Brain Connectivity-Informed Regularization Methods for Regression
Tóm tắt
One of the challenging problems in brain imaging research is a 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 use external information from the structural brain connectivity and 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. Here, we address both theoretical and computational issues. The approach is first illustrated using simulated data and compared with other penalized regression methods. We then apply our regularization method to study the associations between the alcoholism phenotypes and brain cortical thickness using a diffusion imaging derived measure of structural connectivity. Using the proposed methodology in 148 young male subjects with a risk for alcoholism, we found a negative associations between cortical thickness and drinks per drinking day in bilateral caudal anterior cingulate cortex, left lateral OFC, and left precentral gyrus.
Tài liệu tham khảo
Belge M, Kilmer ME, Miller EL (2002) Efficient determination of multiple regularization parameters in a generalized l-curve framework. Inverse Probl 18(4):1161–1183
Bertero M, Boccacci P (1998) Introduction to inverse problems in imaging. Institute of Physics, Bristol
Bjorck A (1996) Numerical methods for least squares problems. SIAM, Philadelphia
Blondel VD, Guillaume J-L, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp. https://doi.org/10.1088/1742-5468/2008/10/P10008
Brezinski C, Redivo-Zaglia M, Rodriguez G, Seatzu S (2003) Multi-parameter regularization techniques for ill-conditioned linear systems. Numer Math 94(2):203–228
Charpentier J, Dzemidzic M, West J, Oberlin BG 2nd, Eiler W, Saykin AJ, Kareken DA (2016) Externalizing personality traits, empathy, and gray matter volume in healthy young drinkers. Psychiatry Res 248:64–72
Chung F (2005) Laplacians and the Cheeger inequality for directed graphs. Ann Comb 9(1):1–19
Cole MW, Bassett DS, Power JD, Braver TS, Petersen SE (2014) Intrinsic and task-evoked network architectures of the human brain. Neuron 83(1):238–251
Craven P, Wahba G (1979) Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer Math 31:377–403
Csardi G, Nepusz T (2006) The igraph software package for complex network research. InterJournal Complex Systems 1695. http://igraph.org
Demidenko E (2004) Mixed models: theory and applications. Wiley, Hoboken
Desikan RS, Segonne F, Fischl B, Quinn BT, Dickerson BC, Blacker D, Buckner RL, Dale AM, Maguire RP, Hyman BT, Albert MS, Killiany RJ (2006) An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage 31(3):968–80
Elden L (1982) A weighted pseudoinverse, generalized singular values, and constrained least squares problems. BIT 22:487–502
Engl HW, Hanke M, Neubauer A (2000) Regularization of inverse problems. Kluwer, Dordrecht
Fischl B (2012) FreeSurfer. Neuroimage 62(2):774–781. https://doi.org/10.1016/j.neuroimage.2012.01.021. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3685476/
Freytag S, Manitz J, Schlather M, Kneib T, Amos CI, Risch A, Chang-Claude J, Heinrich J, Bickeböller H (2014) A network-based kernel machine test for the identification of risk pathways in genome-wide association studies. Hum Hered 76(2):64–75
Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1):1–22. http://www.jstatsoft.org/v33/i01/
Golub G, Van Loan C (2013) Matrix computations, 4th edn. Johns Hopkins University Press, Baltimore
Hagmann P, Cammoun L, Gigandet X, Meuli R, Honey CJ, Wedeen VJ, Sporns O (2008) Mapping the structural core of human cerebral cortex. PLoS Biol 6(7):e159
Hansen PC (1998) Rank-deficient and discrete III-posed problems: numerical aspects of linear inversion. SIAM, Philadelphia
Hastie T, Buja A, Tibshirani R (1995) Penalized discriminant analysis. Ann Stat 23(1):73–102
Huang J, Shen H, Buja A (2008) Functional principal components analysis via penalized rank one approximation. Electron J Stat 2:678–695
