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Part I → Part II → Part III → Part IV → Part V

              Other Issues
Part IV: Outline
       Testing Homophily/Influence
       Learning Influence Models
       Model-based versus Memory-based
        Approaches
       Influence vs. Adoption/Revenue
       Handling Competition
       Participation Maximization
       Paying Attention to Budget and Time

2
3
Testing Homophily/Influence




4
Sources of Correlation
       Social influence (induction)
        ◦ One person performing an action causes
          people connected to her to do the same

       Homophily (selection)
        ◦ Similar individuals are more likely to be
          connected: proverbial birds of a feather …

       Confounding factors: external influences
        Friends likely to live in same city and upload
        pix of same landmarks; a lot of users rate
        avatar ‘cos of its popularity; …
5                         [Anagnostopoulos, Kumar, & Mahdian KDD 2008]
Shuffle test (1/3)
       Want to test if there is correlation in node
        activation, given D = (G, W).
        ◦ G – social graph; W = {𝑢1 , … , 𝑢 𝑚 } – nodes that
          acted (along with timestamps).

       Influence model: each user flips a coin at
        each time t, to decide to (not) act.
       Prob. depends on time, user, and their
        #active friends. Fit a logistic function for
        estimating probs:                      correlation

            𝑝 𝑘 = 𝑒𝛼    𝑙𝑛 𝑘+1 +𝛽
                                    /[1 + 𝑒 𝛼   𝑙𝑛 𝑘+1 +𝛽
                                                             ]
6                                       [Anagnostopoulos et al. KDD 2008]
Shuffle test (2/3)
       Learn correlation on both original data D
        = (G,W) and on D’ = (G,W’) obtained by
        a random shuffle: randomly permute
        activation times of 𝑢1 , … , 𝑢 𝑚 .  𝛼, 𝛼 ′ .

       If original data D came from an
        influence model, 𝛼 ′ should significantly
        drop from 𝛼.


7
Shuffle test (3/3)
       Infer influence
        weights
       Randomizeempirical finding:
              A Key
        activation times in in flickr
              Tagging behavior
        each cannot be attributed to
              cascade
              influence.
       Infer influence
        weights again
        ◦ Should be lower



8                                 [Anagnostopoulos et al. KDD 2008]
Matched sampling
       Match pairs of nodes that are “twins”
        ◦ E.g. same age, same location, etc.
        ◦ Match a node with no adopting friends, with a
          node with 𝑘 adopting friends

       Verify if the node with adopting friends is more
        likely to adopt

       Main finding: matching random pairs reveals
        gross overestimates of influence by traditional
        methods: homophily explains >50% of perceived
        contagion.
        ◦ Data: Yahoo! IM network, adoption of mobile app.
9                                           [Aral et al. PNAS 2009]
Effect of rating from friends
        Do WoM recommendations influence user ratings? If yes,
         how do you quantify it?
         ◦ Focus on posterior evaluation; surprising findings.

        For a given item 𝑖 and a user 𝑢, build a triple
          𝑓𝑟𝑖𝑒𝑛𝑑𝑅𝑒𝑐(𝑖, 𝑢), 𝑟𝑎𝑡𝑖𝑛𝑔(𝑖, 𝑢), 𝑓𝑟𝑖𝑒𝑛𝑑𝑅𝑎𝑡𝑖𝑛𝑔(𝑖, 𝑢) = <m’,r,r’>


     Group by (similarity on)
      𝑓𝑟𝑖𝑒𝑛𝑑𝑅𝑎𝑡𝑖𝑛𝑔 𝑖, 𝑢 and in
     each bucket test if
      𝒓𝒂𝒕𝒊𝒏𝒈(𝒊, 𝒖) is
     independent from
      𝒇𝒓𝒊𝒆𝒏𝒅𝑹𝒆𝒄(𝒊, 𝒖)

     Experimental results: not
     independent friend
     adoption influences
10   user’s ratings                    [Huang, Cheng,Shen, Zhou, Jin WSDM 2012]
Learning Influence Models




11
Where do the numbers come from?
12
Learning influence models
        Where do influence probabilities come from?
         ◦   Real world social networks don’t have probabilities!
         ◦   Can we learn the probabilities from action logs?
         ◦   Sometimes we don’t even know the social network
         ◦   Can we learn the social network, too?

        Does influence probability change over time?
         ◦ Yes! How can we take time into account?
         ◦ Can we predict the time at which user is most likely
           to perform an action?



13
Where do the weights come from?
        Influence Maximization – Gen 0:
         academic collaboration networks (real)
         with weights assigned arbitrarily using
         some models:
         ◦ Trivalency: weights chosen uniformly at
           random from {0.1, 0.01, 0.001}.
                                             0.1
                                                     0.001

                                                     0.01
                                             0.001

                                             0.01    0.01
14
Where do the weights come from?
        Influence Maximization – Gen 0:
         academic collaboration networks (real)
         with weights assigned arbitrarily using
         some models:
                                           1
         ◦ Weighted Cascade: 𝑤 𝑢𝑣 =               .
                                           𝑑 𝑖𝑛
                                             𝑣

                                                      1/3
                                                            1/3
     Other variants: uniform (constant),
     WC with parallel edges.                                1/3

     Weight assignment not                            1/3
     backed by real data.                            1/3   1/3
15
Inference problems
        Given a log 𝐴 = { 𝑢1 , 𝑎1 , 𝑡1 , … }

