# Differentially Private Hierarchical Count-of-Counts Histograms

arXiv: https://arxiv.org/abs/1804.00370 · HTML: https://mlsanity.com/paper/1804.00370/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2018.

## Built on by (most cited first, 4 of 4)

- [Private Convex Optimization via Exponential Mechanism](https://mlsanity.com/paper/2203.00263/) (2022)
- [ResidualPlanner+: a scalable matrix mechanism for marginals and beyond](https://mlsanity.com/paper/2305.08175/) (2023)
- [Optimal Allocation of Privacy Budget on Hierarchical Data Release](https://mlsanity.com/paper/2505.10871/) (2025)
- [An exponential mechanism based on quadratic approximations for fine-tuning machine learning models with privacy guarantees](https://mlsanity.com/paper/2605.20521/) (2026)

## Abstract (arXiv)

We consider the problem of privately releasing a class of queries that we call hierarchical count-of-counts histograms. Count-of-counts histograms partition the rows of an input table into groups (e.g., group of people in the same household), and for every integer j report the number of groups of size j. Hierarchical count-of-counts queries report count-of-counts histograms at different granularities as per hierarchy defined on an attribute in the input data (e.g., geographical location of a household at the national, state and county levels). In this paper, we introduce this problem, along with appropriate error metrics and propose a differentially private solution that generates count-of-counts histograms that are consistent across all levels of the hierarchy.