Decoupled smoothing on graphs Alex Chin, Yatong Chen , Kristen M. - - PowerPoint PPT Presentation

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Decoupled smoothing on graphs Alex Chin, Yatong Chen , Kristen M. - - PowerPoint PPT Presentation

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Decoupled smoothing on graphs Alex Chin, Yatong Chen , Kristen M. Altenburger, Johan Ugander Stanford University The Web Conference, San Francisco May 17, 2019 1 Attribute prediction on graphs 2 Attribute prediction on graphs Given: Social

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Decoupled smoothing on graphs

Alex Chin, Yatong Chen, Kristen M. Altenburger, Johan Ugander Stanford University

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The Web Conference, San Francisco May 17, 2019

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Attribute prediction on graphs

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Attribute prediction on graphs

Given:

  • Social Network

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Yatong Chen, Stanford University, WWW 2019

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Attribute prediction on graphs

Given:

  • Social Network
  • Labels for some subset nodes

Male Female

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Yatong Chen, Stanford University, WWW 2019

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Given:

  • Social Network
  • Labels for some subset nodes

Goal:

  • Infer labels for unlabeled nodes

Attribute prediction on graphs

Male Female ? ? ?

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Yatong Chen, Stanford University, WWW 2019

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Semi-supervised learning Problem

Given:

  • Social Network
  • Labels for some subset nodes

Goal:

  • Infer labels for unlabeled nodes

Male Female ? ? ?

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Yatong Chen, Stanford University, WWW 2019

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Approaches for attribute prediction

  • Approach 1: Graph Smoothing based on Gaussian

Random Field [Zhu, Ghahramani, Lafferty 2003]

○ Assumption: Gaussian Markov Random Field Prior on true label of all the nodes ○ Get the Bayes estimator of on unlabeled nodes under the GMRF prior ○ Be referred as ZGL later

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Approaches for attribute prediction

  • Approach 2: LINK classification [Lu-Getoor 2003]

○ Learn a function F: F(row i in adjacency matrix) = i’s label ○ Example F: regularized logistic regression

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? [1,0,...0,1] [0,1, ...0,1] ? [1,0,...0,1] [0,1, ...0,1] [0,0,..,0,1] [0,0,..,0,1] Labeled Labeled regularized logistic regression

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ZGL’s assumption: Homophily

  • Homophily [one-hop similarity]:

○ Individuals are similar to their friends

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Yatong Chen, Stanford University, WWW 2019

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ZGL’s assumption: Homophily

  • Homophily [one-hop similarity]:

○ ZGL assumes information of a given node decays smoothly across the topology of the graph (by imposing the GMRF prior)

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？ ？ ？ ? ? ? ？

Labeled Labeled smooth!

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Homophily Assumption: NOT always necessary!

  • [Altenburger-Ugander 2018]：

○ LINK does well even without assuming homophily ○ Homophily assumption is not necessary for inference to succeed

  • ...but ZGL and a lot of other graph smoothing methods

all assumes homophily. Can we do graph smoothing without it? ○ Yes (this talk)

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Yatong Chen, Stanford University, WWW 2019

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  • Gender example:

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Male Female

Yatong Chen, Stanford University, WWW 2019

A situation where Homophily assumption fails

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A situation where Homophily assumption fails

  • Gender example:

○ Want to predict the gender of the center node

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Male Female

Yatong Chen, Stanford University, WWW 2019 ?

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A situation where Homophily assumption fails

  • Gender example:

○ Want to predict the gender of the center node: ■ Assume Homophily (1-hop majority vote): false

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Male Female

Yatong Chen, Stanford University, WWW 2019 ? ？

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A situation where Homophily assumption fails

  • Observation: there are difference between one’s

identity and preference

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Identity: male Preference: female

Male Female

Yatong Chen, Stanford University, WWW 2019

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Decoupled smoothing Method

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Decoupled smoothing: idea

  • Idea: decoupling one’s “identity” and “preference”
  • Use separate parameters to model them accordingly!

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Identity: male Preference: female

Male Female

Without homophily (or heterophily) assumption

Yatong Chen, Stanford University, WWW 2019

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Decoupled smoothing: idea

  • Idea: decoupling one’s “identity” and “preference”

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Yatong Chen, Stanford University, WWW 2019

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Decoupled smoothing: idea

  • Idea: decoupling one’s “identity” and “preference”
  • Intuition: a person’s identity will reveal information

about their friend’s preference, and vice versa

identity preference

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Decoupled smoothing: idea

  • Idea: decoupling one’s “identity” and “preference”
  • Intuition: a person’s identity will reveal information

about their friend’s preference, and vice versa

identity preference: can’t observe, how to reveal?

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?

