Stochastic Models of UserContributory Web Sites

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Stochastic Models of User-Contributory Web Sites

• Tad Hogg
• HP Labs
• Kristina Lerman
• USC Information Sciences Institute

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The Social Web
Bugzilla
essembly
delicious
wisdom of crowds
3
Activities

• View existing content
• Rate existing content
• simple vote
• complex write a review
• Add new content
• Link to other users

focus of this presentation
4
Aggregate group behavior

• Determines structure and usefulness of
  user-participatory sites
• Models enable
• Predicting trends or behaviors
• E.g., which newly contributed content will become
  popular
• Designing web sites
• E.g., productive information displays
• Altering user incentives
• E.g., improve content quality or participation

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Stochastic Modeling summary

• Start with individual user behavior
• Specify states and transitions between states
• Determine collective behavior
• Aggregate behavior of interest
• Individual user behaviors create transitions
  among aggregate states
• Rate equations give dynamics
• How average collective behavior changes in time
• How collective behavior depends on user
  characteristics

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Illustration Stochastic Model of Digg

• Phenomenology of Digg
• Users submit and vote on news stories
• Digg promotes popular stories to front page
• Digg allows social networking
• Users can designate Friends
• and view their friends activity on Digg
• Directed social network
• Friends of user A are everyone A is watching
• Fans of A are all users who are watching A

Alices friend
Alice
Bob
Bobs fan
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Lifecycle of a story

• User submits a story to the Upcoming Stories
  queue
• Others vote on (digg) the story
• If story accumulates enough votes in short time,
  it is promoted to the Front page
• The Friends Interface lets users see
• Stories friends submitted
• Stories friends voted on,

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Model of Digg voting behavior

• Stochastic model based on Digg user interface
• visibility and interestingness ? votes
• Extension to prior model Lerman 2007
• law of surfing for viewing web pages Huberman
  et al, 1998
• instead of geometric distribution
• incremental average growth in number of voters
  fans
• i.e., people who can see story via friends
  interface
• Related work aggregate phenomenological models
• behavior for Digg, Wikipedia, YouTube, .
• e.g., Wu Huberman 2007 Crane Sornette 2008
  Wilkinson 2008

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Voting on stories

• combination of
• visibility does user see the story?
• user interface
• browse
• recommended by friends
• search
• interest does user like the story?
• novelty,

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Story location

• Digg shows stories as lists
• most recent first
• 15 stories per page
• user must click to view subsequent pages
• visibility decreases with distance from top of
  list
• A given story
• moves down the list as new stories added
• eventually moves to later pages
• switches from upcoming to top of front page if
  promoted

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User behavioral model
upcomingq
upcoming1

r
c
n
r
front1
Ø
frontp

vote
r
wS
friends
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Dynamical model of aggregate behavior

• How number of votes Nvote(t) for a story changes
• nf - rate users find story on the front page
  queue
• nu - rate users find story on the upcoming
  stories queue
• nfriends - rate users find story through the
  friends interface
• r fraction of users who see the story choose to
  vote for it

visibility
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Estimating model parameters

• Need model parameters for
• Story visibility
• Story interestingness
• Estimate from behavior of sample of users

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Digg data set

• Stories from front and upcoming pages
• number of votes vs. time since submission
• for several days in May 2006
• prior to availability of Digg API
• sampled more extensively from front than upcoming
  pages
• Number of fans for active users
• 2152 stories with at least 4 observations
• submitted by 1212 distinct users
• 510 of these stories promoted to front page

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Story visibility

• User viewing behavior not available
• which stories users look at
• how they find stories
• front page, friends interface,
• Estimate indirectly from models data

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Modeling story visibility

• Story location
• Navigating web sites
• Number of fans

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Story location vs. time in each list

• For upcoming and front page lists
• location on page (1 to 15), which page (1st, 2nd,
  )
• distance from top of list increases linearly with
  time

• Rate story position increases
• front page 0.2 pages/hr
• upcoming 4 pages/hr
• 1/15th the rates new stories are
• promoted to front page (3/hr)
• submitted as new stories (60/hr)
• since each page holds 15 stories
• Averages over hourly variation
• Szabo Huberman 2008

examples
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Story location promotion to front page

• Digg promotion decision algorithm not public
• based on popularity expressed by user votes
• Approximation from data
• story promoted if
• at least 40 votes within 24 hours of submission

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Modeling story visibility

• Story location
• Navigating web sites
• Number of fans

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Navigating through a web site

• Empirical model of user following links on a Web
  site
• law of surfing Huberman et al. 1998
• Inverse Gaussian distribution of pages viewed
  before leaving web site

few users go beyond 1st page
parameters estimated from Digg data model
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Modeling story visibility

• Story location
• Navigating web sites
• Number of fans visibility via friends interface

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Story visibility via friends interface

• Each voter enables their fans to see story
• via friends interface
• Model of number of fans not yet viewing story,
  s(t)
• based on number of votes on the story
• story visible to submitters fans at submission
  time s(0)

fans of prior voters visit Digg
new fans from new votes
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Story interestingness

• Reasons users vote for story not available, e.g.,
• topic
• novelty Wu Huberman 2007
• popularity (determining interest, not just
  visibility)
• e.g., cool fashion or gadgets
• One approach web-based experiments
• e.g., Salganik et al. 2006
• Estimate from models data
• from vote history after accounting for visibility

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Model results
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Solutions votes vs. time
model vs. observations for 6 stories

• model captures qualitative features
• slow growth initially
• influence of fans on promotion
• rapid growth if story promoted (much more
  visible to users)

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Model requirements for promotion

• Values of S and r to get the story on front page

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Promotion to front page model prediction vs.
data 95 accurate
promotion threshold from model
logarithmic scale
most stories not promoted, and from people with
no fans
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Additional model insights

• Heterogeneity
• users activity
• content quality (interestingness)
• Predictability from early reactions to new story

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Story interestingness

• Long-tail distribution (lognormal)
• a few stories much more interesting than average
• after accounting for visibility via user
  interface part of model
• Open question why?
• A multiplicative process underlying user
  interests?

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Predictions from early behavior

• Estimate story interestingness
• from full history, or
• using initial votes
• Behavior predictable from early reaction to story
• also with YouTube
• e.g., Crane Sornette 2008 Lerman Galstyan
  2008 Szabo Huberman 2008

example use first 4 observations r estimates
correlate 0.9 with those based on full
history prediction of final votes account for
75 of variance rms prediction error 244 votes
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Model based on votes only?

• Estimate based on initial votes only
• not including visibility model
• i.e., ignore effects of law of surfing and
  social network

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Model based on votes only?
full model is better than not including
visibility (differences significant, p-value
lt10-4)
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Future work on models of activities new content
links

• View existing content
• Rate existing content
• Add new content
• What motivates high-quality contribution?
• Link to other users
• How do users chose who to link to?
• What does link signify?
• common interests?
• trust in recommendations?

focus of this presentation
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Conclusion

• Stochastic process approach
• connect user and system behaviors
• Applicability
• users have limited information and actions
• limited use of personalized history
• e.g., user communities on the web
• not face-to-face small group interactions
• Example news aggregator Digg
• votes from visibility interestingness
• user model from info and actions provided by Digg
  UI