Research

We study the problem of robustly estimating the parameter pof 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 Õ (√ p(1 − p) / n + γ √ p(1 − p) / √ 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.