A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis

Calibrating Noise to Sensitivity in Private Data Analysis

“…The seminal paper of Blum et al (2008) showed that data-dependent noise could allow one to release exponentially many such queries with high accuracy. This led to a large body of follow-up work, for example, the development of on-line techniques based on the multiplicative weights algorithm Hardt and Rothblum (2010), and geometric techniques that vastly generalize Section 3.3 (e.g., Hardt and Talwar (2010)). These investigations have also led to a fascinating interplay with computational complexity theory (e.g., Vadhan (2016)).…”

Differential Privacy in Practice

“…Some open questions in the median mechanism are solved in the so-called private multiplicative weights (PMW) mechanism by Hardt and Rothblum [30]. The main result is achieving a running time only linear in N (for each of the k queries), nearly tight with previous cryptographic hardness results [32], while the error scales roughly as 1/ .log k. Moreover, the proposed mechanism makes partial progress for side-stepping previous negative results [32] by relaxing the utility requirement.…”

“…They showed that in order to achieve privacy against a polynomially bounded adversary, one has to add perturbation of magnitude Ω( ). Large numbers of queries in interactive setting were revisited in recent studies [29,30].…”

“…The main result is achieving a running time only linear in N (for each of the k queries), nearly tight with previous cryptographic hardness results [32], while the error scales roughly as 1/ .log k. Moreover, the proposed mechanism makes partial progress for side-stepping previous negative results [32] by relaxing the utility requirement. Specifically, Hardt and Rothblum [30] considered accuracy guarantees for the class of pseudo-smooth databases with sublinear (or even polylogarithmic) running time. The main idea of PMW is to use a privacy-preserving multiplicative weights mechanism.…”

Privacy and Data-Based Research

“…This substantial literature, beginning with Blum, Ligett and Roth (2008) and continuing most recently with Hardt and Rothblum (2010) and Hardt, Ligett and McSherry (2012), develops techniques for generating "synthetic data"-a set of valid database rows-that approximate the correct answers to all of a large, fixed set of queries. The techniques go far beyond simply perturbing the data, involving ideas from geometry and computational learning theory; individual records in the resulting synthetic data are artificially generated in a sophisticated manner and cannot be connected with a single or small number of records in the original data.…”