May 08, 2014
210

# Time-sensitive Network Inference in Diffusion Networks

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

May 08, 2014

## Transcript

1. ### Time-sensitive Network Inference in Continuous-Time Diffusion Networks Emaad Ahmed Manzoor

CS229: Final Presentation

t 4

t 4

t 4
18. ### 0 T Transmission Times 0.1 0.7 0.1 0.4 0.7 0.3

0.5 0.8 0.6 0.9

time t i
20. ### 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
21. ### 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 )

observations
26. ### Set C of cascades Each cascade is a set of

observations Each cascade is observed until a horizon time
27. ### 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
28. ### 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
29. ### 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

32. ### 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
33. ### 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
34. ### 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"

40. ### Contribution 1: Formulate a time-dependent transmission function as a discrete

mixture of distributions.
41. ### Contribution 1: Formulate a time-dependent transmission function as a discrete

mixture of distributions.
42. ### Contribution 1: Formulate a time-dependent transmission function as a discrete

mixture of distributions.

44. ### Per node Per edge Unknowns How do we fit these

from the data?
45. ### 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
46. ### Contribution 3: EM algorithm to fit the unknown parameters from

the data 4. Reassign new states S ic to nodes in each cascade

48. ### 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.

50. ### Algorithm: Continuous states Remove stationarity assumption Implementation: Parallelism Speed Experiments:

Real data New synthetic data