Year: 2021
Type: preprint
Abstract: We study the problem of robustly estimating the parameter $p$ of an Erdős-Rényi random graph on $n$ nodes, where a $γ$ 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 $\tilde O(\sqrt{p(1-p)}/n + γ\sqrt{p(1-p)} /\sqrt{n}+ γ/n)$ for $γ< 1/60$. Furthermore, we give an inefficient algorithm with similar accuracy for all $γ<1/2$, 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.
Source: arXiv (Cornell University)
Authors: Acharya, Jayadev, Jain, Ayush, Kamath, Gautam, Suresh, Ananda Theertha, Zhang, Huanyu
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: CIF: Medium: Collaborative Research: Learning in High Dimensions: From Theory to Data and Back, CAREER: Statistical Inference Under Information Constraints: Efficient Algorithms and Fundamental Limits, CIF: SMALL: Information Theoretic Foundations of Data Science, G6671297155, CIF: Small: Learning Quantum Information Measures
OpenAlex ID: W3214109067