# Does Privacy Always Harm Fairness? Data-Dependent Trade-offs via Chernoff Information Neural Estimation

arXiv: https://arxiv.org/abs/2601.13698 · HTML: https://mlsanity.com/paper/2601.13698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 30 of 30)

- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Scalable Private Learning with PATE](https://mlsanity.com/paper/1802.08908/) (2018)
- [Easily Accessible Text-to-Image Generation Amplifies Demographic Stereotypes at Large Scale](https://mlsanity.com/paper/2211.03759/) (2022)
- [Fair Diffusion: Instructing Text-to-Image Generation Models on Fairness](https://mlsanity.com/paper/2302.10893/) (2023)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [On the Privacy Risks of Algorithmic Fairness](https://mlsanity.com/paper/2011.03731/) (2020)
- [Differentially Private Fair Learning](https://mlsanity.com/paper/1812.02696/) (2018)
- [Differentially Private Representation for NLP: Formal Guarantee and An Empirical Study on Privacy and Fairness](https://mlsanity.com/paper/2010.01285/) (2020)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Differential Privacy and Fairness in Decisions and Learning Tasks: A Survey](https://mlsanity.com/paper/2202.08187/) (2022)
- [Decision Making with Differential Privacy under a Fairness Lens](https://mlsanity.com/paper/2105.07513/) (2021)
- [A Stochastic Optimization Framework for Fair Risk Minimization](https://mlsanity.com/paper/2102.12586/) (2021)
- [Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values](https://mlsanity.com/paper/2109.10431/) (2021)
- [Differentially Private Empirical Risk Minimization with Input Perturbation](https://mlsanity.com/paper/1710.07425/) (2017)
- [Differential Privacy has Bounded Impact on Fairness in Classification](https://mlsanity.com/paper/2210.16242/) (2022)
- [Fairness in Supervised Learning: An Information Theoretic Approach](https://mlsanity.com/paper/1801.04378/) (2018)
- [To Split or Not to Split: The Impact of Disparate Treatment in Classification](https://mlsanity.com/paper/2002.04788/) (2020)
- [Not one but many Tradeoffs: Privacy Vs. Utility in Differentially Private Machine Learning](https://mlsanity.com/paper/2008.08807/) (2020)
- [DP-UTIL: Comprehensive Utility Analysis of Differential Privacy in Machine Learning](https://mlsanity.com/paper/2112.12998/) (2021)
- [Input Perturbation: A New Paradigm between Central and Local Differential Privacy](https://mlsanity.com/paper/2002.08570/) (2020)
- [Differentially Private Fair Binary Classifications](https://mlsanity.com/paper/2402.15603/) (2024)

## Abstract (arXiv)

Fairness and privacy are two vital pillars of trustworthy machine learning. Despite extensive research on these individual topics, their relationship has received significantly less attention. In this paper, we utilize an information-theoretic measure Chernoff Information to characterize the fundamental trade-off between fairness, privacy, and accuracy, as induced by the input data distribution. We first propose Chernoff Difference, a notion of data fairness, along with its noisy variant, Noisy Chernoff Difference, which allows us to analyze both fairness and privacy simultaneously. Through simple Gaussian examples, we show that Noisy Chernoff Difference exhibits three qualitatively distinct behaviors depending on the underlying data distribution. To extend this analysis beyond synthetic settings, we develop the Chernoff Information Neural Estimator (CINE), the first neural network-based estimator of Chernoff Information for unknown distributions. We apply CINE to analyze the Noisy Chernoff Difference on real-world datasets. Together, this work fills a critical gap in the literature by providing a principled, data-dependent characterization of the fairness-privacy interaction.