The Annals of Applied Statistics

Locally adaptive dynamic networks

Daniele Durante and David B. Dunson

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


Our focus is on realistically modeling and forecasting dynamic networks of face-to-face contacts among individuals. Important aspects of such data that lead to problems with current methods include the tendency of the contacts to move between periods of slow and rapid changes, and the dynamic heterogeneity in the actors’ connectivity behaviors. Motivated by this application, we develop a novel method for Locally Adaptive DYnamic (LADY) network inference. The proposed model relies on a dynamic latent space representation in which each actor’s position evolves in time via stochastic differential equations. Using a state-space representation for these stochastic processes and Pólya-gamma data augmentation, we develop an efficient MCMC algorithm for posterior inference along with tractable procedures for online updating and forecasting of future networks. We evaluate performance in simulation studies, and consider an application to face-to-face contacts among individuals in a primary school.

Article information

Ann. Appl. Stat., Volume 10, Number 4 (2016), 2203-2232.

Received: May 2015
Revised: August 2016
First available in Project Euclid: 5 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Face-to-face dynamic contact network latent space nested Gaussian process online updating Pólya-gamma state-space model


Durante, Daniele; Dunson, David B. Locally adaptive dynamic networks. Ann. Appl. Stat. 10 (2016), no. 4, 2203--2232. doi:10.1214/16-AOAS971.

