Robust Estimation for Random Graphs

• URL: http://arxiv.org/abs/2111.05320v1
• Date: Tue, 9 Nov 2021 18:43:25 GMT
• Title: Robust Estimation for Random Graphs
• Authors: Jayadev Acharya, Ayush Jain, Gautam Kamath, Ananda Theertha Suresh, Huanyu Zhang
• Abstract summary: We study the problem of robustly estimating the parameter $p$ of an ErdHos-R'enyi random graph on $n$ nodes. We give an inefficient algorithm with similar accuracy for all $gamma 1/2$, the information-theoretic limit.
• Score: 47.07886511972046
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the problem of robustly estimating the parameter $p$ of an Erd\H{o}s-R\'enyi random graph on $n$ nodes, where a $\gamma$ fraction of nodes may be adversarially corrupted. After showing the deficiencies of canonical estimators, we design a computationally-efficient spectral algorithm which estimates $p$ up to accuracy $\tilde O(\sqrt{p(1-p)}/n + \gamma\sqrt{p(1-p)} /\sqrt{n}+ \gamma/n)$ for $\gamma < 1/60$. Furthermore, we give an inefficient algorithm with similar accuracy for all $\gamma <1/2$, the information-theoretic limit. Finally, we prove a nearly-matching statistical lower bound, showing that the error of our algorithms is optimal up to logarithmic factors.

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