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When Does Label Propagation Fail? A View from a Network Generative Model

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IJCAI 2017 paper presentation

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When Does Label Propagation Fail? A View from a Network Generative Model

  1. 1. When  Does  Label  Propaga1on  Fail?   A  View  from  a  Network  Genera1ve  Model Yuto  Yamaguchi  and  Kohei  Hayashi 17/08/22 IJCAI@Melbourne 1
  2. 2. Node Classification Given Find Partially labeled undirected graph Labels of all nodes 17/08/22 IJCAI@Melbourne 2
  3. 3. Example: User profile inference Friends Soccer Soccer Soccer Tennis Baseball ??? What’s his hobby? Node Classification 17/08/22 IJCAI@Melbourne 3
  4. 4. Label Propagation (1/2) Propagate neighbors’ labels Friends Soccer Soccer Soccer Tennis Baseline ??? Soccer Soccer Soccer Tennis Baseline Soccer [Zhu+, 03], [Zhou+, 03], etc. 17/08/22 IJCAI@Melbourne 4
  5. 5. Label Propagation (2/2) Q F;X,Y,λ( )= 1 2 fi − yi 2 2 i=1 N ∑ + λ 2 xij fi − fj 2 2 j=1 N ∑ i=1 N ∑ Given: adjacency matrix X and labels Y Find: F = { fi } that minimizes Q 17/08/22 IJCAI@Melbourne 5 F ∈ RN x K Y ∈ {0, 1}N x K X ∈ {0, 1}N x N N: # of nodes K: # of labels λ ∈ R+ : user parameter [Zhu+, 03], [Zhou+, 03], etc.
  6. 6. Cases  when  LP  fails  (prac1cally  known) Different labels are connected Label ratio is not uniform Q. So, do we know why LP fails in these cases? A. No. Since it’s not a probabilistic model, we don’t know the assumptions behind the model. 17/08/22 IJCAI@Melbourne 6 Edge probability is not uniform
  7. 7. What  we  do  in  this  work 1.  Prove  a  theore1cal  rela1onship  between  LP   and  Stochas(c  Block  Model,  which  is  a  well-­‐ studied  probabilis1c  genera1ve  model   2.  Find  the  assump(ons  behind  LP  through  the   assump1ons  behind  SBM   3.  Show  when  and  why  LP  fails 17/08/22 IJCAI@Melbourne 7
  8. 8. NETWORK  GENERATIVE  MODELS 17/08/22 IJCAI@Melbourne 8
  9. 9. Stochastic Block Model Generative process Multinomial Bernoulli ① ② ①: Generate cluster assignment for each node (which can be thought of labels) ②: Generate adjacency matrix 17/08/22 IJCAI@Melbourne 9 γ ∈ RK Π ∈ RKxK Parameters:
  10. 10. Proposed: Partially Labeled SBM (PLSBM) Generative process ① ② ③ ②:Generate labels for “labeled nodes” (α large à yi is more likely to be the same as zi) Depends on parameter α 17/08/22 IJCAI@Melbourne 10 γ ∈ RK Π ∈ RKxK α ∈ 0,1[ ] Parameters:
  11. 11. Rela1onships  between  models 17/08/22 IJCAI@Melbourne 11 SBM PLSBM LP Discre1zed  LP Main  result   (next  slide) No  labels Con1nuous   relaxa1on
  12. 12. Main Result Map estimator Z of PLSBM is identical to the solution of (discretized) LP when the following conditions hold Condition 1: Condition 2: Condition 3: Condition 4: (omitted) 17/08/22 IJCAI@Melbourne 12
  13. 13. Condition 1 Implication (implicit assumption of LP) •  Label ratio is uniform 17/08/22 IJCAI@Melbourne 13 Violates this assumption L
  14. 14. Condition 2 Implication (Implicit assumptions of LP) •  Edge probs between the same labels are all the same (μ) •  Edge probs between different labels are all the same (ν) 17/08/22 IJCAI@Melbourne 14 Violates this assumption L
  15. 15. Condition 3 Implication (Implicit assumption of LP) •  Assortative (same labels tend to be connected) 17/08/22 IJCAI@Melbourne 15 Violates this assumption L
  16. 16. Experimental results 17/08/22 IJCAI@Melbourne 16 … Come see full results at the poster session J Better Setups: 1.  Generate datasets by PLSBM 2.  infer labels (Z) by PLSBM, SBM, and LP 3.  Report mean accuracy of 20 trials Assortative Disassortative Agree with theoretical results
  17. 17. Summary •  Proposed  Par1ally-­‐Labeled  SBM  (PLSBM)   •  Proved  the  rela1onship  between  LP  and  SBM  via   PLSBM   •  Showed  cases  when  LP  fails   •  Experimental  and  Theore1cal  results  agree 17/08/22 IJCAI@Melbourne 17 Github: yamaguchiyuto/plsbm

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