The Wasserstein Projection Mechanism (WPM)

The Wasserstein Projection Mechanism (WPM) is a method for drawing samples from a data distribution while protecting individual privacy through differential privacy. It was introduced in the paper "Differentially Private Sampling from Distributions via Wasserstein Projection", published in May 2026 by Shokichi Takakura and two co-authors. Private sampling allows data that reflects sensitive information, such as a person's records, to be released as random samples without revealing individual details. Earlier methods measure how useful these samples are with density-ratio measures such as Kullback–Leibler (KL) divergence. However, such measures ignore how close or far apart data values are, and they cannot be used when the original and released data cover different sets of values.

WPM addresses these limitations by measuring usefulness with the Wasserstein distance. This measures how much "effort" it takes to turn one distribution into another, so it takes the distances between values into account. WPM projects the original distribution onto the set of distributions that satisfy the privacy guarantee, choosing the closest one in Wasserstein distance.

The authors prove that WPM is minimax optimal, meaning it gives the best possible usefulness in the worst case, and that it can be obtained by solving a convex optimisation problem. They also provide a practical algorithm for computing it approximately, with convergence guarantees. Experiments on synthetic and real-world data demonstrate its effectiveness. The work focuses on local differential privacy.

Auto-discovered on 2026-06-08 by OECD Catalogue Automation