Differentially Private Quantiles
This work addresses the need for accurate and efficient differentially private quantile estimation, which is crucial for summarizing sensitive data in fields like healthcare or finance, representing a strong specific gain rather than a foundational advancement.
The paper tackles the problem of computing multiple quantiles under differential privacy, where existing methods suffer from reduced accuracy due to privacy budget splitting or inefficiency. It proposes an efficient exponential mechanism that simultaneously estimates m quantiles in O(mn log(n) + m^2n) time, significantly outperforming state-of-the-art methods in experiments on real and synthetic data.
Quantiles are often used for summarizing and understanding data. If that data is sensitive, it may be necessary to compute quantiles in a way that is differentially private, providing theoretical guarantees that the result does not reveal private information. However, when multiple quantiles are needed, existing differentially private algorithms fare poorly: they either compute quantiles individually, splitting the privacy budget, or summarize the entire distribution, wasting effort. In either case the result is reduced accuracy. In this work we propose an instance of the exponential mechanism that simultaneously estimates exactly $m$ quantiles from $n$ data points while guaranteeing differential privacy. The utility function is carefully structured to allow for an efficient implementation that returns estimates of all $m$ quantiles in time $O(mn\log(n) + m^2n)$. Experiments show that our method significantly outperforms the current state of the art on both real and synthetic data while remaining efficient enough to be practical.