doi: https://doi.org/10.1101/117945
Marta Karas
aIndiana University, Bloomington, IN, USA
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Damian Brzyski
aIndiana University, Bloomington, IN, USA
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Mario Dzemidzic
bIndiana University School of Medicine, Indianapolis, IN, USA
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Joaquin Goni
cPurdue University, West Lafayette, IN, USA
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David A. Kareken
bIndiana University School of Medicine, Indianapolis, IN, USA
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Timothy W. Randolph
dFred Hutchinson Cancer Research Center, Seattle, WA, USA
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Jaroslaw Harezlak
aIndiana University, Bloomington, IN, USA
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Abstract

A challenging problem arising in brain imaging research is principled incorporation of information from different imaging modalities. Frequently 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 to estimate the association between the brain structure features and a scalar outcome within the linear regression framework. Our regularization technique provides a principled approach to utilizing external information arising from the structural brain connectivity to inform the estimation of the regression coefficients. Our proposal extends the classical Tikhonov regularization framework by defining a penalty term based on the structural connectivity-derived Laplacian matrix. In the work presented, we address both theoretical and computational issues. The approach is illustrated using simulated data and compared with other penalized regression methods. Finally, we apply our regularization method to study the associations between the alcoholism phenotypes and brain cortical thickness using a diffusion tensor imaging (DTI) derived measure of structural connectivity.

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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-ND 4.0 International license.
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Posted March 18, 2017.
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Brain connectivity-informed regularization methods for regression
Marta Karas, Damian Brzyski, Mario Dzemidzic, Joaquin Goni, David A. Kareken, Timothy W. Randolph, Jaroslaw Harezlak
bioRxiv 117945; doi: https://doi.org/10.1101/117945
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Brain connectivity-informed regularization methods for regression
Marta Karas, Damian Brzyski, Mario Dzemidzic, Joaquin Goni, David A. Kareken, Timothy W. Randolph, Jaroslaw Harezlak
bioRxiv 117945; doi: https://doi.org/10.1101/117945

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