  Machine learning methods allow us to make recommendations to users in
applications across fields including entertainment, dating, and commerce, by
exploiting similarities in users' interaction patterns. However, in domains
that demand protection of personally sensitive data, such as medicine or
banking, how can we learn such a model without accessing the sensitive data,
and without inadvertently leaking private information? We propose a new
federated approach to learning global and local private models for
recommendation without collecting raw data, user statistics, or information
about personal preferences. Our method produces a set of prototypes that allows
us to infer global behavioral patterns, while providing differential privacy
guarantees for users in any database of the system. By requiring only two
rounds of communication, we both reduce the communication costs and avoid the
excessive privacy loss associated with iterative procedures. We test our
framework on synthetic data as well as real federated medical data and
Movielens ratings data. We show local adaptation of the global model allows our
method to outperform centralized matrix-factorization-based recommender system
models, both in terms of accuracy of matrix reconstruction and in terms of
relevance of the recommendations, while maintaining provable privacy
guarantees. We also show that our method is more robust and is characterized by
smaller variance than individual models learned by independent entities.
