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Apr 10, 2023 112 likes •381 views

Learning Cascaded Influence under Partial Monitoring Learning Cascaded Influence under Partial Monitoring Jiaqi Ma 1 Jie Zhang 2 Jie Tang 3 1 Dept. of Automation, Tsinghua University 2 Dept. of Physics, Tsinghua University 3 Dept. of Computer

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SLIDE 1

Learning Cascaded Influence under Partial Monitoring

Learning Cascaded Influence under Partial Monitoring

Jiaqi Ma1 Jie Zhang2 Jie Tang3

  • 1Dept. of Automation, Tsinghua University
  • 2Dept. of Physics, Tsinghua University
  • 3Dept. of Computer Science, Tsinghua University

ASONAM, 2016

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SLIDE 2

Learning Cascaded Influence under Partial Monitoring

Outline

1 Motivation

Social Influence Cascaded Indirect Influence

2 Challenges 3 Problem Formulation 4 Algorithm 5 Experiments

Datasets Experiments on Normalized Regrets Experiments on Application Improvement

6 Conclusion

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SLIDE 3

Learning Cascaded Influence under Partial Monitoring Motivation Social Influence

Outline

1 Motivation

Social Influence Cascaded Indirect Influence

2 Challenges 3 Problem Formulation 4 Algorithm 5 Experiments

Datasets Experiments on Normalized Regrets Experiments on Application Improvement

6 Conclusion

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SLIDE 4

Learning Cascaded Influence under Partial Monitoring Motivation Social Influence

Social Influence

Social influence is the phenomenon that people’s opinions, emotions or behaviors are affected by others Application: viral marketing, propaganda, advertising promotion...

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SLIDE 5

Learning Cascaded Influence under Partial Monitoring Motivation Cascaded Indirect Influence

Outline

1 Motivation

Social Influence Cascaded Indirect Influence

2 Challenges 3 Problem Formulation 4 Algorithm 5 Experiments

Datasets Experiments on Normalized Regrets Experiments on Application Improvement

6 Conclusion

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SLIDE 6

Learning Cascaded Influence under Partial Monitoring Motivation Cascaded Indirect Influence

Cascaded Indirect Influence

Social influence between non-adjacent users in the social network

s t s t

0.3 0.5 0.2 0.1 0.2 0.1 0.5 0.4 0.1 0.1 0.4 0.7 0.3 0.6 0.8 0.1

?

Cascaded Influence Direct Influence Network

Application: friend recommendation, link prediction, ...

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SLIDE 7

Learning Cascaded Influence under Partial Monitoring Challenges

Challenges

Information about non-adjacent users is rare The number of potential paths between two users is exponentially large Most of the previous works infer the direct influence from the cascade data – partial, sparse and dynamic

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SLIDE 8

Learning Cascaded Influence under Partial Monitoring Problem Formulation

Cascaded Indirect Influence

Given a dynamic influence network Gt = (V , E, Wt) Direct influence we,t =

i e−(t−τi)/δ

Influence path from u to v It(pi) =

e∈pi we,t

Influence probability v is activated by u indirectly It = 1 −

N

  • i=0

(1 − It(pi)) =

N

  • i=0

It(pi) + o(It(pi)) Omit the high-order terms of It(pi) and take the top-k terms

  • f the first-order It(pi)
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SLIDE 9

Learning Cascaded Influence under Partial Monitoring Problem Formulation

Cascaded Indirect Influence

Definition Cascaded Indirect Influence. The cascaded indirect influence from u to v is defined as the sum of the top k influence score among all the paths in P, It = max

Q⊂P

  • pi∈Q

It(pi) s.t. |Q| = k

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SLIDE 10

Learning Cascaded Influence under Partial Monitoring Problem Formulation

Partial Monitoring Setting

The number of the intermediate paths are exponentially large – Intractable to learn indirect influence from all the paths Partial Monitoring Setting & Online Learning Problem min

decision

1 T (max

Q⊂P

  • pi∈Q

T

  • t=1

It(pi) −

T

  • t=1

ˆ It(Dt)) s.t. |Q| = k

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SLIDE 11

Learning Cascaded Influence under Partial Monitoring Problem Formulation

Partial Monitoring Setting

Problem min

decision

1 T (max

Q⊂P

  • pi∈Q

T

  • t=1

It(pi) −

T

  • t=1

ˆ It(Dt)) s.t. |Q| = k Regret Normalized Regret

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SLIDE 12

Learning Cascaded Influence under Partial Monitoring Problem Formulation

Regret

Growth rate of the Regret Our Goal

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SLIDE 13

Learning Cascaded Influence under Partial Monitoring Algorithm

Algorithm – E-EXP3

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SLIDE 14

Learning Cascaded Influence under Partial Monitoring Algorithm

Algorithm – E-EXP3

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SLIDE 15

Learning Cascaded Influence under Partial Monitoring Algorithm

Algorithm – E-EXP3 Example

s t s t

? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

s t

0.3 0.5 ? ? ? 0.1 ? ? 0.1 ? 0.3 ? ? ? 0.8 ? 0.123

s t s t

0.5 ? ? 0.3 ? 0.5 ? 0.4 ? ? ? 0.6 ? 0.18 0.4 ? ?

