Presentation based on paper "Private Distributed Collaborative Filtering Using Estimated Concordance Measures"

1. Private Distributed Collaborative Filtering Using Estimated Concordance Measures Neal Lathia Dr. Stephen Hailes Dr. Licia Capra Department of Computer Science University College London [email_address]

3. Collaborative Filtering: Background a b c d 4 3 3 ? a b c d 4 ? 3 4 Step 1 : Profile Similarity (Correlation) Step 2 : k-Nearest Neighbours Step 3 : Recommendation Aggregation Similarity

5. Privacy: 2 views privacy Controlling the flow of personal information The right to be “left alone” (out of public view)

6. Private Information a b c d 4 ? 3 4 A rating r a,i by user a for item i The full set of ratings r a for user a The mean rating r mean of user a The number of items user a has rated

7. Public Information The total number of items that can be rated A recommendation ( r a,i – r mean ) context: collaboration:

8. Problem? similarity measures are not transitive

9. Concordance: Definition Movie Title x y define : d a,i = r a,i - r mean measure similarity according to proportion of agreement: classify ratings into one of three groups

10. Concordance: Definition “ Waking Life” x y d a,i > 0 and d b,i > 0 concordant : we agree or d a,i < 0 and d b,i < 0

11. Concordance: Definition “ Terminator” x y d a,i > 0 and d b,i < 0 discordant : we dis agree or d a,i < 0 and d b,i > 0

12. Concordance: Definition “ Airplane!” x y d a,i = 0 tied : one of us has no opinion d b,i = 0 one of us has not rated the item

13. Concordance: Definition “ Trainspotting” x y Somers’ d: “ Transformers” x y “ The Godfather” x y … … … measure similarity according to proportion of agreement:

14. Somers’ d vs. Pearson Correlation Coefficient compare performance using netflix data subset 999 users 100 – 500 ratings per user 17,770 movies vs.

15. Accuracy

16. Coverage

17. Problem? similarity measures are not transitive is agreement transitive? four examples:

18. Transitivity of Concordance: Four Examples (1) tied concordant 0.0 0.4 1.2 ms. green and mr. blue are: tied

19. Transitivity of Concordance: Four Examples (2) concordant 0.8 0.4 1.2 concordant ms. green and mr. blue are: concordant

20. Transitivity of Concordance: Four Examples (3) discordant 0.8 - 0.4 1.2 discordant ms. green and mr. blue are: concordant

21. Transitivity of Concordance: Four Examples (4) concordant - 0.8 0.4 1.2 discordant ms. green and mr. blue are: discordant

22. Transitivity of Concordance: Result D T T T T T T T C C C C D D D

23. Private Collaborate Filtering: the idea a b c d 4 3 3 ? a b c d 4 ? 3 4 a b c d 5 3 2 4 C, D, T C, D, T C, D, T

24. a b c d r1 r2 r3 r4 a b c d r1 r2 r3 r4 Tied Pairs: Upper Bound : None of the tied pairs overlap Lower Bound : All the tied pairs overlap Tied Concordant Discordant

25. a b c d r1 r2 r3 r4 a b c d r1 r2 r3 r4 Concordant Pairs: Upper Bound : Maximum overlap of concordant pairs plus minimum overlap of discordant pairs Lower Bound : Minimum overlap of concordant pairs Tied Concordant Discordant

26. Discordant Pairs: 

27. Does this preserve privacy? a b c d 4 ? 3 4 A rating r a,i by user a for item i The full set of ratings r a for user a The mean rating r mean of user a The number of items user a has rated warning : potential inference

29. Evaluation How well does this method estimate the actual coefficients? How well do estimated coefficients work to generate recommendations ? on all datasets? 1) 2)

31. Sparsity Effect

32. Size Effect

33. Evaluation: Simulated Profiles Highest error when dataset is: small and very sparse How well do estimated coefficients work to generate recommendations ? 2)

34. Accuracy

35. Coverage

37. Private Distributed Collaborative Filtering using Estimated Concordance Measures Neal Lathia Dr. Stephen Hailes Dr. Licia Capra Department of Computer Science University College London [email_address]