Differentially private multivariate medians

arXiv:2210.06459v2 Announce Type: replace-cross
Abstract: Statistical tools which satisfy rigorous privacy guarantees are necessary for modern data analysis. It is well-known that robustness against contamination is linked to differential privacy. Despite this fact, using multivariate medians for differentially private and robust multivariate location estimation has not been systematically studied. We develop novel finite-sample performance guarantees for differentially private multivariate depth-based medians, which are essentially sharp. Our results cover commonly used depth functions, such as the halfspace (or Tukey) depth, spatial …

abstract analysis arxiv cs.cr cs.lg data data analysis differential differential privacy location math.st modern multivariate novel performance privacy robust robustness sample statistical stat.ml stat.th tools type