Instance-Optimal Private Density Estimation in the Wasserstein Distance

arXiv:2406.19566v1 Announce Type: cross
Abstract: Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating population densities in a geographic region, a small Wasserstein distance means that the estimate is able to capture roughly where the population mass is. In this work we study differentially private density estimation in the Wasserstein distance. We design and analyze instance-optimal …

arxiv cs.cr cs.ds cs.lg distribution error instance math.st metric private problem settings statistics stat.ml stat.th