The Price of Privacy in Untrusted Recommendation Engines

TL;DR

This paper investigates the impact of local differential privacy on the accuracy of recommender systems, revealing a fundamental trade-off between privacy and the amount of user data needed for effective item-clustering.

Contribution

It introduces new bounds on sample complexity for private item-clustering, develops a novel algorithm MaxSense, and explores the differences between information-rich and information-scarce regimes.

Findings

Spectral clustering achieves optimal sample complexity in information-rich regime.

MaxSense algorithm is optimal in information-scarce regime.

New techniques for bounding mutual information under channel-mismatch.

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, and also propose a new algorithm, MaxSense, and show that it achieves optimal sample-complexity in this setting. The techniques we develop for bounding mutual information may be of broader interest. To illustrate this, we show their applicability to $(i)$ learning based on 1-bit sketches, and $(ii)$ adaptive learning, where queries can be adapted based on answers to past queries.