@inproceedings{
chen2024private,
title={Private Edge Density Estimation for Random Graphs: Optimal, Efficient and Robust},
author={Hongjie Chen and Jingqiu Ding and Yiding Hua and David Steurer},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=4NQ24cHnOi}
}
We give the first polynomial-time, differentially node-private, and robust algorithm for estimating the edge density of Erdős-Rényi random graphs and their generalization, inhomogeneous random graphs. We further prove information-theoretical lower bounds, showing that the error rate of our algorithm is optimal up to logarithmic factors. Previous algorithms incur either exponential running time or suboptimal error rates.

Two key ingredients of our algorithm are (1) a new sum-of-squares algorithm for robust edge density estimation, and (2) the reduction from privacy to robustness based on sum-of-squares exponential mechanisms due to Hopkins et al. (STOC 2023).
Private Edge Density Estimation for Random Graphs: Optimal, Efficient and Robust
Hongjie Chen Jingqiu Ding Yiding Hua David Steurer