Strong Privacy and Utility Guarantee: Over-the-Air Statistical Estimation

TL;DR

This paper introduces an over-the-air estimation method for distributed data privacy that leverages the Gaussian MAC channel's additive property, achieving strong privacy guarantees with minimal estimation error.

Contribution

It proposes a novel over-the-air estimation scheme that maintains privacy without sacrificing utility, outperforming digital methods in terms of error reduction.

Findings

Privacy bounds are derived using mutual information.

The scheme guarantees strong privacy with low estimation error.

Minimax error decreases as 1/n, showing improved performance.

Abstract

We consider the privacy problem of statistical estimation from distributed data, where users communicate to a central processor over a Gaussian multiple-access channel(MAC). To avoid the inevitable sacrifice of data utility for privacy in digital transmission schemes, we devise an over-the-air estimation strategy which utilizes the additive nature of MAC channel. Using the mutual information between the channel outputs and users' data as the metric, we obtain the privacy bounds for our scheme and validate that it can guarantee strong privacy without incurring larger estimation error. Further, to increase the robustness of our methods, we adjust our primary schemes by adding Gaussian noises locally and derive the corresponding minimax mean squared error under conditional mutual information constraints. Comparing the performance of our methods to the digital ones, we show that the minimax error decreases by $O(\frac{1}{n})$ in general, which suggests the advantages of over-the-air estimation for preserving data privacy and utility.