HypTrails: A Bayesian Approach for Comparing Hypotheses about Human Trails on the Web

Talk about HypTrails at WWW 2016

Transcript

1. GESIS  -­‐  Leibniz  Ins.tute  for  the  Social  Sciences  
   HypTrails:  A  Bayesian  Approach  for  Comparing  
   Hypotheses  about  Human  Trails  on  the  Web  
   Philipp  Singer,  Denis  Helic,  Andreas  Hotho  
   and  Markus  Strohmaier  
   www.philippsinger.info/hyptrails  
    
   

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2. Vannevar  Bush  
   2  
   15.05.15   HypTrails  -­‐  Philipp  Singer  
   image courtesy of brucesterling on Flickr
   Bush, V. (1945). As we may think. The Atlantic
   Monthly, 176(1):101– 108. Bush, V. (1945).
   As we may think. The Atlantic Monthly, 176(1):
   101– 108.
   “[The  human  brain]  operates  by  associa5on.    
   With  one  item  in  its  grasp,  it  snaps  instantly  to  the  
    next  that  is  suggested  by  the  associa5on  of  thoughts.”  
   

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3. Human  trails  on  the  Web  
   15.05.15   HypTrails  -­‐  Philipp  Singer   3  
   image courtesy of user Mmxx on Wikipedia
   

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4. Human  trails  on  the  Web  
   18.05.15   HypTrails  -­‐  Philipp  Singer   4  
   image courtesy of user Mmxx on Wikipedia
   ?  
   ?  
   ?  
   ?  
   ?  
   What  are  the  mechanisms  
   producing  human  trails  on  
   the  Web?  
   

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5. Example:  Human  navigaRonal  trails  
   •  Humans  prefer  to  navigate  …  
   –  H1:  over  semanRcally  similar  websites    
   –  H2:  via  self-­‐loops  (e.g.,  refreshing)    
   –  H3:  by  using  the  structural  link  network  
   –  H4:  by  preferring  similar  categories  
   –  H5:  by  uRlizing  structural  properRes  
   –  H6:  by  informaRon  scent  
    
   [West  et  al.  IJCAI  2009],  [Singer  et  al.  IJSWIS  2013],  [West  &  Leskovec  WWW  2012],  [Chi  et  al.  CHI  
   2001]  
   18.05.15   HypTrails  -­‐  Philipp  Singer   5  
   

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6. Example:  Human  navigaRonal  trails  
   •  Humans  prefer  to  navigate  …  
   –  H1:  over  semanRcally  similar  websites    
   –  H2:  via  self-­‐loops  (e.g.,  refreshing)    
   –  H3:  by  using  the  structural  link  network  
   –  H4:  by  preferring  similar  categories  
   –  H5:  by  uRlizing  structural  properRes  
   –  H6:  by  informaRon  scent  
    
   [West  et  al.  IJCAI  2009],  [Singer  et  al.  IJSWIS  2013],  [West  &  Leskovec  WWW  2012],  [Chi  et  al.  CHI  
   2001]  
   18.05.15   HypTrails  -­‐  Philipp  Singer   6  
   What  is  the  relaRve  
   plausibility  of  these  
   hypotheses  given  data?  
   

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7. HypTrails  in  a  nutshell  
   •  Goal:  Express  and  compare  hypotheses  about  human  trails  
   in  a  coherent  research  approach  
    
   •  Method:    
   –  First-­‐order  Markov  chain  model  
   –  Bayesian  inference  
    
   •  Idea:    
   –  Incorporate  hypotheses  as  priors  
   –  URlize  sensiRvity  of  marginal  likelihood  on  the  prior  
   •  Outcome:  ParRal  ordering  of  hypotheses  
   15.05.15   HypTrails  -­‐  Philipp  Singer   7  
   

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8. Markov  chain  model  
   •  StochasRc  model  
   •  TransiRon  probabiliRes  between  states  
   15.05.15   HypTrails  -­‐  Philipp  Singer   8  
   0
   B
   B
   B
   @
   p1,1 p1,2 . . . p1,j
   p2,1 p2,2 . . . p2,j
   .
   .
   .
   .
   .
   .
   ...
   .
   .
   .
   pi,1 pi,2 . . . pi,j
   1
   C
   C
   C
   A
   S1  
   S2   S3  
   1/2   1/2  
   1/3  
   2/3  
   1  
   

