The Annals of Applied Statistics

Learning population and subject-specific brain connectivity networks via mixed neighborhood selection

Ricardo Pio Monti, Christoforos Anagnostopoulos, and Giovanni Montana

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In neuroimaging data analysis, Gaussian graphical models are often used to model statistical dependencies across spatially remote brain regions known as functional connectivity. Typically, data is collected across a cohort of subjects and the scientific objectives consist of estimating population and subject-specific connectivity networks. A third objective that is often overlooked involves quantifying inter-subject variability, and thus identifying regions or subnetworks that demonstrate heterogeneity across subjects. Such information is crucial to thoroughly understand the human connectome. We propose Mixed Neighborhood Selection to simultaneously address the three aforementioned objectives. By recasting covariance selection as a neighborhood selection problem, we are able to efficiently learn the topology of each node. We introduce an additional mixed effect component to neighborhood selection to simultaneously estimate a graphical model for the population of subjects as well as for each individual subject. The proposed method is validated empirically through a series of simulations and applied to resting state data for healthy subjects taken from the ABIDE consortium.

Article information

Ann. Appl. Stat. Volume 11, Number 4 (2017), 2142-2164.

Received: December 2015
Revised: January 2017
First available in Project Euclid: 28 December 2017

Permanent link to this document

Digital Object Identifier

Functional connectivity neuroimaging graphical models inter-subject variability


Monti, Ricardo Pio; Anagnostopoulos, Christoforos; Montana, Giovanni. Learning population and subject-specific brain connectivity networks via mixed neighborhood selection. Ann. Appl. Stat. 11 (2017), no. 4, 2142--2164. doi:10.1214/17-AOAS1067.

