# Fisher information under local differential privacy

arXiv: https://arxiv.org/abs/2005.10783 · HTML: https://mlsanity.com/paper/2005.10783/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2020.

## Built on by (most cited first, 22 of 22)

- [Generalized Linear Bandits with Local Differential Privacy](https://mlsanity.com/paper/2106.03365/) (2021)
- [Privacy Amplification via Compression: Achieving the Optimal Privacy-Accuracy-Communication Trade-off in Distributed Mean Estimation](https://mlsanity.com/paper/2304.01541/) (2023)
- [Local Differential Privacy Is Equivalent to Contraction of Eγ-Divergence](https://mlsanity.com/paper/2102.01258/) (2021)
- [Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints](https://mlsanity.com/paper/2301.03566/) (2023)
- [Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.06755/) (2024)
- [Contraction of Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2210.13386/) (2022)
- [The Role of Interactivity in Structured Estimation](https://mlsanity.com/paper/2203.06870/) (2022)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [On the Statistical Complexity of Estimation and Testing under Privacy Constraints](https://mlsanity.com/paper/2210.02215/) (2022)
- [Robust Estimation of Discrete Distributions under Local Differential Privacy](https://mlsanity.com/paper/2202.06825/) (2022)
- [Continual Mean Estimation Under User-Level Privacy](https://mlsanity.com/paper/2212.09980/) (2022)
- [Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints](https://mlsanity.com/paper/2106.08597/) (2021)
- [Over-the-Air Statistical Estimation](https://mlsanity.com/paper/2103.04014/) (2021)
- [Private Statistical Estimation of Many Quantiles](https://mlsanity.com/paper/2302.06943/) (2023)
- [Locally Private Sampling with Public Data](https://mlsanity.com/paper/2411.08791/) (2024)
- [Sequential Estimation under Multiple Resources: a Bandit Point of View](https://mlsanity.com/paper/2109.14703/) (2021)
- [One-bit Submission for Locally Private Quasi-MLE: Its Asymptotic Normality and Limitation](https://mlsanity.com/paper/2202.07194/) (2022)
- [Differentially Private Online Bayesian Estimation With Adaptive Truncation](https://mlsanity.com/paper/2301.08202/) (2023)
- [Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanism](https://mlsanity.com/paper/2405.07020/) (2024)
- [Optimal Federated Learning for Functional Mean Estimation under Heterogeneous Privacy Constraints](https://mlsanity.com/paper/2412.18992/) (2024)
- [Characterizing the Accuracy-Communication-Privacy Trade-off in Distributed Stochastic Convex Optimization](https://mlsanity.com/paper/2501.03222/) (2025)
- [A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning](https://mlsanity.com/paper/2605.19813/) (2026)

## Abstract (arXiv)

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter varepsilon under local differential privacy constraints. These bounds are valid under general conditions on the distribution of the score of the statistical model, and they elucidate under which conditions the dependence on varepsilon is linear, quadratic, or exponential. We show how these inequalities imply order optimal lower bounds for private estimation for both the Gaussian location model and discrete distribution estimation for all levels of privacy varepsilon>0. We further apply these inequalities to sparse Bernoulli models and demonstrate privacy mechanisms and estimators with order-matching squared ℓ2 error.