Personalized Social Recommendations Accurate or Private

Transcription

1 Personalized Social Recommendations Accurate or Private Presented by: Lurye Jenny Paper by: Ashwin Machanavajjhala, Aleksandra Korolova, Atish Das Sarma

2 Outline Introduction Motivation The model General Lower Bounds Privacy preserving algorithms Experiments

3 Personalized Recommendations Advertisement Products People content

4 Personalized Recommendations Advertisement Products People content

5 Personalized Recommendations Advertisement Products People content

6 Personalized Recommendations Advertisement Products People content

7 Recommendation Algorithms

8 Traditional Based on generic recommendation & history. Other users that bought this book also bought

9 Social aware Based on active friends. Your friend already bought this book!

10 G V, E Facebook's Open Graph API & Google s Social Graph API

11 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

12 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

13 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

14 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

15 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

16 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

17 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

18 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

19 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

20 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

21 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

22 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

23 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

24 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

25 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

26 Sensitive information Friends Location Professional info Hobbies Sexual Orientation Relationship Status Contact info Date of Birth Traveling info

27 Outline Introduction Motivation The model General Lower Bounds Privacy preserving algorithms Experiments

28 Motivation Increase user s degree of engagement Avoid privacy breach

29 G V, E Can a recommendation algorithm be accurate while not breaching one s privacy?

30 Tradeoff Sensitive information usage vs. better recommendation

31 Outline Introduction Motivation The model General Lower Bounds Privacy preserving algorithms Experiments

32 G V, E The Model The network graph V entities: people, products. E connections

33 G V, E The Utility function u Gr, i The utility of recommending node i to node r # of common neighbors # of weighted paths Page Rank

34 G V, E The Utility by # of common neighbors

35 G V, E The Social Recommendation Algorithm (R) R is a probability vector on all nodes: p Gr, i R The probability of R recommending node i to node r

36 G V, E The Social Recommendation Algorithm (R) R : p, p, p, p G, Blue Guy G, Blue Guy G, Blue Guy G, Blue Guy Dog Book Camera MacBook Shoe R1 : 0.5, 0.2, 0.2, 0. 1 R 2 : ,,,

37 G V, E Why do we need R to be probabilistic?

38 G V, E The Social Recommendation Algorithm (R) Example: R best p G, blue guy Macbook R best 0 p G, blue guy camera R best 0 p G, blue guy red shoes R best 0 p G, blue guy Dog book R best 1

39 G V, E OK, so why not recommend randomly?

40 G V, E R R

41 G V, E Maximizing the expected utility Max i G, r G, r i i u p R

42 G V, E Simplifying the notation G and r are constant: u p Gr, i Gr, i ui p i

43 G V, E R s Accuracy R is (1-δ) accurate if for any r: i i max i u p R u 1

44 G V, E Example R max 1 2 i u i u p i R :.1 : R

45 G V, E Privacy Definition Differential Privacy an algorithm preserves privacy of an entity if the algorithm's output is not sensitive to the presence or absence of the entity's information in the input data set.

46 G V, E Differential Privacy Definition 1: recommendation algorithm R satisfies Ɛ-differential privacy if for any pair of graphs G and G that differ in one edge (i.e., G = G + {e} or vice versa) and every set of possible recommendations S: Pr R G S e Pr R G' S

47 G V, E Differential Privacy Pr RGS e Pr RG ' S R : p, p, p, p Dog Book Camera MacBook shoe R R 1 2 : : 0.5, 0.2, 0.2, ,,, R R 1 2 : : 0.286, 0.286, 0.286, ,,, G 1 0 G'

48 Outline Introduction Motivation The model General Lower Bounds Privacy preserving algorithms Experiments

49 G V, E Problem Statement Given u, determine a recommendation algorithm that : (a) satisfies the Ɛ- differential privacy constraints. (b) maximizes the accuracy of recommendations

50 G V, E Generic Privacy Lower Bounds We focus on: Theoretically determine the bounds on maximum accuracy (1-δ) achievable by any algorithm that satisfies Ɛ- differential privacy.

51 G V, E Exchangeability Let G be a graph & let h be an isomorphism on the nodes giving graph, s.t.: for target node r, h(r) = r. Then: i u G h Gr, i G, r hi : u h

52 G V, E 0 Exchangeability 1 1 2

53 G V, E Monotonicity R is monotonic if: i, j ui u j pi p j

54 G V, E 0 Monotonicity R1 : R :

55 G V, E General Lower Bounds A monotonic recommendation algorithm that: achieves a constant accuracy (1-δ) is based on a utility function that satisfies exchangeability Has a lower bound on it s Ɛ parameter differential privacy Pr R G S e Pr R G ' S :

56 G V, E General Lower Bounds Split V into two groups by utility: c 0,1 V : u (1 c) u V : u (1 c) u high iv high max low i V low max k nodes n k nodes n nodes

