# Differentially Private Learning of Undirected Graphical Models using Collective Graphical Models

arXiv: https://arxiv.org/abs/1706.04646 · HTML: https://mlsanity.com/paper/1706.04646/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2017.

## Built on by (most cited first, 6 of 6)

- [Differentially Private Quantiles](https://mlsanity.com/paper/2102.08244/) (2021)
- [Noise-Aware Statistical Inference with Differentially Private Synthetic Data](https://mlsanity.com/paper/2205.14485/) (2022)
- [DP-CDA: An Algorithm for Enhanced Privacy Preservation in Dataset Synthesis Through Randomized Mixing](https://mlsanity.com/paper/2411.16121/) (2024)
- [Learning from aggregated data with a maximum entropy model](https://mlsanity.com/paper/2210.02450/) (2022)
- [Data Analytics with Differential Privacy](https://mlsanity.com/paper/2311.16104/) (2023)
- [Enhancing Differentially Private Mechanisms via Empirical Bayes](https://mlsanity.com/paper/2606.21107/) (2026)

## Abstract (arXiv)

We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the noisy sufficient statistics "as is" outperforms general-purpose differentially private learning algorithms. However, it has three limitations: it ignores knowledge about the data generating process, rests on uncertain theoretical foundations, and exhibits certain pathologies. We develop a more principled approach that applies the formalism of collective graphical models to perform inference over the true sufficient statistics within an expectation-maximization framework. We show that this learns better models than competing approaches on both synthetic data and on real human mobility data used as a case study.