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Decoupled smoothing: model

  • Intuition: a person’s identity will reveal information

about their friend’s preference, and vice versa

  • Assumption:

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Yatong Chen, Stanford University, WWW 2019

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Decoupled smoothing: model

  • Intuition: a person’s identity will reveal information

about their friend’s preference, and vice versa

  • Assumption:
  • Goal: to obtain predictions for the identity

○

the preference is nuisance!

  • Get the marginal prior for :

○

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Yatong Chen, Stanford University, WWW 2019

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How to estimate W?

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Yatong Chen, Stanford University, WWW 2019

Decoupled smoothing: impose a prior

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How to estimate W?

  • Intuition:

○ Node j’th preference will imply a 2-hop similarity between node i and node k’s identities

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Node i Node j Node k

?

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How to estimate W?

  • Intuition:

○ Node j’th preference will imply a 2-hop similarity between node i and node k’s identities ○ Make use of the information of k when predicting i

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Node i Node j Node k

?

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How to estimate W?

  • Intuition:

○ Node j’th preference will imply a 2-hop similarity between node i and node k’s identities ○ Make use of the information of k when predicting i

  • Assumption:

○ i’s 2-hop friend k has the distribution:

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Node i Node j Node k

?

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How to estimate W?

  • Why as mean:

○ Similarity among i and k

  • Why as variance?

○ The more friends j have→ the better its preference being revealed → the less uncertainty about the similarity between i and k

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Node i Node j Node k

Trust More!

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How to estimate W?

  • Assumption:

○ 2-hop friend k has the distribution ○ Homogeneous standard error

  • Then W can be reduced to

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We get W!

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Decoupled smoothing: model

  • Now we know everything about the marginal prior for :

○

  • Next step:

○ Compute the Bayes estimator of for unlabeled node and then make the prediction (recall ZGL)

  • Done!

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Yatong Chen, Stanford University, WWW 2019

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Relationship between Decoupled smoothing and some phenomenon/concept/method that are related to it

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Decoupled smoothing and Monophily

  • The phenomenon of Monophily [Altenburger-Ugander 2018]

○ Two-hop similarity: individuals are similar to their friends’ friends ○ Innovative concept compared to Homophily

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Identity: male Preference: female

Male Female

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Decoupled smoothing implies Monophily

  • The phenomenon of Monophily [Altenburger-Ugander 2018]

○ Two-hop similarity: ■ similarity among the friends of a person is the result of personal preference ○ The 2 hop similarity phenomenon is implied by our decoupling smoothing idea!

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Identity: male Preference: female

Male Female

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Decoupled smoothing and 2-hop MV

  • Decoupled smoothing reduces to iterative 2-hop

majority vote (under homogeneous standard error):

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2 hop Majority Vote (MV): Average over the labeled nodes in 2-hop friend sets

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Decoupled smoothing and ZGL

  • ZGL:
  • Assume Homophily
  • Prior:
  • Matrix A:

adjacency matrix

  • Reduce to iteratively

1-hop majority vote update method!

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  • Decoupled smoothing:

○ Don’t assume Homophily ○ Prior: ○ Auxiliary matrix: ○ Reduce to iteratively 2-hop majority vote update method!

Decoupled smoothing and ZGL

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Empirical Results

Yatong Chen, Stanford University, WWW 2019

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Dataset

  • Facebook 100: Single-day snapshots of Facebook in

September 2005.

  • Goal: gender prediction

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School Name Number of Nodes Number of Edges Amherst 2032 78733 Reed 962 18812 Haverford 1350 53904 Swarthmore 1517 53725

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Decoupled smoothing: empirical result

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Reed Swarthmore

Yatong Chen, Stanford University, WWW 2019

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Decoupled smoothing: empirical result

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Reed

Yatong Chen, Stanford University, WWW 2019

Swarthmore

ZGL ZGL

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Decoupled smoothing: empirical result

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Reed

Yatong Chen, Stanford University, WWW 2019

Swarthmore

ZGL ZGL

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Decoupled smoothing: empirical result

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Haverford Amherst

Yatong Chen, Stanford University, WWW 2019

ZGL ZGL

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Why 2-hop Majority Vote beats Decoupled Smoothing?

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Amherst

Yatong Chen, Stanford University, WWW 2019

ZGL

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Summary

  • Introduce the idea of decoupling one’s “identity”

and “preference”

  • Justify/explain the phenomenon of 2-hop similarity

without assuming homophily

  • Open questions:

○ How to choose the weighted matrix W? ○ Why 2-hop Majority Vote outperforms decoupled smoothing: can you do better?

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Yatong Chen, Stanford University, WWW 2019

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Questions?

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Thank you for your attention!

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