# Information Extraction Under Privacy Constraints

arXiv: https://arxiv.org/abs/1511.02381 · HTML: https://mlsanity.com/paper/1511.02381/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2015.

## Built on by (most cited first, 9 of 9)

- [Bottlenecks CLUB: Unifying Information-Theoretic Trade-offs Among Complexity, Leakage, and Utility](https://mlsanity.com/paper/2207.04895/) (2022)
- [On the Asymptotic Mean Square Error Optimality of Diffusion Models](https://mlsanity.com/paper/2403.02957/) (2024)
- [Summary Statistic Privacy in Data Sharing](https://mlsanity.com/paper/2303.02014/) (2023)
- [Lossy Compression of Noisy Data for Private and Data-Efficient Learning](https://mlsanity.com/paper/2202.02892/) (2022)
- [Classification Utility, Fairness, and Compactness via Tunable Information Bottleneck and R'enyi Measures](https://mlsanity.com/paper/2206.10043/) (2022)
- [Deep Privacy Funnel Model: From a Discriminative to a Generative Approach with an Application to Face Recognition](https://mlsanity.com/paper/2404.02696/) (2024)
- [Lower Bounds on the MMSE of Adversarially Inferring Sensitive Features](https://mlsanity.com/paper/2505.09004/) (2025)
- [Minimax Quantile Lower Bounds for Interactive Statistical Decision Making with Privacy](https://mlsanity.com/paper/2606.23096/) (2026)
- [Information Bottleneck under Perfect Privacy](https://mlsanity.com/paper/2608.11003/) (2026)

## Abstract (arXiv)

A privacy-constrained information extraction problem is considered where for a pair of correlated discrete random variables (X,Y) governed by a given joint distribution, an agent observes Y and wants to convey to a potentially public user as much information about Y as possible without compromising the amount of information revealed about X. To this end, the so-called em rate-privacy function is introduced to quantify the maximal amount of information (measured in terms of mutual information) that can be extracted from Y under a privacy constraint between X and the extracted information, where privacy is measured using either mutual information or maximal correlation. Properties of the rate-privacy function are analyzed and information-theoretic and estimation-theoretic interpretations of it are presented for both the mutual information and maximal correlation privacy measures. It is also shown that the rate-privacy function admits a closed-form expression for a large family of joint distributions of (X,Y). Finally, the rate-privacy function under the mutual information privacy measure is considered for the case where (X,Y) has a joint probability density function by studying the problem where the extracted information is a uniform quantization of Y corrupted by additive Gaussian noise. The asymptotic behavior of the rate-privacy function is studied as the quantization resolution grows without bound and it is observed that not all of the properties of the rate-privacy function carry over from the discrete to the continuous case.