Efficient and Private Mean Estimation with ProjUnit: Low Complexity, Optimal Error

Introducing the ProjUnit Algorithmic Framework for Private Mean Estimation

The problem of locally private mean estimation of high-dimensional vectors in the Euclidean ball is a challenging one. Existing algorithms either don’t perform well or have high communication and run-time complexity. But now, a new algorithmic framework called ProjUnit has been proposed that aims to solve these issues.

What is ProjUnit and How Does it Work?

The ProjUnit framework is designed to tackle the issue of private mean estimation by using a simple approach. Each randomizer in the framework projects its input to a random low-dimensional subspace, normalizes the result, and then runs an optimal algorithm in the lower-dimensional space.

Why ProjUnit Stands Out

The algorithms produced by ProjUnit are computationally efficient, have low communication complexity, and incur optimal error up to a 1+o(1)-factor. By appropriately correlating the random projection matrices across devices, fast server run-time can also be achieved.

The Results

Mathematical analysis of the error of the algorithm in terms of properties of the random projections has been conducted, along with the study of two instantiations. Experiments for private mean estimation and private federated learning have shown that the algorithms obtain nearly the same utility as optimal ones, while having significantly lower communication and computational cost.

In conclusion, the ProjUnit algorithmic framework presents a promising solution to the problem of private mean estimation in high-dimensional vectors. This new approach offers computational efficiency, low communication complexity, and optimal error performance.

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