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]

Outline Background Motivation – Privacy Concordance Transitivity of Concordance Private Collaborative Filtering Evaluation Conclusion – Future Work

Background

Motivation – Privacy

Concordance

Transitivity of Concordance

Private Collaborative Filtering

Evaluation

Conclusion – Future Work

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

Who do you trust? Distributed, peer-to-peer recommender system scenario: How do we bootstrap cooperation when we do not know how much to trust the community? Estimate profile similarity with privacy Cooperation? Malicious behaviour? Trust?

Distributed, peer-to-peer recommender system scenario:

How do we bootstrap cooperation when we do not know how much to trust the community?

Estimate profile similarity with privacy

Cooperation?

Malicious behaviour?

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

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

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

Problem? similarity measures are not transitive

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

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

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

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

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

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

Accuracy

Coverage

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

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

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

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

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

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

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

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

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

Discordant Pairs: 

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

Does this preserve privacy? worst case scenario: full profile disclosed a b c d 4 3 3 4 a b c d 5 3 2 4 C C C C solution? collaboratively create random set

worst case scenario: full profile disclosed

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

Evaluation: simulated profiles The estimation should be independent of what the ratings actually are: 1)

simulated profiles

Sparsity Effect

Size Effect

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

Accuracy

Coverage

Future Work full analysis of concordance -based similarity measures (better evaluation!) analysis of the effect of correlation coefficients on communities of recommenders related work, research: mobblog.cs.ucl.ac.uk

full analysis of concordance -based similarity measures (better evaluation!)

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]