Identifying anomalies in data is vital in many domains, including medicine, finance, and national security. However, privacy concerns pose a significant roadblock to carrying out such an analysis. Since existing privacy definitions do not allow good accuracy when doing outlier analysis, the notion of sensitive privacy has been recently proposed to deal with this problem. Sensitive privacy makes it possible to analyze data for anomalies with practically meaningful accuracy while providing a strong guarantee similar to differential privacy, which is the prevalent privacy standard today. In this work, we relate sensitive privacy to other important notions of data privacy so that one can port the technical developments and private mechanism constructions from these related concepts to sensitive privacy. Sensitive privacy critically depends on the underlying anomaly model. We develop a novel n-step lookahead mechanism to efficiently answer arbitrary outlier queries, which provably guarantees sensitive privacy if we restrict our attention to common a class of anomaly models. We also provide general constructions to give sensitively private mechanisms for identifying anomalies and show the conditions under which the constructions would be optimal.
Keywords: anomaly identification; differential privacy; outlier analysis; outlier detection; sensitive privacy.