Paper:
Controlling privacy in recommender systems
Recommender systems involve an inherent trade-off between accuracy of recommendations and the extent to which users are willing to release information about their preferences. In this paper, we explore a two-tiered notion of privacy where there is a small set of "public" users who are willing to share their preferences openly, and a large set of "private" users who require privacy guarantees. We show theoretically and demonstrate empirically that a moderate number of public users with no access to private user information already suffices for reasonable accuracy. Moreover, we introduce a new privacy concept for gleaning relational information from private users while maintaining a first order deniability. We demonstrate gains from controlled access to private user preferences.

Review:
This paper proposes a privacy-preserving mechanism for recommender systemswhich are based on the popular matrix factorization. Specifically, theauthors propose splitting users into disjoint groups of public and privateusers. Private users do not share any information (ratings) with thesystem while public users share all of their information. The authors showthat under certain technical conditions one can bound the estimationaccuracy of the item features based on the number of observed ratings.This estimate can further be used to bound the reconstruction error of theprivate users. The authors further demonstrate the empirical performanceof their approach using the Movielens 10M dataset.Privacy in recommender systems is an important problem that we are onlybeginning to explore. As far as I know most formal previous approachesrely on differential privacy. This paper considers that even therecommender engine is not safe. This seems like a reasonable practicalsetting. In that setting the authors develop an interesting framework.The formalism developed in this paper is clear and seems sound as are thederivations. The results (bounding the error of the item factors andconsequently the errors of the reconstruction) are interesting. It wouldbe nice to give a bit more intuition about Theorem 3.5.Overall the paper is well written and easy to follow.The experiments are also reasonable. They demonstrate what is needed andthe comparisons to other methods is reasonably convincing.In the first set of experiments, it would be good to clarify what thelabel "Percentage of Users" mean. I understood it to mean the percentageof all users that were public.The second set of experiments uses 100 public users and up to 400 privateusers. It is a bit unclear why the authors are not reporting results withmore private uses (the dataset contains 10K users). What happens in thatsetting? Do any of the DP methods (especially LAP eps=5) reach similarperformance as PMC and PMD. Was there a reason for stopping at 400 privateusers? It would be good to show that PMC and PMD do well in a lesssynthetic setting. It would also be nice to provide results in the casewhere the private users aren't the ones that have necessarily consumed themost items.