Dynamic Network Model from Par5al Observa5ons Elahe Ghalebi 1 , - - PowerPoint PPT Presentation

Dynamic Network Model from Par5al Observa5ons

Elahe Ghalebi 1, Baharan Mirzasoleiman 2, Radu Grosu 1, Jure Leskovec 2

NeurIPS 2018

1 TU Wien and 2 Stanford University

• In many applicaGons, the edges of a dynamic network might not be observed
• We can only observe the dynamics of stochasGc cascading process e.g.

informaGon diffusion, virus propagaGon occurring over the unobserved network

Can evolving network be inferred and modeled without directly observing their nodes and edges?

! " # $ % & ' () (* (+ (, (- (. ! " # $ % & ' () (* (+ (, (- (. ! " # $ % & ' ! " # $ % & ' () (* (+ (, (- (.

1- Extrac5ng Observa5on from Diffusion Data

DYFERENCE framework

e a d t1 t2 t3 t5 t4 f b

c1

a b d c g t1 t5 t4 t2 t3 e d b c t1 t4 t2 t3

t1 < t2 < . . .

Sample a set Sc of θ ( | Ec | ) edges based on marginal probabiliGes

Find the set of possible edges in each cascade as Eci = {euv|tci

u < tci v < ∞}

ci

c2 c3

Ec1

e a d t1 t2 t3 t5 t4 f b

Ec2

a b d c g t1 t5 t4 t2 t3

Ec3

e d b c t1 t4 t2 t3

DYFERENCE framework

e a d t1 t2 t3 t5 t4 f b

c1

a b d c g t1 t5 t4 t2 t3 e d b c t1 t4 t2 t3

Calculate probability distribuGon over edges consistent with each cascade Eci

t1 < t2 < . . .

Sample a set Sc of θ ( | Ec | ) edges based on marginal probabiliGes

S1

e a d f c t1 t2 t3 t5 t4

S2

a b d c g t1 t5 t4 t2 t3

S3

e d b c t1 t4 t2 t3

1- ExtracGng ObservaGon from Diffusion Data

Calculate marginal probability of every edge in each Eci Sample a set of edges based on marginal probabiliGes θ(|Eci|) Sci Round #1

c2 c3

Ec1

e a d t1 t2 t3 t5 t4 f b

Ec2

a b d c g t1 t5 t4 t2 t3

Ec3

e d b c t1 t4 t2 t3

DYFERENCE framework

Sample a set Sc of θ ( | Ec | ) edges based on marginal probabiliGes

e a d t1 t2 t3 t5 t4 f b

c1

a b d c g t1 t5 t4 t2 t3 e d b c t1 t4 t2 t3

a b d c f e a b c f g

X1 = {S1, S2, S3}

d f e a b c f g

1- ExtracGng ObservaGon from Diffusion Data

S1

e a d f c t1 t2 t3 t5 t4

S2

a b d c g t1 t5 t4 t2 t3

S3

e d b c t1 t4 t2 t3

Calculate probability distribuGon over edges consistent with each cascade Eci Calculate marginal probability of every edge in each Eci

2- Update the model with the extracted observa5on using a collapsed Gibbs sampler

X1 Sample a set of edges based on marginal probabiliGes θ(|Eci|) Sci

Round #1

c2 c3

For the model, we use mixture of Dirichlet network distribuGons (MDND) [Williamson’16]

Ec1

e a d t1 t2 t3 t5 t4 f b

Ec2

a b d c g t1 t5 t4 t2 t3

Ec3

e d b c t1 t4 t2 t3

DYFERENCE framework

Calculate probability distribuGon over each using updated edge probabiliGes from model Eci Sample a set Sc of θ ( | Ec | ) edges based on marginal probabiliGes

e a d t1 t2 t3 t5 t4 f b

c1

a b d c g t1 t5 t4 t2 t3 e d b c t1 t4 t2 t3

S1 e a d f c t1 t2 t3 t5 t4

S2

a b d c g t1 t5 t4 t2 t3

e d b c t1 t4 t2 t3 S3

a b d c f e a b c f g d f e a b c f g

1- ExtracGng ObservaGon from Diffusion Data

X2 = {S1, S2, S3}

Round #2

Calculate marginal probability of every edge in each Eci Sample a set of edges based on marginal probabiliGes θ(|Eci|) Sci

2- Update the model with the extracted observaGon using a collapsed Gibbs sampler

X2

c2 c3

Ec1

e a d t1 t2 t3 t5 t4 f b

Ec2

a b d c g t1 t5 t4 t2 t3

Ec3

e d b c t1 t4 t2 t3

Online Dynamic Network Inference

• 1. DiscreGze Gme into intervals with length ω
• 2. Consider only infecGon Gmes in current interval

tc ∈ [(i − 1)ω, iω], ∀c ∈ C

• 3. Update model with the observaGons in current ω

Dynamic Bankruptcy Prediction

Performance Evalua5on

European country’s financial transacGons: 1,197,116 transacGons;103,497 companies

Our algorithm significantly outperforms the baselines

Conclusion

✓Our algorithm provides a genera&ve probabilis&c model which:

✦ IdenGfies the underlying Gme-varying community structure ✦ Can be used for diffusion predicGon, predicGng the most

influenGal nodes, and bankruptcy predicGon

Poster: Today (Wed Dec 5th. @ Room 210 & 230) #7

✦ Obtains dynamic predicGve distribuGon over the edges