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IJCAI 2017 paper presentation

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- 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. Node Classiﬁcation Given Find Partially labeled undirected graph Labels of all nodes 17/08/22 IJCAI@Melbourne 2
- 3. Example: User proﬁle inference Friends Soccer Soccer Soccer Tennis Baseball ？？？ What’s his hobby? Node Classiﬁcation 17/08/22 IJCAI@Melbourne 3
- 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. 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. 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. 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. NETWORK GENERATIVE MODELS 17/08/22 IJCAI@Melbourne 8
- 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. 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. Rela1onships between models 17/08/22 IJCAI@Melbourne 11 SBM PLSBM LP Discre1zed LP Main result (next slide) No labels Con1nuous relaxa1on
- 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. Condition 1 Implication （implicit assumption of LP） • Label ratio is uniform 17/08/22 IJCAI@Melbourne 13 Violates this assumption L
- 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. 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. 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. 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