Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, April 10, 2025, 12:15 pm

Duration: 30 minutes

Location: OAT S15

Speaker: Hongjie Chen

Private and Robust Estimation for Random Graphs

The Erdös-Rényi model is (perhaps) the most basic model of network data. Consider the statistical task of edge density estimation for Erdös-Rényi random graphs: Given an n-node graph where each edge is present independently with an unknown probability d/n, estimate the parameter d. It is well-known that the empirical average degree estimates d up to an additive error O(sqrt{d/n}). Moreover, this simple estimator achieves the optimal error guarantee among all estimators, including those computationally inefficient ones. Modern data applications necessitate more properties of estimators in addition to accuracy, such as differential privacy and robustness to data corruptions. In both settings, prior to our work, known estimators incur exponential running time and/or suboptimal error guarantees. In this talk, I will present our polynomial-time estimators with (nearly) optimal error guarantees in both settings, and how we achieve this by exploiting the intimate connection between differential privacy and robustness. Based on joint works with Jingqiu Ding, Yiding Hua, David Steurer, and Stefan Tiegel (https://arxiv.org/abs/2405.16663 and https://arxiv.org/abs/2503.03923).

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