Understanding the Sparse Vector Technique for Differential Privacy

TL;DR

This paper critically analyzes the Sparse Vector Technique (SVT) in differential privacy, identifies common errors, proposes improvements, and demonstrates that in some cases, the Exponential Mechanism outperforms SVT.

Contribution

The paper clarifies misunderstandings about SVT, introduces a new, more utility-efficient version, and shows when SVT can be replaced by the Exponential Mechanism for better accuracy.

Findings

Most SVT variants are not truly private.

A new version of SVT offers improved utility.

In non-interactive settings, EM outperforms SVT.

Abstract

The Sparse Vector Technique (SVT) is a fundamental technique for satisfying differential privacy and has the unique quality that one can output some query answers without apparently paying any privacy cost. SVT has been used in both the interactive setting, where one tries to answer a sequence of queries that are not known ahead of the time, and in the non-interactive setting, where all queries are known. Because of the potential savings on privacy budget, many variants for SVT have been proposed and employed in privacy-preserving data mining and publishing. However, most variants of SVT are actually not private. In this paper, we analyze these errors and identify the misunderstandings that likely contribute to them. We also propose a new version of SVT that provides better utility, and introduce an effective technique to improve the performance of SVT. These enhancements can be applied to improve utility in the interactive setting. Through both analytical and experimental comparisons, we show that, in the non-interactive setting (but not the interactive setting), the SVT technique is unnecessary, as it can be replaced by the Exponential Mechanism (EM) with better accuracy.