# The Bounded Laplace Mechanism in Differential Privacy

arXiv: https://arxiv.org/abs/1808.10410 · HTML: https://mlsanity.com/paper/1808.10410/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2018.

## Built on by (most cited first, 13 of 13)

- [Echo of Neighbors: Privacy Amplification for Personalized Private Federated Learning with Shuffle Model](https://mlsanity.com/paper/2304.05516/) (2023)
- [Holistic Survey of Privacy and Fairness in Machine Learning](https://mlsanity.com/paper/2307.15838/) (2023)
- [De-Identification of French Unstructured Clinical Notes for Machine Learning Tasks](https://mlsanity.com/paper/2209.09631/) (2022)
- [Private and Utility Enhanced Recommendations with Local Differential Privacy and Gaussian Mixture Model](https://mlsanity.com/paper/2102.13453/) (2021)
- [Learning Numeric Optimal Differentially Private Truncated Additive Mechanisms](https://mlsanity.com/paper/2107.12957/) (2021)
- [Privacy Amplification for the Gaussian Mechanism via Bounded Support](https://mlsanity.com/paper/2403.05598/) (2024)
- [Multi-Task Model Personalization for Federated Supervised SVM in Heterogeneous Networks](https://mlsanity.com/paper/2303.10254/) (2023)
- [Privacy Preserving Reinforcement Learning for Population Processes](https://mlsanity.com/paper/2406.17649/) (2024)
- [PLRV-O: Advancing Differentially Private Deep Learning via Privacy Loss Random Variable Optimization](https://mlsanity.com/paper/2509.06264/) (2025)
- [Distributed Transition Systems with Tags for Privacy Analysis](https://mlsanity.com/paper/2204.02602/) (2022)
- [Fast, Distribution-free Predictive Inference for Neural Networks with Coverage Guarantees](https://mlsanity.com/paper/2306.06582/) (2023)
- [Differentially Private Federated Learning without Noise Addition: When is it Possible?](https://mlsanity.com/paper/2405.04551/) (2024)
- [Lap2: Revisiting Laplace DP-SGD for High Dimensions via Majorization Theory](https://mlsanity.com/paper/2602.23516/) (2026)

## Abstract (arXiv)

The Laplace mechanism is the workhorse of differential privacy, applied to many instances where numerical data is processed. However, the Laplace mechanism can return semantically impossible values, such as negative counts, due to its infinite support. There are two popular solutions to this: (i) bounding/capping the output values and (ii) bounding the mechanism support. In this paper, we show that bounding the mechanism support, while using the parameters of the pure Laplace mechanism, does not typically preserve differential privacy. We also present a robust method to compute the optimal mechanism parameters to achieve differential privacy in such a setting.