Export citation


  • Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. Science 286 509–512.
  • Belilovsky, E., Varoquaux, G. and Blaschko, M. (2016). Testing for differences in Gaussian graphical models: Applications to brain connectivity. In Neural Information Processing Systems 595–603.
  • Bullmore, E. and Sporns, O. (2009). Complex brain networks: Graph theoretical analysis of structural and functional systems. Nat. Rev., Neurosci. 10 186–198.
  • Chung, M., Hanson, J., Ye, J., Davidson, R. and Pollak, S. (2015). Persistent homology in sparse regression and its application to brain morphometry. IEEE Trans. Med. Imag. 34 1928–1939.
  • Damoiseaux, J., Rombouts, S., Barkhof, F., Scheltens, P., Stam, C., Smith, S. and Beckmann, C. (2006). Consistent resting-state networks across healthy subjects. Proc. Natl. Acad. Sci. USA 103 13848–13853.
  • Danaher, P., Wang, P. and Witten, D. M. (2014). The joint graphical lasso for inverse covariance estimation across multiple classes. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 373–397.
  • Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B. Stat. Methodol. 39 1–38.
  • Di Martino, A., Yan, C., Li, Q., Denio, E., Castellanos, F., Alaerts, K., Anderson, J., Assaf, M., Bookheimer, S. and Dapretto, M. (2014). The Autism Brain Imaging Data Exchange: Towards a large-scale evaluation of the intrinsic brain architecture in Autism. Mol. Psychiatry 19 659–667.
  • Dubois, J. and Adolphs, R. (2016). Building a science of individual differences from fMRI. Trends Cogn. Sci. 20 425–443.
  • Fair, D., Dosenbach, N., Church, J., Cohen, A., Brahmbhatt, S., Miezin, F., Barch, D., Raichle, M., Petersen, S. and Schlaggar, B. (2007). Development of distinct control networks through segregation and integration. Proc. Natl. Acad. Sci. USA 104 13507–13512.
  • Fair, D. A., Cohen, A. L., Power, J. D., Dosenbach, N. U. F., Church, J. A., Miezin, F. M., Schlaggar, B. L. and Petersen, S. E. (2009). Functional brain networks develop from a “local to distributed” organization. PLoS Comput. Biol. 5 e1000381.
  • Fallani, F., Richiardi, J., Chavez, M. and Achard, S. (2014). Graph analysis of functional brain networks: Practical issues in translational neuroscience. Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369 1–17.
  • Fox, M. and Greicius, M. (2010). Clinical applications of resting state functional connectivity. Front. Syst. Neurosci. 4 1–13.
  • Friedman, J., Hastie, T. and Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics 9 432–441.
  • Friedman, J., Hastie, T., Höfling, H. and Tibshirani, R. (2007). Pathwise coordinate optimization. Ann. Appl. Stat. 1 302–332.
  • Friston, K. (2011). Functional and effective connectivity: A review. Brain Connect. 1 13–36.
  • Greicius, M., Krasnow, B., Reiss, A. and Menon, V. (2003). Functional connectivity in the resting brain: A network analysis of the default mode hypothesis. Proc. Natl. Acad. Sci. USA 100 253–258.
  • Gusnard, D. and Raichle, M. (2001). Searching for a baseline: Functional imaging and the resting human brain. Nat. Rev., Neurosci. 2 685–694.
  • Kanai, R. and Rees, G. (2011). The structural basis of inter-individual differences in human behaviour and cognition. Nat. Rev., Neurosci. 12 231–242.
  • Kelly, C., Biswal, B., Craddock, C., Castellanos, X. and Milham, M. (2012). Characterizing variation in the functional connectome: Promise and pitfalls. Trends Cogn. Sci. 16 181–188.
  • Krzanowski, W. J. and Hand, D. J. (2009). ROC Curves for Continuous Data. Monographs on Statistics and Applied Probability 111. CRC Press, Boca Raton, FL.
  • Lee, H., Lee, D., Kang, H., Kim, B. and Chung, M. (2011). Sparse brain network recovery under compressed sensing. IEEE Trans. Med. Imag. 30 1154–1165.
  • Lindquist, M. A. (2008). The statistical analysis of fMRI data. Statist. Sci. 23 439–464.
  • McLachlan, G. J. and Krishnan, T. (2007). The EM Algorithm and Extensions. Wiley Series in Probability and Statistics 382. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ.
  • Meinshausen, N. and Bühlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436–1462.
  • Meng, X.-L. and van Dyk, D. (1998). Fast EM-type implementations for mixed effects models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 60 559–578.
  • Monti, R. P., Anagnostopoulos, C. and Montana, G. (2017). Supplement to “Learning population and subject-specific brain connectivity networks via mixed neighborhood selection.” DOI:10.1214/17-AOAS1067SUPPA, DOI:10.1214/17-AOAS1067SUPPB.
  • Mueller, S., Wang, D., Fox, M., Yeo, T., Sepulcre, J., Sabuncu, M., Shafee, R., Lu, J. and Liu, H. (2013). Individual variability in functional connectivity architecture of the human brain. Neuron 77 586–595.
  • Narayan, M., Allen, G. and Tomson, S. (2015). Two sample inference for populations of graphical models with applications to functional connectivity. Preprint. Available at arXiv:1502.03853.
  • Nielsen, J., Zielinski, B., Fletcher, T., Alexander, A., Lange, N., Bigler, E., Lainhart, J. and Anderson, J. (2013). Multisite functional connectivity MRI classification of autism: ABIDE results. Front. Human Neurosci. 7 72–83.
  • Pinheiro, J. and Bates, D. (2000). Mixed-Effects Models in S and S-PLUS. Springer Science & Business Media, Berlin.
  • Power, J., Barnes, K., Snyder, A., Schlaggar, B. and Petersen, S. (2012). Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion. NeuroImage 59 2142–2154.
  • Rubinov, M. and Sporns, O. (2010). Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52 1059–1069.
  • Schelldorfer, J., Bühlmann, P. and van de Geer, S. (2011). Estimation for high-dimensional linear mixed-effects models using $\ell_{1}$-penalization. Scand. J. Stat. 38 197–214.
  • Smith, S. (2012). The future of fMRI connectivity. NeuroImage 62 1257–1266.
  • Smith, S., Miller, K., Salimi-Khorshidi, G., Webster, M., Beckmann, C., Nichols, T., Ramsey, J. and Woolrich, M. (2011). Network modelling methods for fMRI. NeuroImage 54 875–891.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B. Stat. Methodol. 58 267–288.
  • Van Den Heuvel, M. and Pol, H. (2010). Exploring the brain network: A review on resting-state fMRI functional connectivity. Eur. Neuropsychopharmacol. 20 519–534.
  • Varoquaux, G. and Craddock, C. (2013). Learning and comparing functional connectomes across subjects. NeuroImage 80 405–415.
  • Varoquaux, G., Gramfort, A., Poline, J. and Thirion, B. (2010). Brain covariance selection: Better individual functional connectivity models using population prior. In Neural Information Processing Systems 2334–2342.
  • Zuo, X., Di Martino, A., Kelly, C., Shehzad, Z., Gee, D., Klein, D., Castellanos, X., Biswal, B. and Milham, M. (2010). The oscillating brain: Complex and reliable. NeuroImage 49 1432–1445.

Supplemental materials

  • Supplement A. A pdf document consisting of parts A, B, C and D. This supplement contains further details of the various simulation settings employed throughout the manuscript together with an extensive sensitivity analysis of the proposed method. A brief discussion of brain regions studied in the application is also provided.
  • Supplement B. A .zip file consisting of R code implementing the proposed Mixed Neighbourhood Selection algorithm. This code may also be freely downloaded from the Comprehensive R Archive Network (CRAN).