Privacy Preservation for Data Streams

1. Privacy Preservation for Data Streams Feifei Li, Boston University Joint work with: Jimeng Sun (CMU), Spiros Papadimitriou, George A. Mihaila and Ioana Stanoi (IBM T.J. Watson Research Center)

2. P P P Sensitive data Application (1) Corp. A Analytical Services Corp. B Corp. C Finding trends, clusters, patterns, aggregations.

3. Publish data as a service Subscribe data to identify trends, patterns, classes Application (2) Client A Information Hub Corp. A P Client B

4. Identify trends Target Application value stream 1 time value Cluster/ classification stream 2 time value stream 3 time value stream 4 time

5. A1 A1t A2 + Online generated noise, one vector at a time AN t Problem Formulation time time …….. time

6. Given σ2, obtain A* online, s.t. D(A, A*) = σ2, and for given R, D(A, A~) is close to σ2 x Offline and Online Problem Formulation (continued) time time ……. R time

7. Data Perturbation Random i.i.d noise time time + time time time time time time i.i.d: identical independently distributed

8. Principal Component Analysis: PCA i.i.d Noise

9. Principal Component Analysis: PCA Correlated Noise

10. A* Added Noise: Utility Removed Noise σ2 Projection Error A~ Remaining Noise Privacy PCA Based Data Reconstruction A: Original Data A*: Perturbed Data A~: Reconstructed Data A Principal Direction

11. Added Noise: Utility σ2 A* Projection Error A~ Remaining Noise Privacy PCA Based Data Reconstruction Correlated Noise! A: Original Data A*: Perturbed Data A~: Reconstructed Data A Principal Direction

12. Data Perturbation: main idea • Observations • The amount of the random noise controls privacy/utility tradeoff • i.i.d (identical independently distributed) noise does not preserve the privacy! Not well enough • Lesson learned • Noise should be correlated with original data • Z. Huang et al. Sigmod 05.

13. Challenge 1: Dynamic Correlation

14. Challenge 1: Dynamic Correlation

15. Challenge 2: Dynamic Autocorrelation

16. Challenge 2: Dynamic Autocorrelation

17. Online Random Noise for Autocorrelation: Stock

18. State of the Art • Privacy Preservation • Given a utility requirement, maximize the privacy • Existing Work (Z. Huang et al. Sigmod05) • Batch mode, static data • And many other works (see our paper for a detailed literature review)

19. At Et A~t + Publish A~t U3x3: online estimation of principal components Update U Generate noise distributed along U S. Papadimitriou et al. VLDB05 Adding Dynamic Correlated Noise A1 A2 A3

20. σ2 σ2 Added to At Rotate back to data space Noise distributed in principal components’ subspace Put it into Algorithm: Distribute Noise k=3, U: eigenvectors, V: eigenvalues

21. Removed noise by online reconstruction Local principal component Local principal component Removed noise by online reconstruction Noise added along global PC -- offline Global principal component Noise added along global PC -- offline why is our algorithm better (state of the art)?

22. Online Reconstruction vs. Offline Reconstruction • Choice of adversary: • Offline reconstruction based on global principal components • Online tracking of the principal components and apply local reconstruction • Please see the details in the paper

23. h streams 1 2 3 2 3 4 3 4 5 4 5 6 Time w1 w2 w3 w4 W = Tracking Autocorrelation a=[1 2 3 4 5 6]T

24. Distribute Noise Avoid adding noise > allowed threshold! And still auto-correlated with the stream 1 2 3 2 3 4 3 4 5 4 5 6 1 2 3 2 3 4 3 4 5 4 5 6 1 2 3 2 3 4 3 4 5 4 5 6 1 2 3 2 3 4 3 4 5 4 5 6 1 2 3 2 3 4 3 4 5 4 5 6 Idea: constraint the next k noise values based on previous h-k noises + current estimation of U  becomes a linear system W =

25. Experiments • Three Real Data Streams • Sensor streams, Lab: Light, Humidity, Volt, Temperature. 7712x198 • Choroline environmental streams: 4310x166 • Stock streams: 8000x2

26. Perturbation vs. Reconstruction streaming auto-correlated additive noise noise correlated with global principal components streaming correlated additive noise take perturbed data as the reconstruction streaming auto-correlated online reconstruction streaming correlated online reconstruction offline-reconstruction based on global principal components noise (discrepancy) is represented by the relative energy as percentage to the original data streams, i.e., D(A, A*)/||A||

27. Reconstruction Error: Online-R vs. Offline-R 10% noise k=10 online reconstruction achieves better accuracy as it minimizes the projection error

28. Reconstruction Error: vary k • online reconstruction achieves better accuracy • large k reduces projection error

29. Privacy vs. Discrepancy, online-R: Lab data

30. Privacy vs. Discrepancy, online-R: Choroline

31. Online Random Noise for Autocorrelation: Choroline

32. Online Random Noise for Autocorrelation: Stock

33. Privacy vs. Discrepancy: Online-R (Choroline)

34. Privacy vs. Discrepancy: Online-R (Stock)

35. Running Time Analysis

36. Running Time Analysis

37. Future Work • Combing correlation and autocorrelation • Other type of data streams, other than numeric data, such as categorical data

38. Questions • Thank you!