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9. Structure  of  HypTrails  
   16.05.15   HypTrails  -­‐  Philipp  Singer   9  
   MC  Model  
   

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10. How  to  express  hypotheses?  
    15.05.15   HypTrails  -­‐  Philipp  Singer   10  
    

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11. Structural  hypothesis  
    15.05.15   HypTrails  -­‐  Philipp  Singer   11  
    1/3  
    1  
    1/3  
    1  
    1/3  
    

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12. Uniform  hypothesis  
    15.05.15   HypTrails  -­‐  Philipp  Singer   12  
    1/3  
    

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13. Empirical  observaRons  
    15.05.15   HypTrails  -­‐  Philipp  Singer   13  
    1.0  
    2/3  
    1/3  
    1  
    

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14. Structure  of  HypTrails  
    16.05.15   HypTrails  -­‐  Philipp  Singer   14  
    MC  Model  
    Hypothesis  
    (H1)  
    Belief  in  parameters  
    

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15. Which  hypothesis  is    
    the  most  plausible  one?  
    15.05.15   HypTrails  -­‐  Philipp  Singer   15  
    

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16. Bayesian  model  comparison:  
    Marginal  likelihood  
    15.05.15   HypTrails  -­‐  Philipp  Singer   16  
    Probability  of  data  given  hypothesis  
    =  Model  evidence  
    

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17. Bayesian  model  comparison:  
    Marginal  likelihood  
    15.05.15   HypTrails  -­‐  Philipp  Singer   17  
    Probability  of  data  given  hypothesis  
    Model  evidence  
    Parameters  are  marginalized  out    
    Probability  of  observing  data  
    given  parameters  and  hypothesis  
    

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18. Bayesian  model  comparison:  
    Marginal  likelihood  
    15.05.15   HypTrails  -­‐  Philipp  Singer   18  
    Probability  of  data  given  hypothesis  
    Model  evidence  
    Parameters  are  marginalized  out    
    Probability  of  observing  data  
    given  parameters  and  hypothesis   Probability  of  parameters  
    before  observing  data  
    

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19. Bayesian  model  comparison:  
    Marginal  likelihood  
    15.05.15   HypTrails  -­‐  Philipp  Singer   19  
    Probability  of  data  given  hypothesis  
    Model  evidence  
    Parameters  are  marginalized  out    
    Probability  of  observing  data  
    given  parameters  and  hypothesis   Probability  of  parameters  
    before  observing  data  
    Hypothesis  
    

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20. Structure  of  HypTrails  
    16.05.15   HypTrails  -­‐  Philipp  Singer   20  
    MC  Model  
    Hypothesis  
    (H1)  
    Belief  in  parameters  
    Prior  (H1)  
    ElicitaRon  
    Data  (Trails)  
    Marginal  
    likelihood  (H1)  
    Influence  
    Influence  
    

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21. How  to  elicit  priors  from  hypotheses?  
    15.05.15   HypTrails  -­‐  Philipp  Singer   21  
    

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22. EliciRng  priors  
    •  (Trial)  roulefe  method  
     
    20.05.15   HypTrails  -­‐  Philipp  Singer   22  
    

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23. •  (Trial)  roulefe  method  
     
    EliciRng  priors  
    20.05.15   HypTrails  -­‐  Philipp  Singer   23  
    

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24. •  (Trial)  roulefe  method  
     
    Prior  distribuRon  
    EliciRng  priors  
    20.05.15   HypTrails  -­‐  Philipp  Singer   24  
    

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25. Conjugate  Dirichlet  prior  
     
