Nonparametric Bayes Modeling of Populations of Networks

Journal of the American Statistical Association

Volumn 112, Issue 520, 2017, Pages 1516-1530

  Durante, Daniele ^a   Dunson, David B ^b   Vogelstein, Joshua T ^c  

^a UNIVERSITY OF PADOVA   (Italy)

^b Duke University   (United States)

^c JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Bayesian nonparametrics; Brain network; Latent space; Matrix factorization; Network valued random variable

Indexed keywords

EID: 85021967028     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2016.1219260     Document Type: Article

References (45)

1. Airoldi, E. M., Blei, D. M., Fienberg, S. E., and Xing, E. P., (2008), “Mixed Membership Stochastic Blockmodels,” Journal of Machine Learning Research, 9, 1981–2014.
2. Barabási, A.-L., and Albert, R., (1999), “Emergence of Scaling in Random Networks,” Science, 286, 509–512.
3. Bhattacharya, A., and Dunson, D. B., (2010), “Nonparametric Bayesian Density Estimation on Manifolds with Applications to Planar Shapes,” Biometrika, 97, 851–865.
4. Bhattacharya, A., and Dunson, D. B., (2011), “Sparse Bayesian Infinite Factor Models,” Biometrika, 98, 291–306.
5. Bullmore, E., and Sporns, O., (2009), “Complex Brain Networks: Graph Theoretical Analysis of Structural and Functional Systems,” Nature Reviews Neuroscience, 10, 186–198.
6. Bullmore, E., and Sporns, O. (2012), “The Economy of Brain Network Organization,” Nature Reviews Neuroscience, 77, 586–595.
7. Choi, H. M., and Hobert, J. P., (2013), “The Polya-Gamma Gibbs Sampler for Bayesian Logistic Regression is Uniformly Ergodic,” Electronic Journal of Statistics, 7, 2054–2064.
8. Craddock, R. C., Jbabdi, S., Yan, C.-G., Vogelstein, J. T., Castellanos, F. X., Martino, A. D., Kelly, C., Heberlein, K., Colcombe, S., and Milham, M. P., (2013), “Imaging Human Connectomes at the Macroscale,” Nature Methods, 10, 524–539.
9. Desikan, R. S., Ségonne, F., Fischl, B., Quinn, B. T., Dickerson, B. C., Blacker, D., Buckner, R. L., Dale, A. M., Maguire, R. P., Hyman, B. T., Albert, M. S., and Killiany, R. J., (2006), “An Automated Labeling System for Subdividing the Human Cerebral Cortex on MRI Scans into Gyral Based Regions of Interest,” NeuroImage, 31, 968–980.
10. Dunson, D. B., and Xing, C., (2009), “Nonparametric Bayes Modeling of Multivariate Categorical Data,” Journal of the American Statistical Association, 104, 1042–1051.
11. Erdös, P., and Rényi, A., (1959), “On Random Graphs,” Publicationes Mathematicae Debrecen, 5, 290–297.
12. Frank, O., and Strauss, D., (1986), “Markov Graphs,” Journal of the American Statistical Association, 81, 832–842.
13. Fruchterman, T. M. J., and Reingold, E. M., (1991), “Graph Drawing by Force-Directed Placement,” Software: Practice and Experience, 21, 1129–1164.
14. Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Aki, V., and Rubin, D. B., (2013), Bayesian Data Analysis (3rd ed.), Boca Raton, FL: Chapman & Hall.
15. Ghosal, S., (2000), “Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity,” Journal of Multivariate Analysis, 74, 49–68.
16. Ghosal, S., and Belitser, E., (2003), “Adaptive Bayesian Inference on the Mean of an Infinite-Dimensional Normal Distribution,” The Annals of Statistics, 31, 536–559.
17. Ghosh, J., and Dunson, D. B., (2009), “Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis,” Journal of Computational and Graphical Statistics, 18, 306–320.
18. Gollini, I., and Murphy, T. B., (2016), “Joint Modelling of Multiple Network Views,” Journal of Computational and Graphical Statistics, 25, 246–265.
19. Gray Roncal, W., Koterba, Z. H., Mhembere, D., Kleissas, D. M., Vogelstein, J. T., Burns, R., Bowles, A. R., Donavos, D. K., Ryman, S., Jung, R. E., Wu, L., Calhoun, V., and Vogelstein, R. J., (2013), “MIGRAINE: MRI Graph Reliability Analysis and Inference for Connectomics,” in Global Conference on Signal and Information Processing (GlobalSIP), 2013 IEEE, pp. 313–316.
20. Hagmann, P., Cammoun, L., Gigandet, X., Meuli, R., Honey, C. J., Wedeen, V. J., and Sporns, O., (2008), “Mapping the Structural Core of Human Cerebral Cortex,” PLoS Biology, 6, e159.