Export citation


  • Airoldi, E. M., Blei, D. M., Fienberg, S. E. and Xing, E. P. (2008). Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9 1981–2014.
  • Barrat, A. and Cattuto, C. (2013). Temporal networks of face-to-face human interactions. In Understanding Complex Systems 191–216. Springer Science Business Media.
  • Butts, C. T. (2008). A relational event framework for social action. Sociol. Method. 38 155–200.
  • Cattuto, C., Van den Broeck, W., Barrat, A., Colizza, V., Pinton, J.-F. and Vespignani, A. (2010). Dynamics of person-to-person interactions from distributed RFID sensor networks. PLoS ONE 5 e11596.
  • Choi, H. M. and Hobert, J. P. (2013). The Polya-gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic. Electron. J. Stat. 7 2054–2064.
  • Desmarais, B. A. and Cranmer, S. J. (2012). Statistical mechanics of networks: Estimation and uncertainty. Phys. A 391 1865–1876.
  • DuBois, C., Butts, C. T., McFarland, D. and Smyth, P. (2013). Hierarchical models for relational event sequences. J. Math. Psych. 57 297–309.
  • Dunson, D. B. and Xing, C. (2009). Nonparametric Bayes modeling of multivariate categorical data. J. Amer. Statist. Assoc. 104 1042–1051.
  • Durante, D. and Dunson, D. B. (2014). Nonparametric Bayes dynamic modelling of relational data. Biometrika 101 883–898.
  • Durante, D., Scarpa, B. and Dunson, D. B. (2014). Locally adaptive factor processes for multivariate time series. J. Mach. Learn. Res. 15 1493–1522.
  • Durbin, J. and Koopman, S. J. (2002). A simple and efficient simulation smoother for state space time series analysis. Biometrika 89 603–616.
  • Durbin, J. and Koopman, S. J. (2012). Time Series Analysis by State Space Methods, 2nd ed. Oxford Statistical Science Series 38. Oxford Univ. Press, Oxford.
  • Fienberg, S. E. and Wasserman, S. (1981). Categorical data analysis of single sociometric relations. Sociol. Method. 12 156–192.
  • Foulds, J., DuBois, C., Asuncion, A. U., Butts, C. T. and Smyth, P. (2011). A dynamic relational infinite feature model for longitudinal social networks. Journal of Machine Learning Research Workshops & Proceedings 15 287–295.
  • Fournet, J. and Barrat, A. (2014). Contact patterns among high school students. PLoS ONE 9 e107878.
  • Friedman, J. H. (1991). Multivariate adaptive regression splines. Ann. Statist. 19 1–141.
  • Fruchterman, T. M. and Reingold, E. M. (1991). Graph drawing by force-directed placement. Softw. Pract. Exp. 21 1129–1164.
  • Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457–511.
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. and Rubin, D. B. (2013). Bayesian Data Analysis, 3rd ed. Taylor & Francis.
  • Gemmetto, V., Barrat, A. and Cattuto, C. (2014). Mitigation of infectious disease at school: Targeted class closure vs school closure. BMC Infect. Dis. 14 695.
  • George, E. I. and McCulloch, R. E. (1993). Variable selection via Gibbs sampling. J. Amer. Statist. Assoc. 88 881–889.
  • Hanneke, S., Fu, W. and Xing, E. P. (2010). Discrete temporal models of social networks. Electron. J. Stat. 4 585–605.
  • Hoff, P. D. (2008). Modeling homophily and stochastic equivalence in symmetric relational data. In Advances in Neural Information Processing Systems 20 (J. C. Platt, D. Koller, Y. Singer and S. T. Roweis, eds.) 657–664. MIT Press, Cambridge.
  • Hoff, P. D., Raftery, A. E. and Handcock, M. S. (2002). Latent space approaches to social network analysis. J. Amer. Statist. Assoc. 97 1090–1098.
  • Holland, P. W. and Leinhardt, S. (1977). A dynamic model for social networks. J. Math. Sociol. 5 5–20.
  • Hunter, D. R., Krivitsky, P. N. and Schweinberger, M. (2012). Computational statistical methods for social network models. J. Comput. Graph. Statist. 21 856–882.
  • Hunter, D. R., Handcock, M. S., Butts, C. T., Goodreau, S. M. and Morris, M. (2008). ergm: A package to fit, simulate and diagnose exponential-family models for networks. J. Stat. Softw. 24 nihpa54860.
  • Isella, L., Stehlé, J., Barrat, A., Cattuto, C., Pinton, J.-F. and Van den Broeck, W. (2011). What’s in a crowd? Analysis of face-to-face behavioral networks. J. Theoret. Biol. 271 166–180.
  • Krivitsky, P. N. and Handcock, M. S. (2014). A separable model for dynamic networks. J. R. Stat. Soc. Ser. B. Stat. Methodol. 76 29–46.
  • Mastrandrea, R., Fournet, J. and Barrat, A. (2015). Contact patterns in a high school: A comparison between data collected using wearable sensors, contact diaries and friendship surveys. PLoS ONE 10 e0136497.
  • Newman, M. E. J. (2003). Mixing patterns in networks. Phys. Rev. E (3) 67 026126, 13.
  • Nowicki, K. and Snijders, T. A. B. (2001). Estimation and prediction for stochastic blockstructures. J. Amer. Statist. Assoc. 96 1077–1087.
  • Polson, N. G., Scott, J. G. and Windle, J. (2013). Bayesian inference for logistic models using Pólya–Gamma latent variables. J. Amer. Statist. Assoc. 108 1339–1349.
  • Robins, G. and Pattison, P. (2001). Random graph models for temporal processes in social networks. J. Math. Sociol. 25 5–41.
  • Robins, G., Snijders, T., Wang, P., Handcock, M. and Pattison, P. (2007). Recent developments in exponential random graph $p^{*}$ models for social networks. Soc. Netw. 29 192–215.
  • Sarkar, P. and Moore, A. W. (2005). Dynamic social network analysis using latent space models. SIGKDD Explorations Newsletter 7 31–40.
  • Sewell, D. K. and Chen, Y. (2015). Latent space models for dynamic networks. J. Amer. Statist. Assoc. 110 1646–1657.
  • Snijders, T. A. B. (2001). The statistical evaluation of social network dynamics. Sociol. Method. 31 361–395.
  • Snijders, T. A. B. (2005). Models for longitudinal network data. In Models and Methods in Social Network Analysis 215–247. Cambridge Univ. Press, Cambridge.
  • Snijders, T. A. B., van de Bunt, G. G. and Steglich, C. E. G. (2010). Introduction to stochastic actor-based models for network dynamics. Soc. Netw. 32 44–60.
  • Stehlé, J., Voirin, N., Barrat, A., Cattuto, C., Isella, L., Pinton, J.-F., Quaggiotto, M., Van den Broeck, W., Régis, C., Lina, B. and Vanhems, P. (2011). High-resolution measurements of face-to-face contact patterns in a primary school. PLoS ONE 6 e23176.
  • Stehlé, J., Charbonnier, F., Picard, T., Cattuto, C. and Barrat, A. (2013). Gender homophily from spatial behavior in a primary school: A sociometric study. Soc. Netw. 35 604–613.
  • Vanhems, P., Barrat, A., Cattuto, C., Pinton, J.-F., Khanafer, N., Régis, C., Kim, B., Comte, B. and Voirin, N. (2013). Estimating potential infection transmission routes in hospital wards using wearable proximity sensors. PLoS ONE 8 e73970.
  • Wyatt, D., Choudhury, T. and Bilmes, J. A. (2008). Learning hidden curved exponential family models to infer face-to-face interaction networks from situated speech data. In AAAI 732–738.
  • Xing, E. P., Fu, W. and Song, L. (2010). A state-space mixed membership blockmodel for dynamic network tomography. Ann. Appl. Stat. 4 535–566.
  • Xu, K. S. (2015). Stochastic block transition models for dynamic networks. Journal of Machine Learning Research Workshops & Proceedings 38 1079–1087.
  • Xu, K. S. and Hero, A. O. (2014). Dynamic stochastic blockmodels for time-evolving social networks. IEEE Journal of Selected Topics in Signal Processing 8 552–562.
  • Yang, T., Chi, Y., Zhu, S., Gong, Y. and Jin, R. (2009). A Bayesian approach toward finding communities and their evolutions in dynamic social networks. In Proceedings of the 2009 SIAM International Conference on Data Mining 990–1001. Society for Industrial & Applied Mathematics (SIAM), Philadelphia.
  • Yang, T., Chi, Y., Zhu, S., Gong, Y. and Jin, R. (2011). Detecting communities and their evolutions in dynamic social networks—a Bayesian approach. Mach. Learn. 82 157–189.
  • Zhu, B. and Dunson, D. B. (2013). Locally adaptive Bayes nonparametric regression via nested Gaussian processes. J. Amer. Statist. Assoc. 108 1445–1456.