    •  Hyperparameters  à  pseudo  counts  
    15.05.15   HypTrails  -­‐  Philipp  Singer   25  
    0
    B
    B
    B
    @
    p1,1 p1,2 . . . p1,j
    p2,1 p2,2 . . . p2,j
    .
    .
    .
    .
    .
    .
    ...
    .
    .
    .
    pi,1 pi,2 . . . pi,j
    1
    C
    C
    C
    A
    MC  parameters  
    0
    B
    B
    B
    @
    ↵1,1 ↵1,2 . . . ↵1,j
    ↵2,1 ↵2,2 . . . ↵2,j
    .
    .
    .
    .
    .
    .
    ...
    .
    .
    .
    ↵i,1 ↵i,2 . . . ↵i,j
    1
    C
    C
    C
    A
    Dirichlet  hyperparameters  
    

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26. EliciRng  priors  from  hypotheses    
    about  human  trails  
    •  AdapRon  of  (trial)  roulefe  method  
    15.05.15   HypTrails  -­‐  Philipp  Singer   26  
    #Chips  =  k  
    Strength  of  hypothesis    
    k  =  18  
    

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27. EliciRng  priors  from  hypotheses    
    about  human  trails  
    •  AdapRon  of  (trial)  roulefe  method  
    16.05.15   HypTrails  -­‐  Philipp  Singer   27  
    #Chips  =  k  
    Strength  of  hypothesis    
    k  =  18  
    à  Dirichlet  hyperparameters  
    

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28. Example:  Structural  hypothesis    
    15.05.15   HypTrails  -­‐  Philipp  Singer   28  
    1/3  
    1  
    1/3  
    1  
    1/3  
    

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29. Example:  Structural  hypothesis    
    19.05.15   HypTrails  -­‐  Philipp  Singer   29  
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.33 0.00 h3
    1.00 0.33 1.00 h1
    0.00 0.33 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    3.01 0.99 3.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    0.01 0.99 0.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    Input  
    Hypothesis  
    Output  
    Dirichlet  prior  
    

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30. Example:  Structural  hypothesis    
    15.05.15   HypTrails  -­‐  Philipp  Singer   30  
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.33 0.00 h3
    1.00 0.33 1.00 h1
    0.00 0.33 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    3.01 0.99 3.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    0.01 0.99 0.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    

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31. Example:  Structural  hypothesis    
    19.05.15   HypTrails  -­‐  Philipp  Singer   31  
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.33 0.00 h3
    1.00 0.33 1.00 h1
    0.00 0.33 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    3.01 0.99 3.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    0.01 0.99 0.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    

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32. Example:  Structural  hypothesis    
    19.05.15   HypTrails  -­‐  Philipp  Singer   32  
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.33 0.00 h3
    1.00 0.33 1.00 h1
    0.00 0.33 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    3.01 0.99 3.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    α
    i
    1
    2
    3 α i
    1
    2
    3
    nr. of chips
    1
    2
    3
    0.00 0.99 0.00 h3
    0.01 0.99 0.01 h1
    0.00 0.99 0.00 h1
    h3
    h1
    h1
    

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33. Structure  of  HypTrails  
    16.05.15   HypTrails  -­‐  Philipp  Singer   33  
    MC  Model  
    Hypothesis  
    (H1)  
    Prior  (H1)  
    Data  (Trails)  
    Marginal  
    likelihood  (H1)  
    Hypothesis  
    (H2)  
    Prior  (H2)  
    Marginal  
    likelihood  (H2)  
    Compare  
    

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34. DemonstraRon  of  general  applicability  
    •  SyntheRc  data  
     
    •  Human  song  trails  (Last.fm)  
    •  Human  review  trails  (Yelp)  
    •  Human  naviga.on  trails  (Wikigame)  
    15.05.15   HypTrails  -­‐  Philipp  Singer   34  
    

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35. Wikigame  
    15.05.15   HypTrails  -­‐  Philipp  Singer   35  
    0 1 2 3 4
    hypothesis weighting factor k
    −1.40
    −1.35
    −1.30
    −1.25
    −1.20
    −1.15
    −1.10
    −1.05
    −1.00
    −0.95
    evidence
    1e8
    uniform
    self-loop
    structural
    similarity
    Higher  
    plausibility  
    Higher  belief  
    (more  chips)  
    