        P1. Social network not given
         ◦ Infer network and edge weights

        P2. Social network given
         ◦ Infer edge weights

        P3. Social network and attribution given
         ◦ Explicit “trackbacks” to parent user
                         𝐴 = 𝑢1 , 𝑎1 , 𝑡1 , 𝑝1 , …
         ◦ Simple counting
16
P1. Social network not given
        Observe activation times, assume
         probability of a successful activation
         decays (e.g., exponentially) with time

                            𝑢1 ,   𝑎1 ,   𝑡1   ,
                            𝑢2 ,   𝑎2 ,   𝑡2   ,
                            𝑢3 ,   𝑎3 ,   𝑡3   ,
                            𝑢4 ,   𝑎4 ,   𝑡4   ,
                                   …
     Actual network                                Learned network



17                      [Gomez-Rodriguez, Leskovec, & Krause KDD 2010]
P2. Social network given
      Input data: (1) social graph and (2) action
      log of past propagations
                    I read this             great           Action   Node   Time
                       article              movie   09:30
                                                              a       u12    1
                                  u45                         a       u45    2
                                                              a       u32    3
     I liked this                                             a       u76    8
                    09:00
        movie                                                 b       u32    1
                                                              b       u45    3
                    u12                                       b       u98    7


                                  u45 follows u12
18
P2. Social network given
        D(0), D(1), … D(t) nodes that acted at time t.

        𝐶 𝑡 =    𝜏≤𝑡   𝐷 𝜏 . → cumulative.

        𝑃 𝑤 𝑡 + 1 = 1 − Π 𝑣∈𝑁 𝑖𝑛   𝑤 ∩𝐷 𝑡   1 − 𝜅 𝑣𝑤 .

        Find 𝜃 = 𝜅 𝑣𝑤 that maximizes likelihood

                   𝑇−1                                                    success
     𝐿 𝜃; 𝐷 = (𝛱 𝑡=0 𝛱 𝑤∈𝐷 𝑡+1 𝑃 𝑤 (𝑡 + 1)) −
              𝑇−1
          (Π 𝑡=0 Π 𝑣∈𝐷 𝑡 Π 𝑤∈𝑁 𝑜𝑢𝑡 𝑣 C 𝑡+1 1 − 𝜅 𝑣𝑤 )                     failure

          Very expensive (not scalable)

          Assumes influence weights remain constant over time
19                                                        [Saito et al. KES 2008]
P2. Social network given
        Several models of influence probability
         ◦ in the context of General Threshold model + time
         ◦ consistent with IC and LT models

        With or without explicit attribution

        Models able to predict whether a user will perform an action or
         not: predict the time at which she will perform it

        Introduce metrics of user and action influenceability
         ◦ high values  genuine influence

        Develop efficient algorithms to learn the parameters of the
         models; minimize the number of scans over the propagation log

        Incrementality property
20
                                     [[Goyal, Bonchi, and L. WSDM2010 ]
Influence models
         Static Models: probabilities are static and do not change over time.

                          Bernoulli:                    Jaccard:

      Continuous Time (CT) Models: probabilities decay exponentially in time



          Not incremental, hence very expensive to apply on large datasets.




     Discrete Time (CT) Models: Active neighbor u of v remains contagious in

      [t, t+ (u,v)], has constant influence prob p(u,v) in the interval and 0 outside.

                        Monotone, submodular, and incremental!
21
Evaluation
        Flickr groups dataset (action=joining)
         ◦ ~1.3M nodes, 40M edges, 36M actions
         ◦ 80/20 training/testing split

        Predict whether user will become active
         or not, given active neighbors
      Ideal Point


        Operating                                       Reality
          Point
                                                        Active    Inactive
                                Prediction   Active       TP        FP
  Binary Classification
                                             Inactive    FN         TN
  (ROC curve)
22                                            Total       P          N
Comparison of Static, CT and DT
     models




        Time-conscious models better than the static model
         ◦ CT and DT models perform equally well

        Static and DT models are far more efficient compared to
         CT models because of their incremental nature
23
Predicting Time – Distribution of
     Error




        Operating Point is chosen corresponding to
         ◦ TPR: 82.5%, FPR: 17.5%.

        Most of the time, error in the prediction is very
         small
24
Learning Influence Probabilities
     Takeaways
        Influence network and weights not always available

        Learn from the action log
         ◦ [Gomez-Rodriguez et al. 2010]: Infer social network and edge
           weights
         ◦ [Saito et al. 2008]: Infer edge weights using EM approach
         ◦ [Goyal et al. 2010]: Infer both static and time-conscious models
           of influence

        Using CT models, it is possible to predict even the time at
         which a user will perform it with a good accuracy.

        Introduce metrics of users and actions influenceability.
         ◦ High values => easier prediction of influence.
         ◦ Can be utilized in Viral Marketing decisions.

25
Memory-based and
     Model-based Approaches
     for Influence Maximization




26
And a little memory always helps!




27
Previous Art                                               Diffusion Model
             Social graph

                                                         .1                         .3
                                                                     .3                       .1




                                   Learn probabilities
                                                                               .2

                                                                         .1
                                                         .4                    .3
                                                                    .2        .4         .1
                                                                                                   .4
                                                                          .3
                                                                                    .1
                                                                         .1                        .2
                                                          .2                             .4
                                                               .4
                                                                                              .1

         Propagation log

     Inherently model-based approach
                                                                          Seed set
     Can we instead use memory (of what
     happened in the past) directly?
28
Why learning from data matters
        Methods compared (IC model):
         ◦ WC, TV, UN (no learning)
         ◦ EM (learned from real data – Expectation Maximization method)
         ◦ PT (learned then perturbed  20%)

