This document proposes a method for private distributed collaborative filtering using estimated concordance measures. It defines concordance as a measure of agreement between users' ratings that can be used to estimate similarity in a privacy-preserving way. The method estimates upper and lower bounds on concordance between users to calculate similarity without revealing private rating data. An evaluation shows this approach can accurately estimate similarity coefficients and generate recommendations, especially for larger and denser datasets. Future work is needed to further analyze concordance-based similarity and its effects on trust in distributed recommender systems.

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]

4. problem: i need recommendations: peer-to-peer distributed

5. solution: distributed collaborative filtering 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

6. problem: who do you trust? thief? uncooperative? spammer?

7. problem: who do you trust? how do we bootstrap cooperation when we do not know how much to trust the community? solution: estimate profile similarity with privacy

9. privacy… … the right to be left alone

10. privacy… … the right to control the flow of your personal information

11. 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

12. public information total number of items a recommendation context: collaboration:

13. but even if we did trust some people… … similarity measures are not transitive ? privacy

15. concordance: definition define : d a,i = r a,i - r mean measure similarity according to proportion of agreement: classify ratings into one of three groups

16. concordance: definition concordant : we agree (C) discordant : we dis agree (D) tied : one of us has no opinion (T) +1 +3 -2.7 +1.5

17. concordance: definition measure similarity according to proportion of agreement: somers’ d:

18. accuracy coverage vs. compare performance using netflix data subset

20. concordance-based similarity: … agreement is transitive! ? concordant discordant privacy

21. concordance-based similarity: … agreement is transitive! discordant concordant discordant privacy

22. concordance-based similarity: … agreement is transitive! ? discordant discordant privacy

23. concordance-based similarity: … agreement is transitive! concordant discordant discordant privacy

24. transitivity of concordance: result D T T T T T T T C C C C D D D

26. 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

27. 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 estimate similarity by upper/lower bounds of overlap (full details in paper)

31. sparsity effect – size effect

32. evaluation: Highest error when dataset is: small and very sparse How well do estimated coefficients work to generate recommendations ? 2) return to the netflix dataset..

33. accuracy -- coverage

36. 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] related work, research: mobblog.cs.ucl.ac.uk