Time-sensitive Network Inference in Diffusion Networks

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

Transcript

1. Time-sensitive Network Inference in Continuous-Time Diffusion Networks Emaad Ahmed Manzoor CS229: Final Presentation
2. Networks
3. Social Networks
4. Epidemic Networks Individual stick figures from xkcd.com
5. Information Networks
6. Diffusion
12. 0 T
13. Diffusion Formalization
14. 0 T Cascade
15. 0 T Parents & Children
16. 0 T Infection Times t 1 t 2 t 3 t 4
17. 0 T Observation Limit t 1 t 2 t 3 t 4
18. 0 T Underlying Network t 1 t 2 t 3 t 4
19. 0 T Transmission Times 0.1 0.7 0.1 0.4 0.7 0.3 0.5 0.8 0.6 0.9
20. f(t i ) Probability that node i is infected at time t i
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
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 )
23. Exponential Pairwise Transmission Function
24. Network Inference
25. Set C of cascades
26. Set C of cascades Each cascade is a set of observations
27. Set C of cascades Each cascade is a set of observations Each cascade is observed until a 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
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
30. 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. Metrics Precision Recall
33. State of the Art
34. 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
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
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"
37. Contributions
38. Independent transmission rates
39. Independent transmission rates Bayes network inference?
40. Independent transmission rates Bayes network inference? ?
41. States aSleep Awake
42. Contribution 1: Formulate a time-dependent transmission function as a discrete mixture of distributions.
43. Contribution 1: Formulate a time-dependent transmission function as a discrete mixture of distributions.
44. Contribution 1: Formulate a time-dependent transmission function as a discrete mixture of distributions.
45. Contribution 2: Model the time-dependent priors with circular normal distributions
46. Per node Per edge Unknowns How do we fit these from the data?
47. 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
48. Contribution 3: EM algorithm to fit the unknown parameters from the data 4. Reassign new states S ic to nodes in each cascade
49. Results
50. 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.
51. Future
52. Algorithm: Continuous states Remove stationarity assumption Implementation: Parallelism Speed Experiments: Real data New synthetic data
53. .