        Data:
         ◦ 2 real-world datasets (with social graph + propagation log): Flixster and Flickr
         ◦ On Flixster, we consider “rating a movie” as an action
         ◦ On Flickr, we consider “joining a group” as an action
         ◦ Split the data in training and test sets – 80:20


        Compare the different ways of assigning probabilities:
         1. Seed sets intersection
         2. Given a seed set, we ask to the model to predict its spread (ground truth on
            the test set)
29                                                      [Goyal, Bonchi, & L. VLDB 2012]
Why learning from data matters –
     experiments*
     1.   Seed sets intersection (k = 50)




     2.   Given a seed set, we ask to the IC model to predict its spread (on the
          test set)
30
Memory-based Approach
        Instead of learning probabilities
         from available propagation traces
         (sampling possible worlds from model,
         using simulation to estimate expected
         spread)

        Use the actual/real worlds
         corresponding to the propagations
         that actually happened to estimate
         spread!
31                                     [Goyal et al. VLDB 2012]
Direct mining
          Social graph




                                        MINING
                                                            Seed set




                         Two approaches:
       Propagation log
                         1. Credit Distribution (CD) approach
                         2. A frequent-pattern based approach


32
Expected spread: a different perspective*
     Instead of simulating propagations, use available propagations!

                                             sampling “possible
                                           worlds” (MC simulations)




                                                    Estimate it in “available
                                                        worlds” (i.e., our
                                                      propagation traces)




33                                                  [Goyal et al. VLDB 2012]
The sparsity issue
        We can not estimate directly                      as:

            (# actions in which S is the seed-set and u
                            participates)

               (# actions in which S is the seed-set)
     • None or too few actions where S is effectively the seed
       set i.e., initiators).
     • Take a u-centric perspective instead:
     • Each time u performs an action we distribute influence
       credit for this action, back to her ancestors
     • learns different level of user-influenceability
     • Time-aware
34
Experiments
     Datasets:                    Flixster   Flickr




     Dataset:    Flixster small




35
Influence vs. Adoption/Revenue




36
I want to buy it but …




37
Influence vs. Adoption vs. Profit
        If a user gets influenced, it doesn’t
         necessarily imply she’ll adopt the
         product.

        Classical models:
         ◦ influenced  adopt.
         ◦ Profit captured by proxy: expected spread!

        Need models and algorithms for VM
         taking these distinctions into account.
38
                                  [Bhagat, Goyal, & L. WSDM 2012]
Influence ⇏ Adoption
        Observation: Only a subset of influenced
         users actually adopt the marketed product




                  Influenced    Adopt


        Awareness/information spreads in an epidemic-
         like manner while adoption depends on factors
         such as product quality and price

39                                            [Kalish MS, 95]
Influence ⇏ Adoption
        Moreover, there exist users who help in
         information propagation without actually
         adopting the product – tattlers.




40
Our Model (LT-C)
                                                          αv   Adopt
                                       fv (A )
                            Inactive             Active
                                                                         βv      Promote
                                                      1 − αv   Tattle
                               1 − fv (A )
                                                                        1 − βv    Inhibit
     Active                                          User v
     Friends
          Model Parameters
           ◦ A is the set of active friends
           ◦ fv(A) is the activation function
           ◦ ru,i is the (predicted) rating for product i given by user u
           ◦ αv is the probability of user v adopting the product
           ◦ βv is the probability of user v promoting the product

41
Maximizing Product Adoption
        Problem: Given a social network and
         product ratings, find k users such that by
         targeting them the expected spread
         (expected number of adopters) under the LT-
         C model is maximized
        Problem is NP-hard
        The spread function is monotone and
         submodular yielding a (1-1/e)-approximation
         to the optimal using a greedy approach


42
Evaluation: Spread Estimates




         Flixster


                        MovieLens


        Our model (LT-C) better            Last.fm
         predicts spread for all datasets

43
Spread depends on product
     quality

                         Better quality products
                         have better coverage

                         Classical LT model on the
                         other hand predicts equal
                         coverage for all products




44
Key Takeaways
        Only a fraction of users who are
         influenced do adopt the product
        The influence of an adopter on her friends
         is a function of the adopter’s experience
         with the product, in addition to
         propagation probability
        Non-adopters can play a role of
         “information bridges” helping in spreading
         the influence/information, and thus
         adoption by other users

45
Handling Competitions




46
47
Competitive influence diffusion
     •   Influence maximization vs. influence
         blocking maximization

     •   Modeling competitive diffusion

     •   Endogenous competition: emergence
         and propagation of negative opinions



48
Influence blocking maximization
     •       Problem:
         •    Given the negative activation status,
         •    find 𝑘 positive seeds
         •    minimize the further negative influence, or
              maximize the expected number of “saved” or
              “blocked” nodes from negative influence ---
              negative influence reduction
     • Extension of the IC model [Budak et al.
       WWW 2011]
     • Extension of the LT model [He et al. SDM
       2012]
49
Multiple Campaign IC model
     •       Two campaigns, positive vs. negative
     •       General case:
         •    each campaign has an independent set of
              IC parameters
         •    negative influence reduction is not
              submodular
     •       Special cases:
         •    high effectiveness property: positive
              campaign has propagation probability of
              one
         •    campaign oblivious IC : positive and
              negative campaigns have the same
              parameters
         •    tie-breaking rule: positive campaign
              dominance
         •    negative influence reduction is submodular
50                                         [Budak, Agrawal and Abbadi, WWW 2011]
Competitive linear threshold
     model
     •   two campaigns, each has a different set of
         LT parameters (influence weights)
     •   each nodes has two thresholds, negative
         and positive thresholds, drawn uniformly at
         random from [0,1]
     •   positive and negative campaigns use their
         own LT parameters to diffuse
     •   negative campaign dominates (could be
         changed to an arbitrary dominance
         probability)
51                                      [He et al. SDM 2012]
Influence blocking maximization
     under CLT
     •   negative influence reduction is
         submodular

