The Price of Privacy in Untrusted Recommendation Engines

Abstract

Recent increase in online privacy concerns prompts the following question: can a recommender system be accurate if users do not entrust it with their private data? To answer this, we study the problem of learning item-clusters under local differential privacy, a powerful, formal notion of data privacy. We develop bounds on the sample-complexity of learning item-clusters from privatized user inputs. Significantly, our results identify a sample-complexity separation between learning in an information-rich and an information-scarce regime, thereby highlighting the interaction between privacy and the amount of information (ratings) available to each user. In the information-rich regime, where each user rates at least a constant fraction of items, a spectral clustering approach is shown to achieve a sample-complexity lower bound derived from a simple information-theoretic argument based on Fano’s inequality. However, the information-scarce regime, where each user rates only a vanishing fraction of items, is found to require a fundamentally different approach both for lower bounds and algorithms. To this end, we develop new techniques for bounding mutual information under a notion of channel-mismatch. These techniques may be of broader interest, and we illustrate this by applying them to (i) learning based on 1-bit sketches, and (ii) adaptive learning. Finally, we propose a new algorithm, MaxSense, and show that it achieves optimal sample-complexity in the information-scarce regime.

Publication
IEEE Journal of Selected Topics in Signal Processing

Earlier conference version: Banerjee et al. (2012).

Siddhartha Banerjee
Siddhartha Banerjee
Associate Professor

Sid Banerjee is an associate professor in the School of Operations Research at Cornell, working on topics at the intersection of data-driven decision-making, market design, and algorithms for large-scale networks.

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