1. Joint Label Inference in Networks
Stanislav Funiak
Jonathan Chang
Sofus A. Macskassy
Joint Label Inference in Networks
Deepayan Chakrabarti

2. Profile Inference A complete profile is a boon: Profile:
Hometown: Palo Alto
High School: Gunn
College: Stanford
Employer: Facebook
Current city: Sunnyvale
Hobbies, Politics, Music, …
A complete profile is a boon:
People are easily searchable
Tailored news recommendations
Group recommendations
Ad targeting (especially local)
How can we fill in missing profile fields? ?

3. Previous Work u Label Propagation [Zhu+/02]
“Propagate” labels through the network
Aggregate hometowns of friends
Iterate until convergence
Repeat for current city, college, and all other label types
H = Palo Alto (…) MPK (…) Atlanta (…)
H = Palo Alto u v1 v2 v3 v4 v5
H = Palo Alto (0.5) MPK (0.25) Atlanta (0.25)
H = Palo Alto
H = ?
H = MPK
H = Atlanta

4. Previous Work Random walks [Talukdar+/09, Baluja+/08]
Statistical Relational Learning [Lu+/03, Macskassy+/07]
Relational Dependency Networks [Neville+/07]
Latent models [Palla+/12]
Either:
too generic; require too much labeled data;
do not handle multiple label types;
are outperformed by label propagation [Macskassy+/07]

5. Interactions between label types are not considered
Problem
H = Kolkata CC = Bangalore
CC = Austin u
H = Kolkata
H = ? CC = ?
CC = Bangalore
H = Kolkata
Interactions between label types are not considered

6. The EdgeExplain Model Explain friendships using shared labels
A friendship between two people is explained if: they share the same hometown OR current city OR high school OR college OR employer

7. We set H and CC so as to jointly explain all friendships
The EdgeExplain Model
H = Kolkata CC = Bangalore
Hometown friends
CC = Austin
Current City friends u
H = ? CC = ?
H = Kolkata
CC = Austin
H = Kolkata
We set H and CC so as to jointly explain all friendships

8. The EdgeExplain Model Latent profile for each person
In practice, only some fields of some profiles are known
Fill in missing profile entries to

9. #shared profile fields
The EdgeExplain Model
Diminishing returns from sharing many profile fields
controls steepness
#shared profile fields
objective function

10. The EdgeExplain Model u objective function objective function
#shared profile fields
objective function
#shared profile fields
objective function u
H = Kolkata
CC = Austin
H = Kolkata CC = Bangalore
H = ? CC = ?

11. The EdgeExplain Model u objective function objective function
#shared profile fields
objective function
#shared profile fields
objective function 1 u
H = Kolkata
CC = Austin
H = Kolkata CC = Bangalore
H = Kolkata CC = ?

12. The EdgeExplain Model u objective function objective function
#shared profile fields
objective function
#shared profile fields
objective function
Small gain with CC = Bangalore 2 1 u
H = Kolkata
CC = Austin
H = Kolkata CC = Bangalore
H = Kolkata CC = Bangalore

13. The EdgeExplain Model u objective function objective function
#shared profile fields
objective function
#shared profile fields
objective function 1 1
Larger gain with CC = Austin u
H = Kolkata
CC = Austin
H = Kolkata CC = Bangalore
H = Kolkata CC = Austin

14. The EdgeExplain Model
This problem is combinatorial and difficult to solve
Relaxation Labeling
Solve a relaxed version with probabilistic profiles
Variational Inference
Maximize a lower bound on the objective
Relaxation labeling works better in general
Full comparison, and a hybrid method, in the journal paper
We will show results with relaxation labeling

15. Experiments 1.1B users of the Facebook social network O(10M) labels
Only public friendships and profiles
Sparsify network
For each person, keep links to top K closest friends by age
Measure recall
Did we get the correct label in our top prediction? Top-3?
5-fold cross-validation

16. Results (versus Label Propagation)
Joint modeling helps most for employer
Significant gains for high school and college as well
Lift of EdgeExplain over Label Propagation
Lift of EdgeExplain over Label Propagation
Hometown
College
High school
Employer
Current city
Hometown
College
Employer
Current city
High school

17. Results (varying closest friends K)
K=100 or K=200 closest friends is best
K=400 hurts; these friendships are probably due to other factors
Lift of EdgeExplain over K=20
Lift of EdgeExplain over K=20
Hometown
College
College
Employer
Hometown
High school
Employer
Current city
High school
Current city

18. Conclusions Assumption: each friendship needs only one reason
Model: explain friendships via shared user profile attributes
Results: up to 120% lift for and 60% for
Extension to Twitter [C., Annals of Applied Stats., 2017]
Each “follow” link has one reason
The follower is interested in multiple topics
The person being followed is perceived as an expert on one topic

19. Lift of EdgeExplain over α=0.1
Result (effect of α)
High α is best  one reason per friendship is enough
Lift of EdgeExplain over α=0.1
College
Employer
Hometown
Current city
High school

20. Profile Inference u Use the social network
and the assumption of homophily
Friendships form between “similar” people
Infer missing labels to maximize similarity between friends
H = Palo Alto E = Microsoft
H = ? E = ? u v1 v2 v3 v4 v5
H = Palo Alto E = ?
H = ? E = ?
H = MPK E = FB
H = Atlanta E = Google