Adaptive Mechanism for Locally Differential Private Mean Estimation

Core Concepts

The proposed advanced adaptive additive (AAA) mechanism is a distribution-aware approach that addresses the average utility and tackles the classical mean estimation problem under local differential privacy constraints.

Abstract

The paper proposes the advanced adaptive additive (AAA) mechanism, which is a distribution-aware approach for locally differential private mean estimation. The key insights are:

Existing solutions for mean estimation under local differential privacy (LDP) focus on improving the worst-case guarantee, but this does not necessarily promise better average performance given the fact that the data in practice obey a certain distribution.

AAA addresses this issue through a two-phase approach:

In the first phase, the data aggregator selects a random subset of individuals to compute a (noisy) quantized data descriptor.
In the second phase, the remaining individuals submit data perturbed in a distribution-aware fashion, by solving an optimization problem formulated with the data descriptor obtained in the first phase.

The perturbation noise in the second phase of AAA has a distribution that depends on the value of the sensitive data, in contrast to classic approaches where the noise is independent of the input. This allows AAA to optimize the average-case utility.

Rigorous privacy proofs and utility analyses are provided for AAA. Extensive experiments demonstrate that AAA consistently outperforms existing solutions by a wide margin in terms of result utility, on a wide range of privacy constraints and real-world and synthetic datasets.

Stats

The variance of the output in Duchi's mechanism reaches its worst case when the input x = 0.
The worst case of the piecewise mechanism (PM) occurs when the absolute value of x is large.

Quotes

None

Key Insights Distilled From

AAA

by Fei Wei,Ergu... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2404.01625.pdf

Deeper Inquiries

How can the proposed AAA mechanism be extended to handle multi-dimensional data beyond the one-dimensional case considered in this paper

The proposed AAA mechanism can be extended to handle multi-dimensional data by applying the same principles used for one-dimensional data to each dimension. One approach is to randomly partition the clients into subsets, with each subset reporting one of the dimensions. This reduces the multi-dimensional data to one-dimensional data, allowing the AAA mechanism to be applied. Additionally, the quantization and distribution estimation steps can be adapted to handle multi-dimensional data by considering each dimension separately and then combining the results.

What are the potential limitations or drawbacks of the distribution-aware approach used in AAA, and how can they be addressed

One potential limitation of the distribution-aware approach used in AAA is the computational complexity involved in estimating the global data distribution and optimizing the perturbation mechanism. This can be addressed by using more efficient algorithms for distribution estimation and optimization. Additionally, the discretization of the optimization problem may lead to loss of information, so techniques like smoothing or interpolation can be applied to mitigate this issue. Furthermore, the choice of parameters such as the quantization constant and the geometric constant in the conditional distribution can impact the performance of the mechanism, so careful tuning and sensitivity analysis are necessary.

How can the insights from the AAA mechanism be applied to other fundamental problems in local differential privacy beyond mean estimation

The insights from the AAA mechanism can be applied to other fundamental problems in local differential privacy beyond mean estimation by adapting the optimization framework to suit the specific task. For example, for tasks like frequency estimation or heavy hitters identification, the objective function and constraints in the optimization problem can be modified to reflect the requirements of the task. The distribution-aware approach can be generalized to different types of data distributions and utility metrics, allowing for a more tailored and effective solution in various scenarios. Additionally, the two-step approach of distribution estimation and perturbation can be applied to different types of data analysis tasks to improve result utility while maintaining privacy guarantees.