# Universal Private Estimators

arXiv: https://arxiv.org/abs/2111.02598 · HTML: https://mlsanity.com/paper/2111.02598/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2021.

## Built on by (most cited first, 3 of 3)

- [Private and polynomial time algorithms for learning Gaussians and beyond](https://mlsanity.com/paper/2111.11320/) (2021)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Differentially Private Covariance Revisited](https://mlsanity.com/paper/2205.14324/) (2022)

## Abstract (arXiv)

We present textituniversal estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary, unknown continuous distribution P over ℝ, while yielding strong utility guarantees except for ill-behaved P. For certain distribution families like Gaussians or heavy-tailed distributions, we show that our universal estimators match or improve existing estimators, which are often specifically designed for the given family and under textita priori boundedness assumptions on the mean and variance of P. This is the first time these boundedness assumptions are removed under pure differential privacy. The main technical tools in our development are instance-optimal empirical estimators for the mean and quantiles over the unbounded integer domain, which can be of independent interest.