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
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
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
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"
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