Graph Analysis with Node Differential Privacy Node Differential - PowerPoint PPT Presentation

Graph Analysis with Node Differential Privacy Node Differential Privacy Sofya Sofya Raskhodnikova Sofya Sofya Raskhodnikova Raskhodnikova Raskhodnikova Penn State University Shiva Kasiviswanathan Shiva Kasiviswanathan (GE Research), Joint work with Kobbi Kobbi Nissim Nissim (Ben-Gurion U. and Harvard U.), Ad Ad Adam Smith Adam Smith (Penn State) S i h S i h (P S ) 1

Publishing information about graphs Many datasets can be represented as graphs • “Friendships” in online social network • “Friendships” in online social network • Financial transactions • Email communication E il i ti • Romantic relationships image source http://community.expressor- software.com/blogs/mtarallo/36-extracting-data- facebook-social-graph-expressor-tutorial.html Privacy is a big issue! big issue! American J. Sociology, Bearman, Moody, Stovel 2

Private analysis of graph data Users Graph G Trusted curator Government, researchers researchers, answers ) ) ( ( queries i businesses (or) malicious malicious adversary • Two conflicting goals: utility and privacy T fli i l ili d i – utility: accurate answers – privacy: ? image source http://www.queticointernetmarketing.com/new-amazing-facebook-photo-mapper/ 3

Differential privacy for graph data Users Graph G Trusted curator Government, researchers, researchers answers ) ) ( ( queries i businesses A (or) malicious malicious adversary • Intuition: neighbors are datasets that differ only in some Intuition: neighbors are datasets that differ only in some information we’d like to hide (e.g., one person’s data) image source http://www.queticointernetmarketing.com/new-amazing-facebook-photo-mapper/ 4

Two variants of differential privacy for graphs • Edge differential privacy G: Two graphs are neighbors if they differ in one edge . • Node differential privacy G: Two graphs are neighbors if one can be obtained from the other by deleting a node and its adjacent edges by deleting a node and its adjacent edges . 5

Node differentially private analysis of graphs Users Graph G Trusted curator Government, researchers researchers, answers ) ) ( ( queries i businesses A (or) malicious malicious adversary • Two conflicting goals: utility and privacy T fli ti l tilit d i – Impossible to get both in the worst case • Previously: no node differentially private • Previously: no node differentially private algorithms that are accurate on realistic graphs image source http://www.queticointernetmarketing.com/new-amazing-facebook-photo-mapper/ 6

Our contributions • First node differentially private algorithms that are accurate for sparse graphs accurate for sparse graphs – node differentially private for all graphs – accurate for a subclass of graphs, which includes acc rate for a s bclass f h hi h i l d • graphs with sublinear (not necessarily constant) degree bound • graphs where the tail of the degree distribution is not too heavy graphs where the tail of the degree distribution is not too heavy • dense graphs • Techniques for node differentially private algorithms ec ques o ode d e e a y p a e a go s • Methodology for analyzing the accuracy of such algorithms on realistic networks algorithms on realistic networks Concurrent work on node privacy [Blocki Blum Datta Sheffet 13 ] Concurrent work on node privacy [Blocki Blum Datta Sheffet 13 ] 7

8 Degrees … … Frequency … Our contributions: algorithms

9 (1+o(1))-approximation Our contributions: accuracy analysis

Previous work on differentially private computations on graphs Edge differentially private algorithms Edge differentially private algorithms • number of triangles , MST cost [Nissim Raskhodnikova Smith 07] • degree distribution [Hay Rastogi Miklau Suciu 09 Hay Li Miklau Jensen 09] • degree distribution [Hay Rastogi Miklau Suciu 09, Hay Li Miklau Jensen 09] • small subgraph counts [Karwa Raskhodnikova Smith Yaroslavtsev 11] • cuts [Blocki Blum Datta Sheffet 12] Edge private against Bayesian adversary ( weaker privacy) • small subgraph counts [Rastogi Hay Miklau Suciu 09] ll b h t [ kl ] Node zero ‐ knowledge private ( stronger privacy) Node zero knowledge private ( stronger privacy) • average degree, distances to nearest connected, Eulerian, cycle ‐ free graphs for dense graphs [Gehrke Lui Pass 12] 10

Differential privacy basics Users Graph G Trusted curator Government, t ti ti f ) researchers researchers, approximation ) ( ( statistic f businesses A (or) malicious malicious to f(G) adversary 11

12 Global sensitivity framework [DMNS’06]

13 “Projections” on graphs of small degree Goal: privacy for all graphs

14 Method 1: Lipschitz extensions

15 t 1' 2' 3' 4' 5' 1 1 1 1 2 3 4 5 s

16 t 1' 2' 3' 4' 5' 1 1 1/ 1/ 1 1 2 3 4 5 s

17 t 6' 6' 1' 2' 3' 4' 5' 1 1 1 1 2 3 4 5 6 6 s

 via Smooth Sensitivity framework [NRS’07]  via Smooth Sensitivity framework [NRS 07] 18

19 } via generic reduction via Lipschitz extensions Our results

Conclusions • It is possible to design node differentially private algorithms with good utility on sparse graphs with good utility on sparse graphs – One can first test whether the graph is sparse privately • Directions for future work – Node ‐ private synthetic graphs – What are the right notions of privacy for network data? 20

21 Lipschitz extensions via linear/convex programs

22 Degrees … … … Frequency … … Our results

23 (1+o(1))-approximation (1 o(1)) approximation … … Our results

24 query f T(G) T S A G

25 Degrees … Generic Reduction via Truncation d Frequency …

26 degree above d) #(nodes of Smooth Sensitivity of Truncation

27 Releasing Degree Distribution via Generic Reduction query f y f q T(G) T(G) T T S A G