Inferring Privacy Information from Social Networks

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Inferring Privacy Information from Social
Networks

• Presenter Ieng-Fat Lam
• Date 2007 / 12 / 25

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Paper to be presented

• Jianming He1, Wesley W. Chu1, and Zhenyu (Victor)
  Liu2, Inferring Privacy Information from Social
  Networks. Lecture Notes in Computer Science,
  page 154-165, Springer-Verlag Berlin Heidelberg,
  2006.
• 1 Computer Science Department UCLA, Los Angeles,
  CA 90095, USA
• 2 Google Inc. USA

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Motivation

• Online social network services
• Become popular
• Privacy confidentiality (??) problem
• Increasingly challenging
• Urgent research issues
• In building next-generation information systems
• Existing techniques and policies such as
• Cryptography and security protocols
• Government policies
• Aim to block direct disclosure of sensitive
  personal information

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Block Direct Disclosure
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Motivation (cont.)

• How about indirect disclosure?
• Can be achieved by pieces of seemingly
• Innocuous (???) information
• Unrelated information
• In Social network
• Same Dance Club
• Same Interest
• Same office
• Similar Professions
• Privacy can be indirectly disclosed
• By their social relations

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Indirect Disclosure
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Problem

• Study the privacy disclosure in social networks
• Indirect disclosure ?
• To what extent (??) ?
• Under what conditions ?

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The Research

• Perform privacy inference
• Map Bayesian networks to social networks
• Model the causal relations (????) among people
• Discuss factors might affect the inference
• Prior probability (????)
• Influence strength
• Society openness
• Conduct extensive (???) experiment
• On a real online social network structure

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Probability Rules for consistent reasoning

• Coxs Two axioms
• First
• If we specify how much we belief something is
  true
• We must have specified (implicitly) how much we
  belief is false.
• Sum rule P(XI) P(XI) 1
• Second
• If we first specify how much we believe Y is true
• State how much we believe X is true given that Y
  is true
• We must have specified how much we believe both X
  and Y are true
• Product ruleP(X,YI) P(XY, I) P(YI)

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Probability Rules for consistent reasoning
(cont.)

• The given condition I
• Denote relevant background information
• There is no such thing in absolute probability
• Although I is often omitted
• We must never forget its existence

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Bayes theorem

• From Product Rule
• P(X,YI) P(XY, I) P(YI)

P(X,YI) P(Y, XI) P(Y X, I) P(XI)
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Bayes theorem (cont.)

• Replace X and Y by hypothesis (??) and data
• P (hypothesis I) Prior probability (????)
• Our state of knowledge about the truth of the
  hypothesis before we have analysis the current
  data
• P (data hypothesis, I) Conditional
  Probability
• Of seeing the data given that the hypothesis is
  true
• P (hypothesis data, I) Posterior probability
  (????)
• Our state of knowledge about the truth of the
  hypothesis in the light of the data

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Bayes theorem (cont.)

• P ( data I ) Marginal Probability (????) of
  data
• Probability of witnessing data
• Under all mutually exclusive hypothesis
• Can be calculate as P ( data I )
• P (data hypothesis, I ) / P ( data I )
• Represent the impact that the data has on belief
  in hypothesis.
• Bayes theorem measure how much data should alter
  a belief in a hypothesis
• Use toss result to infer if a coin a fair

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Bayesian Networks

• A Bayesian network is
• Graph presentation of
• Joint probability distribution (physical or
  Bayesian)
• Over a set of variables
• Include the consideration of network structure
• It is consisted by
• A network structure
• Conditional probability tables (CPT)

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Bayesian Networks (cont.)

• Network structure
• Presented as Directed Acyclic Graph
  (DAG)(directed graph without cycle)
• Each node corresponds to a random variable
• Associated with a CPT
• Each edge indicate dependent relationship
• Between connected variables
• Capture causal relationship
• Conditional probability tables (CPT)
• Enumerates the conditional probability of node
• Quantify causal relationships

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Bayesian Networks (cont.)

• Detecting credit-card fraud (example only)
• We want to solve

Node
Relation (cause to effect)
CPT
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Bayesian Inference

• Problem Statement (indirect inference)
• It is possible to predict someones attributes
• By looking their friends type
• In the real world
• People are acquainted via all types of relations
• A personal attribute may only be sensitive to
  certain types of relations
• To infer peoples privacy from social relations
• Must filter out other types of relations
• Investigate in homogeneous societies (????)

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Bayesian Inference (cont.)