     •   allows greedy approximation algorithm

     •   fast heuristic CLDAG:
         • reduce influence computation on local
           DAGs
         • use dynamic programming for LDAG
           computations
52                                      [He et al. SDM 2012]
Performance of the CLDAG




      • with Greedy algorithm        • without Greedy algorithm
      • 1000 node sampled from a     • 15K node NetHEPT,
        mobile network dataset         collaboration network in arxiv
      • 50 negative seeds with max   • 50 negative seeds with max
        degrees                        degrees
53                                                [He et al. SDM 2012]
Scalability—Real dataset




       Scalability Result for subgraph with greedy algorithm




54                                                              [He et al. SDM 2012]
Attacker/defender game for
     competitive influence diffusion
        a zero-sum game
         ◦ attacker selects negative seeds to maximize its influence
         ◦ defender selects positive seeds to minimize attacker’s influence
        Maximin strategy
         ◦ compute mixed Nash equilibrium for both simultaneous-move and
           leader-follower Stackelberg games
         ◦ inefficient, need full payoff matrix
        Double oracle algorithm
         ◦ attacker uses any influence maximization algo. as attacker oracle
         ◦ defender uses any influence blocking maximization algo. as defender
           oracle
         ◦ iteration: use oracles to enlarge strategy space, use Maximin to
           compute mixed equilibrium on the current strategy space


55                                                [Tsai, Nguyen and Tambe, AAAI 2012]
Endogenous Competition:
     Effect of Negative Opinions




56
57
Endogenous competition
     •   Negative opinion generated from
         product defects
     •   Negative opinion propagates,
         competing with positive opinion
     •   Positive opinions may turn negative, but
         negative opinions will not turn back ---
         negativity bias


58
Influence maximization with
     negative opinions
     •   IC-N: extend the IC model with quality
         factor 𝑞
         •   each positive activation has probability of 1 − 𝑞
             to turn negative
         •   negative opinion propagates as positive
             opinion, but negative activations do not turn
             positive
     • Maximize the positive influence
     • Submodularity still holds
     • MIA-N: fast heuristics using dynamic
       programming for efficient tree based
       influence spread computation
59                                             [Chen et al. SDM 2011]
Performance of MIA-N heuristic




      • 15K node NetHEPT,
                                         • MIA-N achieves 2 orders of
        collaboration network in arxiv
                                           manitude speedup
      • influence spread of MIA-N
        matches Greedy algorithm




60                                                   [Chen et al. SDM 2011]
Key takeaways for handling
     competitions
        Standard models (IC/LT) may be
         generalized for exogenous/endogenous
         competition
         ◦ be careful, may violate submodularity

        Activation timing becomes important,
         due to competitions between positive
         and negative diffusions
         ◦ Greedy algorithm becomes slower
         ◦ Heuristics need dynamic programming
61
Other topics
        Participation maximization
         ◦ from platform provider’s point of view
         ◦ many cascades, maximize overall spread
         ◦ each user can be seeds for a small number of
           cascades
         ◦ see [Ienco, Bonchi and Castillo, ICDM
           Workshops 2010; Sun et al. ICWSM 2011]

        Budget and time
         ◦ Time-critical IM [Chen, Lu, Zhang, AAAI 2012]
         ◦ minimize seed size, or diffusion time [Goyal, et al.
           SNAM 2012]
62
Participation Maximization




63
Seed allocation and participation
     maximization
        Multiple independent cascades from seed sets
        Each user can only act as seed for a fixed
         number of cascades
        Problem: find allocation of seeds to users, to
         maximize the total size of all cascades
         ◦ online version: allocation has to be done when user
           logs in
        Applications:
         ◦ Meme ranking
         ◦ Topic recommendation in online discussion forums
         ◦ Online advertising
64
Application: Meme Ranking
        Users see a selection
         of 𝑘 postings by
         people they follow
         ◦ Which postings?

        Heuristic: observe
         what each user and
         a small sample of
         her followers have                          Goal:
         re-posted                          maximize total re-posting
                                              activity by all users


65                           [Ienco, Bonchi and Castillo, ICDM Workshops 2010]
Application: topic thread rec.
        recommend a small set of
         topic (or thread) to users on
         their sidebars
        maximize total participations
         of all discussion threads
         ◦ diff. from recommender systems: not only increase
           participation of recommended users, but increase
           participation of others via social influence

        Theory: social welfare maximization with
         submodular functions
        RPA (randomized proportional allocation):
         greedy-based, very slow
        TABI: heuristic considering both self and other
         participation via influence
66                                                             [Sun et al. ICWSM 2011]
Paying Attention to
      Budget and Time




67
Time critical influence
     maximization
     •   achieve influence maximization within a
         short deadline
     •   need to model delay in influence diffusion
         •   add meeting probabilities of pair of nodes;
             influence occur only after individuals meet
         •   extend IC and LT models, still satisfy
             submodularity

     •   fast heuristics (for the IC model extension)
         •   MIA-M: need dynamic programming
         •   MIA-C: conversion to standard IC model and
             MIA algorithm
68                                       [Chen, Lu and Zhang, AAAI 2012]
Minimizing Expenses
        MINTSS: Given a target spread you want
         to reach, how to pick the fewest seeds
         that realize the outcome?

