# Private Means and the Curious Incident of the Free Lunch

arXiv: https://arxiv.org/abs/2408.10438 · HTML: https://mlsanity.com/paper/2408.10438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [Refined Differentially Private Linear Regression via Extension of a Free Lunch Result](https://mlsanity.com/paper/2604.11820/) (2026)

## Abstract (arXiv)

We show that the most well-known and fundamental building blocks of DP implementations -- sum, mean, count (and many other linear queries) -- can be released with substantially reduced noise for the same privacy guarantee. We achieve this by projecting individual data with worst-case sensitivity R onto a simplex where all data now has a constant norm R. In this simplex, additional ``free'' queries can be run that are already covered by the privacy-loss of the original budgeted query, and which algebraically give additional estimates of counts or sums.