57 G V, E General Lower Bounds How much probability should we give each group to achieve (1-δ) accuracy? high low p u p 1 c u u p 1 u max max max i high low p p c 1 1 i i accuracy p high c low, p c c 0 high p total probability of V high 1 low p total probability of V low 2 V : u (1 c) u 1 V : u (1 c) u high iv high max low i V low max

58 G V, E General Lower Bounds How much probability should we give each group to achieve (1-δ) accuracy? example: 1c p p high low c c c high p total probability of V high 1 low p total probability of V low 2 V : u (1 c) u 1 V : u (1 c) u high iv high max low i V low max

59 G V, E General Lower Bounds t the number of edges that needs to be added to turn a node with the smallest probability of being recommended from the low utility group Vlow into the node of maximum utility in the modified graph. G' 0 1 t 3 2 1

60 x G 0 G' x G V high G V low G ' V high G' V low 1 k nodes n k nodes k 1 nodes n k nodes p high c low, p c c G x V : p low G x c n x k ck1 p G' c

61 G V, E General Lower Bounds From differential privacy: G1 p e p x p e p G x p e p G x G x 2 1 G' G 2 x x e p x 2 G e p x 3 G p p G ' x G x e t 0 G' 1 2 1

62 General Lower Bounds Let s put it all together!, G V E G' t x G x p e p G p x c n k ' 1 G x c p c k 1 t c n k e k 1 ln ln 1 c n k t k Lower Bound!

63 G V, E General Lower Bounds Important result: cn k 1 1 t n k k 1 e upper bound on accuracy!

64 G V, E General Lower Bounds Example: A social network with 400 million nodes: n Lets assume that for c 0.99, we have k 100 and consider t 150 (which is about the average degree in some social networks). Suppose we want to guarantee 0.1-differential privacy, then we compute the bound on the accuracy : e 410 This suggests that for a differential privacy guarantee of 0.1, no algorithm can guarantee an accuracy better than

65 Outline Introduction Motivation The model General Lower Bounds Privacy preserving algorithms Experiments

66 G V, E Privacy preserving algorithms An algorithm that satisfies differential privacy must recommend every node, even the ones that have zero utility, with a non-zero probability.

67 G V, E Privacy preserving algorithms Let s add some noise! Exponential smoothing mechanism Laplace noise addition mechanism

68 G V, E Exponential smoothing mechanism Creates a smooth probability distribution from the utility vector and samples from it. Given the utilities vector: u,..., 1 un, algorithm AE recommends node i with probability p i n e j1 u f e i u f j u i 0 p i n j1 1 e u f j f is the sensitivity of the utility function (the maximum utility difference caused by adding / removing one edge).

69 G V, E Laplace noise addition mechanism Unlike the Exponential mechanism, the Laplace mechanism more closely mimics the optimal mechanism Rbest. Given nodes with utilities u,..., 1 un algorithm AL first computes a modified utility vector u' 1,..., u' n as follows: u u r ' i i where r is a random variable chosen from the Laplace distribution independently at random for each i. Then, recommends u A max ' i L

70 G V, E Laplace noise addition mechanism Laplace Distribution: 1 f x e 2b x b Laplace Density function b f, 0

71 Outline Introduction Motivation The model General Lower Bounds Privacy preserving algorithms Experiments

72 G V, E Experiments Our Goal: Comparing the theoretical upper bound on accuracy to the de-facto accuracy.

73 G V, E Experiments Settings: real network graphs: Wikipedia vote network G WV Twitter connections network G T utility functions: Common neighbors Number of paths privacy tools: Exponential smoothing mechanism Laplace noise addition mechanism

74 G V, E Wikipedia vote network Some Wikipedia users are administrators, who have access to additional technical features. Users are elected to be administrators via a public vote of other users and administrators. G WV : V users E votes 7, , 762 nodes edges

75 G V, E Twitter connections network Users follow other users. G T : V users E follows 96, 403 nodes 489, 986 edges

76 G V, E Experiments STEPS: Select target node r uniformly at random. Compute utility according to both functions. Fix Ɛ of differential privacy. Compute expected accuracy: Exponential smoothing : directly. Laplace noise addition : average utility of 1000 independent trials Compute theoretical upper bound using: 1 c n k 1 1 t n k k e

77 G V, E Results Experiments show that the Laplace mechanism achieves nearly identical accuracy as the Exponential mechanism. But, Exponential mechanism s accuracy can be computed more efficiently, so we will compare our theoretical bound on accuracy only to it s actual accuracy.

78 G V, E Results # of common neighbors: Wikipedia vote network Twitter connections network X-axis is the accuracy (1-δ). y-axis is the % of nodes receiving recommendations with accuracy < (1-δ)

79 G V, E Results # of weighted paths: Wikipedia vote network Twitter connections network X-axis is the accuracy (1-δ). y-axis is the % of nodes receiving recommendations with accuracy < (1-δ)

80 G V, E Results The low degree nodes are also the most vulnerable to receiving low accuracy recommendations X-axis is the target s node degree. y-axis is the accuracy (1-δ)

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