21. Handcock, M. S., Raftery, A. E., and Tantrum, J. M., (2007), “Model-Based Clustering for Social Networks,” Journal of the Royal Statistical Society, Series A, 170, 301–354.
22. Hoff, P. D., (2005), “Bilinear Mixed-Effects Models for Dyadic Data,” Journal of the American Statistical Association, 100, 286–295.
23. Hoff, P. D., (2008), “Modeling Homophily and Stochastic Equivalence in Symmetric Relational Data,” in Advances in Neural Information Processing Systems (Vol. 20), eds. J., Platt, D., Koller, Y., Singer, and S., Roweis, Cambridge, MA: MIT Press, pp. 657–664.
24. Hoff, P. D., Raftery, A. E., and Handcock, M. S., (2002), “Latent Space Approaches to Social Network Analysis,” Journal of the American Statistical Association, 97, 1090–1098.
25. Hunter, D. R., Goodreau, S. M., and Handcock, M. S., (2008), “Goodness of Fit of Social Network Models,” Journal of the American Statistical Association, 103, 248–258.
26. Kang, X., Herron, T. J., Cate, A. D., Yund, E. W., and Woods, D. L., (2012), “Hemispherically-Unified Surface Maps of Human Cerebral Cortex: Reliability and Hemispheric Asymmetries,” PLoS ONE, 7, e45582.
27. Kolda, T. G., and Bader, B. W., (2009), “Tensor Decompositions and Applications,” SIAM Review, 51, 455–500.
28. Krivitsky, P., and Handcock, M., (2008), “Fitting Latent Cluster Models for Networks with latentnet,” Journal of Statistical Software, 24, 1–23.
29. Krivitsky, P. N., Handcock, M. S., Raftery, A. E., and Hoff, P. D., (2009), “Representing Degree Distributions, Clustering, and Homophily in Social Networks with Latent Cluster Random Effects Models,” Social Networks, 31, 204–213.
30. Landman, B. A., Huang, A. J., Gifford, A., Vikram, D. S., Lim, I. A. L., Farrell, J. A., Bogovic, J. A., Hua, J., Min Chen, S. J., Smith, S. A., Joel, S., Mori, S., Pekar, J. J., Barker, P. B., Prince, J. L., and van Zijl, P. C., (2011), “Multi-Parametric Neuroimaging Reproducibility: A 3-T Resource Study,” NeuroImage, 54, 2854–2866.
31. Lau, J. W., and Green, P. J., (2007), “Bayesian Model-Based Clustering Procedures,” Journal of Computational and Graphical Statistics, 16, 526–558.
32. Medvedovic, M., Yeung, K. Y., and Bumgarner, R. E., (2004), “Bayesian Mixture Model Based Clustering of Replicated Microarray Data,” Bioinformatics, 20, 1222–1232.
33. Nowicki, K., and Snijders, T. A. B., (2001), “Estimation and Prediction for Stochastic Blockstructures,” Journal of the American Statistical Association, 96, 1077–1087.
34. Polson, N. G., Scott, J. G., and Windle, J., (2013), “Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables,” Journal of the American Statistical Association, 108, 1339–1349.
35. Prats-Montalbán, J., De Juan, A., and Ferrer, A., (2011), “Multivariate Image Analysis: A Review with Applications,” Chemometrics and Intelligent Laboratory Systems, 107, 1–23.
36. Ramsay, J. O., and Silverman, B. W., (2005), Functional Data Analysis (2nd ed.), New York: Springer.
37. Rousseau, J., and Mengersen, K., (2011), “Asymptotic Behaviour of the Posterior Distribution in Overfitted Mixture Models,” Journal of the Royal Statistical Society, Series B, 73, 689–710.
38. Scheinerman, E. R., and Tucker, K., (2010), “Modeling Graphs Using Dot Product Representations,” Computational Statistics, 25, 1–16.
39. Schmidt, M. N., and Morup, M., (2013), “Nonparametric Bayesian Modeling of Complex Networks: An Introduction,” IEEE Signal Processing Magazine, 30, 110–128.
40. Stam, C. J., (2014), “Modern Network Science of Neurological Disorders,” Nature Reviews Neuroscience, 15, 683–695.
41. Sussman, D. L., Tang, M., and Priebe, C. E., (2014), “Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 36, 48–57.
42. Tang, M., Sussman, D. L., and Priebe, C. E., (2013), “Universally Consistent Vertex Classification for Latent Positions Graphs,” The Annals of Statistics, 41, 1406–1430.
43. Ullah, S., and Finch, C. F., (2013), “Applications of Functional Data Analysis: A Systematic Review,” BMC Medical Research Methodology, 13, 43.
44. Wang, H., and Marron, J. S., (2007), “Object Oriented Data Analysis: Sets of Trees,” The Annals of Statistics, 35, 1849–1873.
45. Watts, D. J., and Strogatz, S. H., (1998), “Collective Dynamics of Small-World Networks,” Nature, 393, 440–442.