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36. Wikigame  
    15.05.15   HypTrails  -­‐  Philipp  Singer   36  
    0 1 2 3 4
    hypothesis weighting factor k
    −1.40
    −1.35
    −1.30
    −1.25
    −1.20
    −1.15
    −1.10
    −1.05
    −1.00
    −0.95
    evidence
    1e8
    uniform
    self-loop
    structural
    similarity
    

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37. Summary  
    •  Studying  mechanisms  producing  human  trails  
    •  HypTrails:  A  coherent  approach  for  expressing  and    
    comparing  hypotheses  about  human  trails  
    •  Can  be  applied  to  all  kinds  of  human  trails  
    •  ImplementaRons:  www.philippsinger.info/hyptrails  
    19.05.15   HypTrails  -­‐  Philipp  Singer   37  
    

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38. GESIS  -­‐  Leibniz  Ins.tute  for  the  Social  Sciences  
    for  your  afenRon!  
     
    @ph_singer  
    www.philippsinger.info  
    T  
    H  
    A  
    N  
    K  
    S  
    www.philippsinger.info/hyptrails  
     
    

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39. References  1/2  
    •  [West  et  al.  WWW  2015]    
    –  Robert  West,  Ashwin  Paranjape,  and  Jure  Leskovec:  Mining  Missing  Hyperlinks  from  Human  
    NavigaRon  Traces:  A  Case  Study  of  Wikipedia.  24th  InternaRonal  World  Wide  Web  Conference  
    (WWW'15),  Florence,  Italy,  2015.  
    •  [De  Choudhury  et  al.  HT  2010]  
    –  De  Choudhury,  Munmun  and  Feldman,  Moran  and  Amer-­‐Yahia,  Sihem  and  Golbandi,  Nadav  and  
    Lempel,  Ronny  and  Yu,  Cong:  AutomaRc  construcRon  of  travel  iRneraries  using  social  breadcrumbs.  
    21st  ACM  conference  on  Hypertext  and  hypermedia,  2010.  
    •  [Bestavros  CIKM  1995]  
    –  Bestavros,  Azer:  Using  speculaRon  to  reduce  server  load  and  service  Rme  on  the  WWW.”  4th  InternaRonal  
    conference  on  InformaRon  and  knowledge  management.  1995.  
    •  [Perkowitz  IJCAI  1997]  
    –  Perkowitz,  Mike,  and  Oren  Etzioni:  AdapRve  web  sites:  an  AI  challenge.  15th  internaRonal  
    joint  conference  on  ArRfical  intelligence.  1997.  
    •  [West  et  al.  IJCAI  2009]    
    –  West,  Robert,  Joelle  Pineau,  and  Doina  Precup.  "Wikispeedia:  An  Online  Game  for  Inferring  SemanRc  
    Distances  between  Concepts."  IJCAI.  2009.  
    15.05.15   HypTrails  -­‐  Philipp  Singer   39  
    

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40. References  2/2  
    •  [Singer  et  al.  IJSWIS  2013]  
    –  Philipp  Singer,  Thomas  Niebler,  Markus  Strohmaier  and  Andreas  Hotho,  CompuRng  SemanRc  
    Relatedness  from  Human  NavigaRonal  Paths:  A  Case  Study  on  Wikipedia,  InternaRonal  Journal  on  
    SemanRc  Web  and  InformaRon  Systems  (IJSWIS),  vol  9(4),  41-­‐70,  2013  
    •  [West  &  Leskovec  WWW  2012]  
    –  Robert  West  and  Jure  Leskovec:  Human  Wayfinding  in  InformaRon  Networks  21st  InternaRonal  
    World  Wide  Web  Conference  (WWW'12),  pp.  619–628,  Lyon,  France,  2012.  
    •  [Chi  et  al.  CHI  2001]  
    –  Chi,  Ed  H.,  et  al.  "Using  informaRon  scent  to  model  user  informaRon  needs  and  acRons  and  the  
    Web."  Proceedings  of  the  SIGCHI  conference  on  Human  factors  in  compuRng  systems.  ACM,  2001.  
    15.05.15   HypTrails  -­‐  Philipp  Singer   40  
    

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41. Dirichlet  distribuRon:  Simplex  
    20.05.15   HypTrails  -­‐  Philipp  Singer   41  
    

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