Johnson SG (2016) The nlopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt
Karas M (2016) mdpeer: graph-constrained regression with enhanced regularization parameters selection. r package version 0.1.0. https://CRAN.R-project.org/package=mdpeer
Li C, Li H (2008) Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 24(9):1175–1182
Lu S, Pereverzev SV (2011) Multi-parameter regularization and its numerical realization. Numer Math 118(1):1–31
Maldonado YM (2009) Mixed models, posterior means and penalized least-squares. Optimality 57:216–236
McCulloch CE, Neuhaus JM, Searle SR (2008) Generalized, linear, and mixed models, 2nd edn. Wiley, Hoboken
Momenan R, Steckler LE, Saad ZS, van Rafelghem S, Kerich MJ, Hommer DW (2012) Effects of alcohol dependence on cortical thickness as determined by magnetic resonance imaging. Psychiatry Res 204(2–3):101–111
Nakamura-Palacios EM, Souza RS, Zago-Gomes MP, Melo AM, Braga FS, Kubo TT, Gasparetto EL (2014) Gray matter volume in left rostral middle frontal and left cerebellar cortices predicts frontal executive performance in alcoholic subjects. Alcohol Clin Exp Res 38(4):1126–33
Oberlin BG, Dzemidzic M, Tran SM, Soeurt CM, Albrecht DS, Yoder KK, Kareken DA (2013) Beer flavor provokes striatal dopamine release in male drinkers: mediation by family history of alcoholism. Neuropsychopharmacology 38(9):1617–24
Oberlin BG, Dzemidzic M, Tran SM, Soeurt CM, O’Connor SJ, Yoder KK, Kareken DA (2015) Beer self-administration provokes lateralized nucleus accumbens dopamine release in male heavy drinkers. Psychopharmacology (Berl) 232(5):861–70
Paige CC, Saunders MA (2006) Towards a generalized singular value decomposition. SIAM J Numer Anal 18(3):398–405
Pennington DL, Durazzo TC, Schmidt TP, Abe C, Mon A, Meyerhoff DJ (2015) Alcohol use disorder with and without stimulant use: brain morphometry and its associations with cigarette smoking, cognition, and inhibitory control. PLoS ONE 10(3):e0122,505
Phillips D (1962) A technique for the numerical solution of certain integral equations of the first kind. J ACM 9(1):84–97
Purdom E (2011) Analysis of a data matrix and a graph: metagenomic data and the phylogenetic tree. Ann Appl Stat 5(4):2326–2358
Randolph TW, Harezlak J, Feng Z (2012) Structured penalties for functional linear models: partially empirical eigenvectors for regression. Electron J Stat 6:323–353
Reiss PT, Ogden RT (2009) Smoothing parameter selection for a class of semiparametric linear models. J R Stat Soc 71(2):505–523
Rowan T (1990) Functional stability analysis of numerical algorithms. PhD thesis, University of Texas at Austin
Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric regression. Cambridge University Press, Cambridge
Slawski M, Castell WZ, Tutz G (2010) Feature selection guided by structural information. Ann Appl Stat 4(2):1056–1080
Sporns O (2013) Network attributes for segregation and integration in the human brain. Curr Opin Neurobiol 23(2):162–171
Sporns O, Betzel RF (2016) Modular brain networks. Annu Rev Psychol 67:613
Squeglia LM, Sorg SF, Schweinsburg AD, Wetherill RR, Pulido C, Tapert SF (2012) Binge drinking differentially affects adolescent male and female brain morphometry. Psychopharmacology (Berl) 220(3):529–539
Tibshirani R, Taylor J (2011) The solution path of the generalized lasso. Ann Stat 39(3):1335–1371
Tibshirani R, Saunders M, Rosset S, Zhu J, Knight K (2005) Sparsity and smoothness via the fused lasso. J R Stat Soc 67(1):91–108
Tikhonov A (1963) Solution of incorrectly formulated problems and the regularization method. Sov Math 4(4):1035–1038
Weafer J, Dzemidzic M 2nd, Eiler W, Oberlin BG, Wang Y, Kareken DA (2015) Associations between regional brain physiology and trait impulsivity, motor inhibition, and impaired control over drinking. Psychiatry Res 233(2):81–7
Ypma J (2014) nloptr: R interface to NLopt. r package version 1.0.4. https://CRAN.R-project.org/package=nloptr