         • Problem. Given 𝐺 = (𝑉, 𝐸), a threshold 𝜂 on
           expected spread, pick the smallest set of
           seeds 𝑆: 𝜎 𝑆 ≥ 𝜂.
         • For hardness, approximability results and
           algorithms, see paper!


69                      [Goyal, Bonchi, L., & Venkatasubramanian SNAM 2012]
Minimizing Propagation Time
        MINTIME: Given a seed budget and a
         target spread, pick seeds under budget
         so the target is realized as quickly as
         possible.
         • Problem. Given 𝐺 = (𝑉, 𝐸), a seed budget
            𝑘 and a threshold 𝜂 on expected spread,
           choose 𝑘 seeds S: 𝜎 𝑆 ≥ 𝜂 and the time
           horizon in which this happens is min.
         • For hardness, approximability results and
           algorithms, see paper!

70                      [Goyal, Bonchi, L., & Venkatasubramanian SNAM 2012]
Part IV Key Takeaways
        Tests exist for homophily/influence

        Influence weights can be learned from data!

        Bypassing model and direct seed selection is possible

        Better models for Adoption/Revenue vs Influence

        Exogenous and endogenous competition can be modeled with
         care

        Participation maximization considers maximizing multiple
         influence spreads across an entire platform

        Time and budget can be considered in the objective function
71

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Kdd12 tutorial-inf-part-iv

  • 1. Part I → Part II → Part III → Part IV → Part V Other Issues
  • 2. Part IV: Outline  Testing Homophily/Influence  Learning Influence Models  Model-based versus Memory-based Approaches  Influence vs. Adoption/Revenue  Handling Competition  Participation Maximization  Paying Attention to Budget and Time 2
  • 3. 3
  • 5. Sources of Correlation  Social influence (induction) ◦ One person performing an action causes people connected to her to do the same  Homophily (selection) ◦ Similar individuals are more likely to be connected: proverbial birds of a feather …  Confounding factors: external influences Friends likely to live in same city and upload pix of same landmarks; a lot of users rate avatar ‘cos of its popularity; … 5 [Anagnostopoulos, Kumar, & Mahdian KDD 2008]
  • 6. Shuffle test (1/3)  Want to test if there is correlation in node activation, given D = (G, W). ◦ G – social graph; W = {𝑢1 , … , 𝑢 𝑚 } – nodes that acted (along with timestamps).  Influence model: each user flips a coin at each time t, to decide to (not) act.  Prob. depends on time, user, and their #active friends. Fit a logistic function for estimating probs: correlation 𝑝 𝑘 = 𝑒𝛼 𝑙𝑛 𝑘+1 +𝛽 /[1 + 𝑒 𝛼 𝑙𝑛 𝑘+1 +𝛽 ] 6 [Anagnostopoulos et al. KDD 2008]
  • 7. Shuffle test (2/3)  Learn correlation on both original data D = (G,W) and on D’ = (G,W’) obtained by a random shuffle: randomly permute activation times of 𝑢1 , … , 𝑢 𝑚 .  𝛼, 𝛼 ′ .  If original data D came from an influence model, 𝛼 ′ should significantly drop from 𝛼. 7
  • 8. Shuffle test (3/3)  Infer influence weights  Randomizeempirical finding: A Key activation times in in flickr Tagging behavior each cannot be attributed to cascade influence.  Infer influence weights again ◦ Should be lower 8 [Anagnostopoulos et al. KDD 2008]
  • 9. Matched sampling  Match pairs of nodes that are “twins” ◦ E.g. same age, same location, etc. ◦ Match a node with no adopting friends, with a node with 𝑘 adopting friends  Verify if the node with adopting friends is more likely to adopt  Main finding: matching random pairs reveals gross overestimates of influence by traditional methods: homophily explains >50% of perceived contagion. ◦ Data: Yahoo! IM network, adoption of mobile app. 9 [Aral et al. PNAS 2009]
  • 10. Effect of rating from friends  Do WoM recommendations influence user ratings? If yes, how do you quantify it? ◦ Focus on posterior evaluation; surprising findings.  For a given item 𝑖 and a user 𝑢, build a triple 𝑓𝑟𝑖𝑒𝑛𝑑𝑅𝑒𝑐(𝑖, 𝑢), 𝑟𝑎𝑡𝑖𝑛𝑔(𝑖, 𝑢), 𝑓𝑟𝑖𝑒𝑛𝑑𝑅𝑎𝑡𝑖𝑛𝑔(𝑖, 𝑢) = <m’,r,r’> Group by (similarity on) 𝑓𝑟𝑖𝑒𝑛𝑑𝑅𝑎𝑡𝑖𝑛𝑔 𝑖, 𝑢 and in each bucket test if 𝒓𝒂𝒕𝒊𝒏𝒈(𝒊, 𝒖) is independent from 𝒇𝒓𝒊𝒆𝒏𝒅𝑹𝒆𝒄(𝒊, 𝒖) Experimental results: not independent friend adoption influences 10 user’s ratings [Huang, Cheng,Shen, Zhou, Jin WSDM 2012]
  • 12. Where do the numbers come from? 12
  • 13. Learning influence models  Where do influence probabilities come from? ◦ Real world social networks don’t have probabilities! ◦ Can we learn the probabilities from action logs? ◦ Sometimes we don’t even know the social network ◦ Can we learn the social network, too?  Does influence probability change over time? ◦ Yes! How can we take time into account? ◦ Can we predict the time at which user is most likely to perform an action? 13
  • 14. Where do the weights come from?  Influence Maximization – Gen 0: academic collaboration networks (real) with weights assigned arbitrarily using some models: ◦ Trivalency: weights chosen uniformly at random from {0.1, 0.01, 0.001}. 0.1 0.001 0.01 0.001 0.01 0.01 14
  • 15. Where do the weights come from?  Influence Maximization – Gen 0: academic collaboration networks (real) with weights assigned arbitrarily using some models: 1 ◦ Weighted Cascade: 𝑤 𝑢𝑣 = . 𝑑 𝑖𝑛 𝑣 1/3 1/3 Other variants: uniform (constant), WC with parallel edges. 1/3 Weight assignment not 1/3 backed by real data.  1/3 1/3 15
