# Privacy with Estimation Guarantees

arXiv: https://arxiv.org/abs/1710.00447 · HTML: https://mlsanity.com/paper/1710.00447/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2017.

## Built on by (most cited first, 4 of 4)

- [Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees](https://mlsanity.com/paper/2204.09938/) (2022)
- [Summary Statistic Privacy in Data Sharing](https://mlsanity.com/paper/2303.02014/) (2023)
- [Fundamental Limits of Perfect Concept Erasure](https://mlsanity.com/paper/2503.20098/) (2025)
- [Quantum algorithms for SVD-based data representation and analysis](https://mlsanity.com/paper/2104.08987/) (2021)

## Abstract (arXiv)

We study the central problem in data privacy: how to share data with an analyst while providing both privacy and utility guarantees to the user that owns the data. In this setting, we present an estimation-theoretic analysis of the privacy-utility trade-off (PUT). Here, an analyst is allowed to reconstruct (in a mean-squared error sense) certain functions of the data (utility), while other private functions should not be reconstructed with distortion below a certain threshold (privacy). We demonstrate how chi-square information captures the fundamental PUT in this case and provide bounds for the best PUT. We propose a convex program to compute privacy-assuring mappings when the functions to be disclosed and hidden are known a priori and the data distribution is known. We derive lower bounds on the minimum mean-squared error of estimating a target function from the disclosed data and evaluate the robustness of our approach when an empirical distribution is used to compute the privacy-assuring mappings instead of the true data distribution. We illustrate the proposed approach through two numerical experiments.