# Two Views of Constrained Differential Privacy: Belief Revision and Update

arXiv: https://arxiv.org/abs/2303.00228 · HTML: https://mlsanity.com/paper/2303.00228/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions](https://mlsanity.com/paper/1601.03229/) (2016)
- [Bias and Variance of Post-processing in Differential Privacy](https://mlsanity.com/paper/2010.04327/) (2020)
- [Locally Differentially Private Frequency Estimation with Consistency](https://mlsanity.com/paper/1905.08320/) (2019)
- [Differential Privacy as a Causal Property](https://mlsanity.com/paper/1710.05899/) (2017)
- [Congenial Differential Privacy under Mandated Disclosure](https://mlsanity.com/paper/2008.10202/) (2020)
- [Subspace Differential Privacy](https://mlsanity.com/paper/2108.11527/) (2021)
- [Transparent Privacy is Principled Privacy](https://mlsanity.com/paper/2006.08522/) (2020)

## Built on by (most cited first, 2 of 2)

- [Isopignistic Canonical Decomposition via Belief Evolution Network](https://mlsanity.com/paper/2405.02653/) (2024)
- [On Definite Iterated Belief Revision with Belief Algebras](https://mlsanity.com/paper/2505.06505/) (2025)

## Abstract (arXiv)

In this paper, we provide two views of constrained differential private (DP) mechanisms. The first one is as belief revision. A constrained DP mechanism is obtained by standard probabilistic conditioning, and hence can be naturally implemented by Monte Carlo algorithms. The other is as belief update. A constrained DP is defined according to l2-distance minimization postprocessing or projection and hence can be naturally implemented by optimization algorithms. The main advantage of these two perspectives is that we can make full use of the machinery of belief revision and update to show basic properties for constrained differential privacy especially some important new composition properties. Within the framework established in this paper, constrained DP algorithms in the literature can be classified either as belief revision or belief update. At the end of the paper, we demonstrate their differences especially in utility in a couple of scenarios.