• Homogeneous societies
• Reflect small closely related groups
• Office, class or clubs
• Individuals are connected by a single type of
  social relations
• In this case, Friendship
• Impact of every person on friends is the same

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Bayesian Inference (cont.)

• To perform the inference
• Model the causal relation among people
• Infer attribute A for a person X
• 1. Construct Bayesian network from Xs social
  network
• 2. Analyze the Bayesian network
• For the Probability of X has attribute A
• Inference performed
• Single hop Inference
• Only involved direct friends
• Multiple Hops Inference
• Consider friends from multiple hops

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Single hop Inference (method)

• The Case
• We know all direct friends attribute of node X
• Define Yij as jth friend of X at i hops away.
• If a friend can be reached via more than one
  route
• Use shortest path, smaller i
• Let Yi be the set of Yij (1 j ni)
• Where ni is the number of Xs friends at I hops
  away
• For instance, Y1 Y11, Y12, ..., Y1n1
• Direct friends which are one hop away

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Single hop Inference (cont.)

• An example
• Y11, Y12 and Y13 are direct friends of X.
• The attribute values of Y11, Y12 and Y13 are
  known (shaded nodes).

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Single hop Inference (cont.)

• Bayesian Network Construction
• Two assumptions
• Localization Assumption
• Consider only direct friends is sufficient
• Naive Bayesian Assumption
• Remove relationship between friends

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Single hop Inference (cont.)

• Localization Assumption
• Given the attribute values of Xs direct friends
  Y1
• Friends at more than one hop away (i.e., Yi for i
  gt 1)
• Are conditionally independent of X.
• Inference only involved direct friends
• Removed Y21 and Y31
• Decide DAG linking
• No cycle -gt Obtain Bayesian Network Immediately
• Otherwise -gt Remove cycles
• Deletion of edges with the weakest relations
  (approximation conversion)

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Single hop Inference (cont.)

• Reduction via Localization Assumption

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Single hop Inference (cont.)

• Naive Bayesian Assumption (For DAG)
• Given the attribute value of the query node X
• Attribute values of direct friends Y1
• Are conditionally independent of each other.
• Final DAG is obtained
• Removing connection between Y11 and Y12

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Single hop Inference (cont.)

• Reduction via Naive Bayesian Assumption

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Single hop Inference (cont.)

• Bayesian Inference
• Use the Bayes Decision Rule
• To predict the attribute of X
• For a general Bayesian network with maximum depth
  i
• For X, be the attribute value with the
  maximum conditional probability (posterior
  probability)
• Given the observed attribute values of other
  nodes in the network

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Single hop Inference (cont.)

• Bayesian Inference (cont.)
• Use only direct friends (Y1) (localization)
• P( X x Y1)
• Y1 are independent of each other (naïve bayes)
• P(Y11, Y12 X x) P(Y11 X x) P(Y12 X
  x)
• x and y1j are attribute of X and Y1j , (1 j
  n1 , x,yij ? t, f )

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Single hop Inference (cont.)

• Bayesian Inference (cont.)
• Assumed homogeneous network
• CPT for each node is the same
• P(Y1j y1j X x) represent P(Y y X x)
• Posterior probability
• Depends on N1t, number of friends with attribute
  t
• P(X x N1t n1t) represent P(X x Y1)
• If N1t n1t, we obtain

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Single hop Inference (cont.)

• Bayesian Inference (cont.)
• To compute (3) we need conditional probability
• P(Y y X x)
• We apply the parameter estimation
• Substituting (4) and (3) into (1) yields x.

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Multiple hop Inference

• In the real world
• People may hide their information
• Localization Assumption is not applicable
• Proposed generalized localization assumption
• Generalized Localization Assumption
• Given the attribute of jth friend of X as i hops,
  Yij
• Attribute of X is conditionally independent of
• Descendants (??) of Yij

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Multiple hop Inference (cont.)

• Generalized Localization Assumption (cont.)
• If the attribute of Xs direct friend Y1j is
  unknown
• The attribute of X is conditionally dependent on
• Attribute for direct friends of Y1j
• Continue until we reach a Y1js descendent with
  known attribute.

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Multiple hop Inference (cont.)

• Generalized Localization Assumption (cont.)
• Interpretation of this model
• When we predict attribute of X
• We treat him / her as egocentric person
• Influences his / her friends but not vice versa
• Attribute value of X can reflected by friends
• We still apply the Bayes Decision Rule
• Calculation of posterior probability is more
  complicated
• Use variable elimination
• Adopt same techniques to derive the x in (1)

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Experimental Study

• The performance metric we consider
• Inference accuracy
• Percentage of nodes predicted correctly by
  inference
• Three Characters of social network
• Prior Probability
• Influence Strength
• Society Openness
• Might affect Bayesian influence

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Experimental Study (cont.)

