Time-sensitive Network Inference in Diffusion Networks

Time-sensitive Network Inference in Diffusion Networks

Final project presentation for the CS229 (machine learning) course of Spring 2014, at KAUST.

Ed09e933a899fcae158439f11f66fed0?s=128

Emaad Manzoor

May 08, 2014
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Transcript

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    f(t i ) Probability that node i is infected at

    time t i f(t i |t j ) Probability that node i is infected at time t i given that node j is infected at time t j
  8. 22.

    f(t i ) Probability that node i is infected at

    time t i f(t i |t j ) Probability that node i is infected at time t i given that node j is infected at time t j f(t i |t j ) = f ij (t i - t j )
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    Set C of cascades Each cascade is a set of

    observations Each cascade is observed until a horizon time
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    Set C of cascades Each cascade is a set of

    observations Each cascade is observed until a horizon time Nodes not infected before this horizon time
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    Set C of cascades Each cascade is a set of

    observations Each cascade is observed until a horizon time Nodes not infected before this horizon time Pairwise transmission functions
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    Set C of cascades Each cascade is a set of

    observations Each cascade is observed until a horizon time Nodes not infected before this horizon time Pairwise transmission functions Find transmission rates that maximise the likelihood of the observed cascades
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    Uncovering the temporal dynamics of diffusion networks Influence maximisation in

    continuous-time diffusion networks Scalable influence estimation in continuous time diffusion networks Rodriguez et al. ICML '11 Rodriguez et al. ICML '12 Du et al. NIPS '13
  15. 35.

    Rodriguez et al. ICML '11 Uncovering the temporal dynamics of

    diffusion networks 1. Define cascade likelihood as the objective function 2. Since this function is convex, the problem is a constrained maximisation problem over transmission rates
  16. 36.

    Rodriguez et al. ICML '11 Uncovering the temporal dynamics of

    diffusion networks "Our formulation thus does not depend on the absolute time of infection of the root node" "Transmission functions are shift invariant, and do not depend on the absolute times of infection of the pair of nodes"
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    Contribution 3: EM algorithm to fit the unknown parameters from

    the data 1. Initialize the state for each node in each cascade randomly; S ic = random(A, S) 2. Estimate and d for every pair of nodes using convex optimisation (Manuel et al., 2011). 3. Estimate and using closed- form maximum-likelihood estimates. 4. Reassign new states S ic to nodes in each cascade
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    Contribution 3: EM algorithm to fit the unknown parameters from

    the data 4. Reassign new states S ic to nodes in each cascade
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    Synthetic data: 1024 nodes Kronecker core-periphery (Leskovec, '08), transmission times

    and root nodes chosen uniformly at random, 1000 cascades. Real data: Memetracker, 1M nodes, >100K cascades.
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