Databeers Dub #6 - Alberto Caimo - Investigating the local dependencies of network data, the Bayesian way
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This document discusses using Bayesian methods to model and analyze network data, specifically whole-brain networks across the lifespan. It summarizes using exponential random graph models (ERGMs) to probabilistically describe network structure and generatively explain how links are formed. It then discusses challenges in Bayesian computation for ERGMs and introduces the Bergm package for simulation-based computation. Results show that whole-brain network structures remain stable across adulthood but that damage to hub nodes has stronger effects in people over 70 years old. The document concludes by noting various applications of Bayesian ERGM modeling through the Bergm package.
Databeers Dub #6 - Alberto Caimo - Investigating the local dependencies of network data, the Bayesian way
- 1. Investigating the local dependencies of network data, the Bayesian way Alberto Caimo acaimo.github.io New Relic October 3, 2018
- 3. Network graph Adjacency matrix Network data
- 4. Whole-brain network Modelling brain networks
- 5. Identify how local network structures are evolving across the lifespan, and how sensitive these are to random / targeted lesions Whole-brain network Research objective Modelling brain networks
- 6. Identify how local network structures are evolving across the lifespan, and how sensitive these are to random / targeted lesions Whole-brain network Research objective Statistical network analysis Modelling brain networks
- 7. Graph changes across lifespan ng percentages of nodes with the highest betweenness centrality. uated the consequences of random-node and hub-node damage ocal structure parameters (e.g. edges, GWESP, GWNSP, and hemi- nodematch). The effect of simulated damage between percentages ated nodes was quantified with 95% credibility intervals obtained difference between the posterior distributions. 3. Results 3.1. Network matrices and model parameters We generated group-based networks for each age category are depicted in Fig. 3 as network graph representations (for Age 20-34 Age 20-34 vs Age 35-50 lost connections new connections
- 8. Probabilistic: describe the probability of the network structure Generative: try to explain how the network structure might have been generated Assumption: links formation depend on the relative presence / absence of some local network structures Exponential random graphs
- 12. Sparsity Transitivity Prior Posterior — — — + Density Multiple Closure ERGM … the Bayesian way… Multiple Connectivity
- 13. Sparsity Transitivity Prior Posterior computationally doubly-intractable! — — — + Simulation-based computation Density Multiple Closure ERGM … the Bayesian way… Multiple Connectivity
- 14. The Bergm package for On CRAN: CRAN.R-project.org/package=Bergm Website: acaimo.github.io/Bergm Bayesian Analysis Exponential Random Graph Models Missing Data Imputation Parameter InferenceBergm Model Selection Model Assessment
- 15. Results Fig. 5. Network parameters across lifespan. Edges, GWESP, GWNSP, and hemispheric nodematch for age categories 20–34, 35–50, 51–70, and N70 years of age. 86 M.R.T. Sinke et al. / NeuroImage 135 (2016) 79–91 Density Multiple Closure Multiple Connectivity Hemispheric Density Age groups Age groups Structural networks remain stable across the lifespan
- 16. Results organization (Bullmore and Sporns, dematch values indicate a tendency (Dennis et al., 2013; Gong et al., 2009; Hagmann et al., 201 Montembeault et al., 2012; Otte et al., 2015; Wu et al., 2012; Z Density Multiple Closure Multiple Connectivity Hemispheric Density Age groups Age groups Hub-node damage has stronger effects in people above 70 years of age
- 17. BERGM: many applications! Knowledge transfer in organisations Foreign direct investment flow dynamics Sustainable energy district planning More info: acaimo.github.io