  • 16. Inference problems  Given a log 𝐴 = { 𝑢1 , 𝑎1 , 𝑡1 , … }  P1. Social network not given ◦ Infer network and edge weights  P2. Social network given ◦ Infer edge weights  P3. Social network and attribution given ◦ Explicit “trackbacks” to parent user 𝐴 = 𝑢1 , 𝑎1 , 𝑡1 , 𝑝1 , … ◦ Simple counting 16
  • 17. P1. Social network not given  Observe activation times, assume probability of a successful activation decays (e.g., exponentially) with time 𝑢1 , 𝑎1 , 𝑡1 , 𝑢2 , 𝑎2 , 𝑡2 , 𝑢3 , 𝑎3 , 𝑡3 , 𝑢4 , 𝑎4 , 𝑡4 , … Actual network Learned network 17 [Gomez-Rodriguez, Leskovec, & Krause KDD 2010]
  • 18. P2. Social network given Input data: (1) social graph and (2) action log of past propagations I read this great Action Node Time article movie 09:30 a u12 1 u45 a u45 2 a u32 3 I liked this a u76 8 09:00 movie b u32 1 b u45 3 u12 b u98 7 u45 follows u12 18
  • 19. P2. Social network given  D(0), D(1), … D(t) nodes that acted at time t.  𝐶 𝑡 = 𝜏≤𝑡 𝐷 𝜏 . → cumulative.  𝑃 𝑤 𝑡 + 1 = 1 − Π 𝑣∈𝑁 𝑖𝑛 𝑤 ∩𝐷 𝑡 1 − 𝜅 𝑣𝑤 .  Find 𝜃 = 𝜅 𝑣𝑤 that maximizes likelihood 𝑇−1 success 𝐿 𝜃; 𝐷 = (𝛱 𝑡=0 𝛱 𝑤∈𝐷 𝑡+1 𝑃 𝑤 (𝑡 + 1)) − 𝑇−1 (Π 𝑡=0 Π 𝑣∈𝐷 𝑡 Π 𝑤∈𝑁 𝑜𝑢𝑡 𝑣 C 𝑡+1 1 − 𝜅 𝑣𝑤 ) failure Very expensive (not scalable) Assumes influence weights remain constant over time 19 [Saito et al. KES 2008]
  • 20. P2. Social network given  Several models of influence probability ◦ in the context of General Threshold model + time ◦ consistent with IC and LT models  With or without explicit attribution  Models able to predict whether a user will perform an action or not: predict the time at which she will perform it  Introduce metrics of user and action influenceability ◦ high values  genuine influence  Develop efficient algorithms to learn the parameters of the models; minimize the number of scans over the propagation log  Incrementality property 20 [[Goyal, Bonchi, and L. WSDM2010 ]
  • 21. Influence models Static Models: probabilities are static and do not change over time. Bernoulli: Jaccard: Continuous Time (CT) Models: probabilities decay exponentially in time Not incremental, hence very expensive to apply on large datasets. Discrete Time (CT) Models: Active neighbor u of v remains contagious in [t, t+ (u,v)], has constant influence prob p(u,v) in the interval and 0 outside. Monotone, submodular, and incremental! 21
  • 22. Evaluation  Flickr groups dataset (action=joining) ◦ ~1.3M nodes, 40M edges, 36M actions ◦ 80/20 training/testing split  Predict whether user will become active or not, given active neighbors Ideal Point Operating Reality Point Active Inactive Prediction Active TP FP Binary Classification Inactive FN TN (ROC curve) 22 Total P N
  • 23. Comparison of Static, CT and DT models  Time-conscious models better than the static model ◦ CT and DT models perform equally well  Static and DT models are far more efficient compared to CT models because of their incremental nature 23
  • 24. Predicting Time – Distribution of Error  Operating Point is chosen corresponding to ◦ TPR: 82.5%, FPR: 17.5%.  Most of the time, error in the prediction is very small 24
  • 25. Learning Influence Probabilities Takeaways  Influence network and weights not always available  Learn from the action log ◦ [Gomez-Rodriguez et al. 2010]: Infer social network and edge weights ◦ [Saito et al. 2008]: Infer edge weights using EM approach ◦ [Goyal et al. 2010]: Infer both static and time-conscious models of influence  Using CT models, it is possible to predict even the time at which a user will perform it with a good accuracy.  Introduce metrics of users and actions influenceability. ◦ High values => easier prediction of influence. ◦ Can be utilized in Viral Marketing decisions. 25
  • 26. Memory-based and Model-based Approaches for Influence Maximization 26
  • 27. And a little memory always helps! 27
  • 28. Previous Art Diffusion Model Social graph .1 .3 .3 .1 Learn probabilities .2 .1 .4 .3 .2 .4 .1 .4 .3 .1 .1 .2 .2 .4 .4 .1 Propagation log Inherently model-based approach Seed set Can we instead use memory (of what happened in the past) directly? 28
  • 29. Why learning from data matters  Methods compared (IC model): ◦ WC, TV, UN (no learning) ◦ EM (learned from real data – Expectation Maximization method) ◦ PT (learned then perturbed  20%)  Data: ◦ 2 real-world datasets (with social graph + propagation log): Flixster and Flickr ◦ On Flixster, we consider “rating a movie” as an action ◦ On Flickr, we consider “joining a group” as an action ◦ Split the data in training and test sets – 80:20  Compare the different ways of assigning probabilities: 1. Seed sets intersection 2. Given a seed set, we ask to the model to predict its spread (ground truth on the test set) 29 [Goyal, Bonchi, & L. VLDB 2012]
  • 30. Why learning from data matters – experiments* 1. Seed sets intersection (k = 50) 2. Given a seed set, we ask to the IC model to predict its spread (on the test set) 30
  • 31. Memory-based Approach  Instead of learning probabilities from available propagation traces (sampling possible worlds from model, using simulation to estimate expected spread)  Use the actual/real worlds corresponding to the propagations that actually happened to estimate spread! 31 [Goyal et al. VLDB 2012]
  • 32. Direct mining Social graph MINING Seed set Two approaches: Propagation log 1. Credit Distribution (CD) approach 2. A frequent-pattern based approach 32