Cascaded Influence Exploration Exploitation Top k = 2

Edge Bandit

Original (a) (b) (c)

Exploration & Exploitation

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SLIDE 16

Learning Cascaded Influence under Partial Monitoring Algorithm

Algorithm Theory Analysis

Parameter mixing coefficient : γ =

  • |C| ln N

(e − 1)T learning rate : η = 1 K

  • ln N

(e − 1)|C|T Regret Upper Bound 2K

  • (e − 1)T|C| ln N

More Proof Details: http://www.jiaqima.me/papers/learning-cascaded- influence.pdf

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SLIDE 17

Learning Cascaded Influence under Partial Monitoring Algorithm

Algorithm – RE-EXP3

Algorithm 1: Preprocessing Schedule of RE-EXP3 Input : Preprocessing Round Tp γ, K, |C| Output: η

1 η ← γ/K|C| 2 G ← ∅ 3 foreach t in range(Tp) do 4

Choose Dt with E-EXP3

5

G ← G ∪ {g′

i,t : i ∈ Dt} 6 η ← η × min{ 1 mean(G)+3var(G), 1}

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SLIDE 18

Learning Cascaded Influence under Partial Monitoring Experiments Datasets

Outline

1 Motivation

Social Influence Cascaded Indirect Influence

2 Challenges 3 Problem Formulation 4 Algorithm 5 Experiments

Datasets Experiments on Normalized Regrets Experiments on Application Improvement

6 Conclusion

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SLIDE 19

Learning Cascaded Influence under Partial Monitoring Experiments Datasets

Experiments: Datasets

Synthetic Networks

2000 vertexes edge generation probability 0.01 edge weight U[0, 0.3] or U[0.6, 1] 60,000 times

WeiBo

1,776,950 users 308,739,489 following relationships 23,755,810 retweets 100 time stamps

Aminer

231,728 papers 269,508 authors 347,735 citation relationships 44 time stamps

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SLIDE 20

Learning Cascaded Influence under Partial Monitoring Experiments Experiments on Normalized Regrets

Outline

1 Motivation

Social Influence Cascaded Indirect Influence

2 Challenges 3 Problem Formulation 4 Algorithm 5 Experiments

Datasets Experiments on Normalized Regrets Experiments on Application Improvement

6 Conclusion

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SLIDE 21

Learning Cascaded Influence under Partial Monitoring Experiments Experiments on Normalized Regrets

Experiments on Normalized Regrets(Synthetic)

10000 20000 30000 40000 50000 60000

Time Stamp

3 4 5 6 7 8 9 10

NR NR on Synthetic

RE-EXP3 E-EXP3 P-EXP3 CUCB Random

(a) NR

10000 20000 30000 40000 50000 60000

Time Stamp

0.4 0.6 0.8 1.0 1.2 1.4

RNR RNR on Synthetic

RE-EXP3 E-EXP3 P-EXP3 CUCB Random

(b) RNR

Figure: Normalized Regret on Synthetic Data

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SLIDE 22

Learning Cascaded Influence under Partial Monitoring Experiments Experiments on Normalized Regrets

Experiments on Normalized Regrets(Weibo & Aminer)

20 40 60 80 100

Time Stamp

0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05

Average RNR Average RNR on Weibo

RE-EXP3 E-EXP3 P-EXP3 CUCB Random

(a) Average RNR on Weibo

5 10 15 20 25 30 35 40

Time Stamp

0.80 0.85 0.90 0.95 1.00 1.05

Average RNR Average RNR on AMiner

RE-EXP3 E-EXP3 P-EXP3 CUCB Random

(b) Average RNR on AMiner

Figure: Average Normalized Regret on real social networks (1500 pairs of users)

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SLIDE 23

Learning Cascaded Influence under Partial Monitoring Experiments Experiments on Application Improvement

Outline

1 Motivation

Social Influence Cascaded Indirect Influence

2 Challenges 3 Problem Formulation 4 Algorithm 5 Experiments

Datasets Experiments on Normalized Regrets Experiments on Application Improvement

6 Conclusion

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SLIDE 24

Learning Cascaded Influence under Partial Monitoring Experiments Experiments on Application Improvement

Experiments on Application Improvement(Weibo)

Table: Application Improvement - Logistic Regression

Methods Accuracy Precision Recall F1 score PF 0.55 0.58 0.45 0.51 P-EXP3 0.57 0.58 0.55 0.57 E-EXP3 0.59 0.61 0.55 0.58 RE-EXP3 0.64 0.65 0.63 0.64 FO 0.70 0.77 0.60 0.68

Table: Application Improvement - SVM

Methods Accuracy Precision Recall F1 score PF 0.58 0.57 0.72 0.63 P-EXP3 0.56 0.58 0.53 0.55 E-EXP3 0.58 0.60 0.55 0.57 RE-EXP3 0.63 0.65 0.61 0.63 FO 0.70 0.77 0.57 0.66

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SLIDE 25

Learning Cascaded Influence under Partial Monitoring Conclusion

Conclusion

Formalized a novel problem of cascade indirect influence based on IC model Proposed two online learning algorithms (E-EXP3 and RE-EXP3) in the partial monitoring setting Theoretically proved that E-EXP3 has a cumulative regret bound of O( √ T). Compared the algorithms with three baseline methods on both synthetic and real networks (Weibo and AMiner). Applied the learned cascaded influence to help behavior prediction