dynamic structural equation models for tracking cascades over social networks
DESCRIPTION
Dynamic Structural Equation Models for Tracking Cascades over Social Networks. Brian Baingana, Gonzalo Mateos and Georgios B. Giannakis. Acknowledgments: NSF ECCS Grant No. 1202135 and NSF AST Grant No. 1247885. December 17, 2013. Context and motivation. Contagions. I nfectious diseases. - PowerPoint PPT PresentationTRANSCRIPT
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Brian Baingana, Gonzalo Mateos and Georgios B. Giannakis
Dynamic Structural Equation Models for Tracking Cascades over Social Networks
Acknowledgments: NSF ECCS Grant No. 1202135 and NSF AST Grant No. 1247885
December 17, 2013
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Context and motivation
2
Popular news stories
Infectious diseases Buying patterns
Propagate in cascades over social networks
Network topologies:
Unobservable, dynamic, sparse
Topology inference vital:
Viral advertising, healthcare policy
B. Baingana, G. Mateos, and G. B. Giannakis, ``Dynamic structural equation models for social network topology inference,'' IEEE J. of Selected Topics in Signal Processing, 2013 (arXiv:1309.6683 [cs.SI])
Goal: track unobservable time-varying network topology from cascade traces
Contagions
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Contributions in context
3
Contributions
Dynamic SEM for tracking slowly-varying sparse networks
Accounting for external influences – Identifiability [Bazerque-Baingana-GG’13]
ADMM-based topology inference algorithm
Related work
Static, undirected networks e.g., [Meinshausen-Buhlmann’06], [Friedman et al’07]
MLE-based dynamic network inference [Rodriguez-Leskovec’13]
Time-invariant sparse SEM for gene network inference [Cai-Bazerque-GG’13]
Structural equation models (SEM): [Goldberger’72]
Statistical framework for modeling causal interactions (endo/exogenous effects)
Used in economics, psychometrics, social sciences, genetics… [Pearl’09]
J. Pearl, Causality: Models, Reasoning, and Inference, 2nd Ed., Cambridge Univ. Press, 2009
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Cascades over dynamic networks
4
Example: N = 16 websites, C = 2 news event, T = 2 days
Unknown (asymmetric) adjacency matrices
N-node directed, dynamic network, C cascades observed over
Event #1
Event #2
Cascade infection times depend on:
Causal interactions among nodes (topological influences)
Susceptibility to infection (non-topological influences)
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Model and problem statement
5
Captures (directed) topological and external influences
Problem statement:
Data: Infection time of node i by contagion c during interval t:
external influence
un-modeled dynamics
Dynamic SEM
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Exponentially-weighted LS criterion
6
Structural spatio-temporal properties
Slowly time-varying topology
Sparse edge connectivity,
Sparsity-promoting exponentially-weighted least-squares (LS) estimator
(P1)
Edge sparsity encouraged by -norm regularization with
Tracking dynamic topologies possible if
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Topology-tracking algorithm
7
Alternating-direction method of multipliers (ADMM), e.g., [Bertsekas-Tsitsiklis’89]
Each time interval
(P2)
Acquire new data
Recursively update data sample (cross-)correlations
Solve (P2) using ADMM
Attractive features Provably convergent, close-form updates (unconstrained LS and soft-thresholding)
Fixed computational cost and memory storage requirement per
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ADMM iterations
8
Sequential data terms: , ,
can be updated recursively:
denotes row i of
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Simulation setup Kronecker graph [Leskovec et al’10]: N = 64, seed graph
cascades, ,
Non-zero edge weights varied for
Uniform random selection from
Non-smooth edge weight variation
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Simulation results Algorithm parameters
Initialization
Error performance
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The rise of Kim Jong-un
t = 10 weeks t = 40 weeks
Web mentions of “Kim Jong-un” tracked from March’11 to Feb.’12
N = 360 websites, C = 466 cascades, T = 45 weeks
11Data: SNAP’s “Web and blog datasets” http://snap.stanford.edu/infopath/data.html
Kim Jong-un – Supreme leader of N. Korea
Increased media frenzy following Kim Jong-un’s ascent to power in 2011
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LinkedIn goes public Tracking phrase “Reid Hoffman” between March’11 and Feb.’12
N = 125 websites, C = 85 cascades, T = 41 weeks
t = 5 weeks t = 30 weeks
12Data: SNAP’s “Web and blog datasets” http://snap.stanford.edu/infopath/data.html
US sites
Datasets include other interesting “memes”: “Amy Winehouse”, “Syria”, “Wikileaks”,….
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Conclusions
13
Dynamic SEM for modeling node infection times due to cascades
Topological influences and external sources of information diffusion
Accounts for edge sparsity typical of social networks
ADMM algorithm for tracking slowly-varying network topologies
Corroborating tests with synthetic and real cascades of online social media
Key events manifested as network connectivity changes
Thank You!
Ongoing and future research
Identifiabiality of sparse and dynamic SEMs Statistical model consistency tied to Large-scale MapReduce/GraphLab implementations Kernel extensions for network topology forecasting
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ADMM closed-form updates
14
Update with equality constraints:
,
:
Update by soft-thresholding operator