# Privacy utility trade offs for parameter estimation in degree heterogeneous higher order networks

arXiv: https://arxiv.org/abs/2602.03948 · HTML: https://mlsanity.com/paper/2602.03948/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 50 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 21 of 21)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Differentially Private Assouad, Fano, and Le Cam](https://mlsanity.com/paper/2004.06830/) (2020)
- [Uncertainty quantification in the Bradley-Terry-Luce model](https://mlsanity.com/paper/2110.03874/) (2021)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Private estimation algorithms for stochastic block models and mixture models](https://mlsanity.com/paper/2301.04822/) (2023)
- [Optimal Full Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2101.08421/) (2021)
- [Detecting Communities under Differential Privacy](https://mlsanity.com/paper/1607.02060/) (2016)
- [β models for random hypergraphs with a given degree sequence](https://mlsanity.com/paper/1407.1004/) (2014)
- [Graph-based Clustering under Differential Privacy](https://mlsanity.com/paper/1803.03831/) (2018)
- [A Sparse Beta Regression Model for Network Analysis](https://mlsanity.com/paper/2010.13604/) (2020)
- [PriME: Privacy-aware Membership profile Estimation in networks](https://mlsanity.com/paper/2406.02794/) (2024)
- [Analysis of Networks via the Sparse β-Model](https://mlsanity.com/paper/1908.03152/) (2019)
- [Edge differentially private estimation in the β-model via jittering and method of moments](https://mlsanity.com/paper/2112.10151/) (2021)
- [Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph boldsymbolβ-Model](https://mlsanity.com/paper/2307.02818/) (2023)
- [Time-varying β-model for dynamic directed networks](https://mlsanity.com/paper/2304.02421/) (2023)
- [Modelling Directed Networks with Reciprocity](https://mlsanity.com/paper/2411.12871/) (2024)
- [Optimal Differentially Private Ranking from Pairwise Comparisons](https://mlsanity.com/paper/2507.09388/) (2025)
- [Regression Analysis of Reciprocity in Directed Networks](https://mlsanity.com/paper/2507.21469/) (2025)

## Abstract (arXiv)

In sensitive applications involving relational datasets, protecting information about individual links from adversarial queries is of paramount importance. In many such settings, the available data are summarized solely through the degrees of the nodes in the network. We adopt the β model, which is the prototypical statistical model adopted for this form of aggregated relational information, and study the problem of minimax-optimal parameter estimation under both local and central differential privacy constraints. We establish finite sample minimax lower bounds that characterize the precise dependence of the estimation risk on the network size and the privacy parameters, and we propose simple estimators that achieve these bounds up to constants and logarithmic factors under both local and central differential privacy frameworks. Our results provide the first comprehensive finite sample characterization of privacy utility trade offs for parameter estimation in β models, addressing the classical graph case and extending the analysis to higher order hypergraph models. We further demonstrate the effectiveness of our methods through experiments on synthetic data and a real world communication network.