  • 33. Expected spread: a different perspective* Instead of simulating propagations, use available propagations! sampling “possible worlds” (MC simulations) Estimate it in “available worlds” (i.e., our propagation traces) 33 [Goyal et al. VLDB 2012]
  • 34. The sparsity issue We can not estimate directly as: (# actions in which S is the seed-set and u participates) (# actions in which S is the seed-set) • None or too few actions where S is effectively the seed set i.e., initiators). • Take a u-centric perspective instead: • Each time u performs an action we distribute influence credit for this action, back to her ancestors • learns different level of user-influenceability • Time-aware 34
  • 35. Experiments Datasets: Flixster Flickr Dataset: Flixster small 35
  • 37. I want to buy it but … 37
  • 38. Influence vs. Adoption vs. Profit  If a user gets influenced, it doesn’t necessarily imply she’ll adopt the product.  Classical models: ◦ influenced  adopt. ◦ Profit captured by proxy: expected spread!  Need models and algorithms for VM taking these distinctions into account. 38 [Bhagat, Goyal, & L. WSDM 2012]
  • 39. Influence ⇏ Adoption  Observation: Only a subset of influenced users actually adopt the marketed product Influenced Adopt  Awareness/information spreads in an epidemic- like manner while adoption depends on factors such as product quality and price 39 [Kalish MS, 95]
  • 40. Influence ⇏ Adoption  Moreover, there exist users who help in information propagation without actually adopting the product – tattlers. 40
  • 41. Our Model (LT-C) αv Adopt fv (A ) Inactive Active βv Promote 1 − αv Tattle 1 − fv (A ) 1 − βv Inhibit Active User v Friends  Model Parameters ◦ A is the set of active friends ◦ fv(A) is the activation function ◦ ru,i is the (predicted) rating for product i given by user u ◦ αv is the probability of user v adopting the product ◦ βv is the probability of user v promoting the product 41
  • 42. Maximizing Product Adoption  Problem: Given a social network and product ratings, find k users such that by targeting them the expected spread (expected number of adopters) under the LT- C model is maximized  Problem is NP-hard  The spread function is monotone and submodular yielding a (1-1/e)-approximation to the optimal using a greedy approach 42
  • 43. Evaluation: Spread Estimates Flixster MovieLens  Our model (LT-C) better Last.fm predicts spread for all datasets 43
  • 44. Spread depends on product quality Better quality products have better coverage Classical LT model on the other hand predicts equal coverage for all products 44
  • 45. Key Takeaways  Only a fraction of users who are influenced do adopt the product  The influence of an adopter on her friends is a function of the adopter’s experience with the product, in addition to propagation probability  Non-adopters can play a role of “information bridges” helping in spreading the influence/information, and thus adoption by other users 45
  • 47. 47
  • 48. Competitive influence diffusion • Influence maximization vs. influence blocking maximization • Modeling competitive diffusion • Endogenous competition: emergence and propagation of negative opinions 48
  • 49. Influence blocking maximization • Problem: • Given the negative activation status, • find 𝑘 positive seeds • minimize the further negative influence, or maximize the expected number of “saved” or “blocked” nodes from negative influence --- negative influence reduction • Extension of the IC model [Budak et al. WWW 2011] • Extension of the LT model [He et al. SDM 2012] 49
  • 50. Multiple Campaign IC model • Two campaigns, positive vs. negative • General case: • each campaign has an independent set of IC parameters • negative influence reduction is not submodular • Special cases: • high effectiveness property: positive campaign has propagation probability of one • campaign oblivious IC : positive and negative campaigns have the same parameters • tie-breaking rule: positive campaign dominance • negative influence reduction is submodular 50 [Budak, Agrawal and Abbadi, WWW 2011]
  • 51. Competitive linear threshold model • two campaigns, each has a different set of LT parameters (influence weights) • each nodes has two thresholds, negative and positive thresholds, drawn uniformly at random from [0,1] • positive and negative campaigns use their own LT parameters to diffuse • negative campaign dominates (could be changed to an arbitrary dominance probability) 51 [He et al. SDM 2012]
  • 52. Influence blocking maximization under CLT • negative influence reduction is submodular • allows greedy approximation algorithm • fast heuristic CLDAG: • reduce influence computation on local DAGs • use dynamic programming for LDAG computations 52 [He et al. SDM 2012]
  • 53. Performance of the CLDAG • with Greedy algorithm • without Greedy algorithm • 1000 node sampled from a • 15K node NetHEPT, mobile network dataset collaboration network in arxiv • 50 negative seeds with max • 50 negative seeds with max degrees degrees 53 [He et al. SDM 2012]
  • 54. Scalability—Real dataset  Scalability Result for subgraph with greedy algorithm 54 [He et al. SDM 2012]
