Private Multivariate

Private multivariate median estimation focuses on developing algorithms that compute robust location estimates from datasets while guaranteeing differential privacy, protecting individual data points. Current research explores various depth-based medians (e.g., Tukey, spatial, integrated dual depth) and employs mechanisms like propose-test-release and the exponential mechanism to achieve privacy. These methods aim to provide strong finite-sample guarantees and address challenges posed by heavy-tailed distributions and high dimensionality, improving the robustness and privacy of statistical analyses in sensitive applications.