• Prior Probability
• P(X t)
• The probability of people in social network have
  attribute A.
• Naïve inference
• if P(X t) 0.5, we predict every query node
  has value t
• Otherwise has value f
• Average naive inference accuracy
• max (P(X t), 1 - P(X t)).
• We use as reference to compare Bayesian Inference

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Experimental Study (cont.)

• Influence Strength
• P(Y t X t)
• Conditional Probability
• Y has attribute A Given that direct friend X has
  same attribute
• Measures how X influence its friend Y
• Higher influence strength, higher probability
  that X and Y have attribute A
• Society Openness
• O(A)
• Percentage of people in society who release
  attribute A

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Experimental Study (cont.)

• Data Set
• 66,766 profiles from Livejournal (2.6 million
  active members)
• 4, 031, 348 Friend relations
• Attribute assignment
• For each member, as assign a CPT
• Determine the actual attribute value
• Based on parents values and assigned CPT
• Start from set of nodes whose in-degree is 0
• Explore rest of network though friendship links
• All members assigned with same CPT
• Use different CPT to evaluate inference
  performance.

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Experimental Study (cont.)

• After attribute assignment
• We obtain a social network
• To infer each individual
• Built a corresponding Bayesian network
• Conduct Bayesain Inference

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Experimental Result

• Comparison of Bayesian and Naive Inference
• Prior probability 0.3
• Influence strength 0.1 to 0.9

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Experimental Study (cont.)

• Effect of Influence Strength and Prior
  Probability
• Prior probability 0.05, 0.1, 0,3 and 0.5
• Influence strength 0.1 to 0.9
• Lowest accuracy occurs when
• Influence strength prior probability
• Knowing friend relations provide no more
  information than knowing the prior probability
• People are actually interdependent
• Better Bayesian Inference
• High difference between influence strength and
  prior probability
• Stronger influence of parent on children ( no
  matter positive or negative)

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Experimental Result
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Experimental Study (cont.)

• Society Openness
• Assume the society openness is 100
• All friends attribute value are known
• Study inference at different levels of openness
• Randomly hide the attribute of a certain
  percentage of members (from 10 to 90)
• Setting
• Prior probability P(X t) 0.3
• Society Openness O(A) 10, 50 and 90

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Experimental Result
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Experimental Result

• Inference Accuracy
• Decrease when more attributes are hidden
• But is relatively small
• Generally should drop drastically
• Discuss on Society Openness

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Discussions on Society Openness

• Single Hop Inference
• The Bayesian network is two-level tree
• Derive the variation of posterior probability
• Due to change of openness
• N1t and N1t is number of friends have attribute
  t
• Before and after hiding h friends
• Hiding is the same as remove in inference
• ?P(X t N1t n1t,N1t n1t)
• Result
• 70 to 90 of the cases, the variation is less
  then 0.1
• Unlikely to be varied greatly due to hiding nodes
  randomly

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Discussions on Society Openness (cont.)
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Discussions on Society Openness (cont.)

• Multiple Hop Inference
• Use complete k-ary trees
• All internal nodes have k children
• Hide a node with all of its ancestors (??)
• Check the variation of posterior probability
• Number of children k
• Maximum depth of hidden nodes d
• Prior probability 0.3
• Influence strength 0.7
• Result
• When k 1, posterior probability varies
  significant by more hidden nodes
• When k gt 1, posterior probability does not varies
  very much

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Discussions on Society Openness (cont.)

• Multiple Hop Inference (cont.)
• k 2 and d 2 (Y11 and Y21 are hidden)

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Discussions on Society Openness (cont.)
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Conclusions

• Privacy may be indirectly released via social
  relations
• Inference accuracy of privacy information
• Closely related to the inference strength between
  friends
• Even in a society where people hide their
  attributes, privacy still could be inferred from
  Bayesian inference.
• Protect Privacy
• Hide friendship relation
• Or ask friends to hide attributes

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Thank you!

• References
• 1 David Heckerman, A Tutorial on Learning With
  Bayesian Networks. Microsoft Research, Advanced
  Technology Division, 1996
• 2 D.S. Sivia, Data Analysis A Bayesian
  Tutorial. Oxford University Press, 1996.
• Questions?

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