Free Gap Information from the Differentially Private Sparse Vector and Noisy Max Mechanisms

TL;DR

This paper demonstrates that the Noisy Max and Sparse Vector differential privacy mechanisms can release additional useful information without extra privacy cost, improving accuracy and efficiency in data analysis.

Contribution

It introduces methods to extract free additional information from Noisy Max and Sparse Vector mechanisms, enhancing their utility without increasing privacy loss.

Findings

Noisy Max can release the noisy gap between top queries at no privacy cost.

Sparse Vector can adaptively control privacy budget for better query processing.

These techniques improve accuracy and query capacity in differential privacy applications.

Abstract

Noisy Max and Sparse Vector are selection algorithms for differential privacy and serve as building blocks for more complex algorithms. In this paper we show that both algorithms can release additional information for free (i.e., at no additional privacy cost). Noisy Max is used to return the approximate maximizer among a set of queries. We show that it can also release for free the noisy gap between the approximate maximizer and runner-up. This free information can improve the accuracy of certain subsequent counting queries by up to 50%. Sparse Vector is used to return a set of queries that are approximately larger than a fixed threshold. We show that it can adaptively control its privacy budget (use less budget for queries that are likely to be much larger than the threshold) in order to increase the amount of queries it can process. These results follow from a careful privacy analysis.