  • 55. Attacker/defender game for competitive influence diffusion  a zero-sum game ◦ attacker selects negative seeds to maximize its influence ◦ defender selects positive seeds to minimize attacker’s influence  Maximin strategy ◦ compute mixed Nash equilibrium for both simultaneous-move and leader-follower Stackelberg games ◦ inefficient, need full payoff matrix  Double oracle algorithm ◦ attacker uses any influence maximization algo. as attacker oracle ◦ defender uses any influence blocking maximization algo. as defender oracle ◦ iteration: use oracles to enlarge strategy space, use Maximin to compute mixed equilibrium on the current strategy space 55 [Tsai, Nguyen and Tambe, AAAI 2012]
  • 56. Endogenous Competition: Effect of Negative Opinions 56
  • 57. 57
  • 58. Endogenous competition • Negative opinion generated from product defects • Negative opinion propagates, competing with positive opinion • Positive opinions may turn negative, but negative opinions will not turn back --- negativity bias 58
  • 59. Influence maximization with negative opinions • IC-N: extend the IC model with quality factor 𝑞 • each positive activation has probability of 1 − 𝑞 to turn negative • negative opinion propagates as positive opinion, but negative activations do not turn positive • Maximize the positive influence • Submodularity still holds • MIA-N: fast heuristics using dynamic programming for efficient tree based influence spread computation 59 [Chen et al. SDM 2011]
  • 60. Performance of MIA-N heuristic • 15K node NetHEPT, • MIA-N achieves 2 orders of collaboration network in arxiv manitude speedup • influence spread of MIA-N matches Greedy algorithm 60 [Chen et al. SDM 2011]
  • 61. Key takeaways for handling competitions  Standard models (IC/LT) may be generalized for exogenous/endogenous competition ◦ be careful, may violate submodularity  Activation timing becomes important, due to competitions between positive and negative diffusions ◦ Greedy algorithm becomes slower ◦ Heuristics need dynamic programming 61
  • 62. Other topics  Participation maximization ◦ from platform provider’s point of view ◦ many cascades, maximize overall spread ◦ each user can be seeds for a small number of cascades ◦ see [Ienco, Bonchi and Castillo, ICDM Workshops 2010; Sun et al. ICWSM 2011]  Budget and time ◦ Time-critical IM [Chen, Lu, Zhang, AAAI 2012] ◦ minimize seed size, or diffusion time [Goyal, et al. SNAM 2012] 62
  • 64. Seed allocation and participation maximization  Multiple independent cascades from seed sets  Each user can only act as seed for a fixed number of cascades  Problem: find allocation of seeds to users, to maximize the total size of all cascades ◦ online version: allocation has to be done when user logs in  Applications: ◦ Meme ranking ◦ Topic recommendation in online discussion forums ◦ Online advertising 64
  • 65. Application: Meme Ranking  Users see a selection of 𝑘 postings by people they follow ◦ Which postings?  Heuristic: observe what each user and a small sample of her followers have Goal: re-posted maximize total re-posting activity by all users 65 [Ienco, Bonchi and Castillo, ICDM Workshops 2010]
  • 66. Application: topic thread rec.  recommend a small set of topic (or thread) to users on their sidebars  maximize total participations of all discussion threads ◦ diff. from recommender systems: not only increase participation of recommended users, but increase participation of others via social influence  Theory: social welfare maximization with submodular functions  RPA (randomized proportional allocation): greedy-based, very slow  TABI: heuristic considering both self and other participation via influence 66 [Sun et al. ICWSM 2011]
  • 67. Paying Attention to Budget and Time 67
  • 68. Time critical influence maximization • achieve influence maximization within a short deadline • need to model delay in influence diffusion • add meeting probabilities of pair of nodes; influence occur only after individuals meet • extend IC and LT models, still satisfy submodularity • fast heuristics (for the IC model extension) • MIA-M: need dynamic programming • MIA-C: conversion to standard IC model and MIA algorithm 68 [Chen, Lu and Zhang, AAAI 2012]
  • 69. Minimizing Expenses  MINTSS: Given a target spread you want to reach, how to pick the fewest seeds that realize the outcome? • Problem. Given 𝐺 = (𝑉, 𝐸), a threshold 𝜂 on expected spread, pick the smallest set of seeds 𝑆: 𝜎 𝑆 ≥ 𝜂. • For hardness, approximability results and algorithms, see paper! 69 [Goyal, Bonchi, L., & Venkatasubramanian SNAM 2012]
  • 70. Minimizing Propagation Time  MINTIME: Given a seed budget and a target spread, pick seeds under budget so the target is realized as quickly as possible. • Problem. Given 𝐺 = (𝑉, 𝐸), a seed budget 𝑘 and a threshold 𝜂 on expected spread, choose 𝑘 seeds S: 𝜎 𝑆 ≥ 𝜂 and the time horizon in which this happens is min. • For hardness, approximability results and algorithms, see paper! 70 [Goyal, Bonchi, L., & Venkatasubramanian SNAM 2012]
  • 71. Part IV Key Takeaways  Tests exist for homophily/influence  Influence weights can be learned from data!  Bypassing model and direct seed selection is possible  Better models for Adoption/Revenue vs Influence  Exogenous and endogenous competition can be modeled with care  Participation maximization considers maximizing multiple influence spreads across an entire platform  Time and budget can be considered in the objective function 71