IFML Seminar: 09/11/26 - Robust Statistical Estimators with Bounded Empirical Sensitivity

Abstract: We introduce a new measure of robustness for statistical estimators, which we call \emph{empirical sensitivity}. An estimator $\hat\theta$ has bounded empirical sensitivity if, with high probability over a dataset $X = (X_1, \dots, X_n) \sim \mathcal{D}^{\otimes n}$, for any dataset $Y$ obtained by modifying at most $\eta n$ points in $X$, we have that $\hat \theta(Y)$ is close to $\hat \theta(X)$.  

We study bounds on this quantity for the prototypical problem of Gaussian mean estimation. We prove new lower bounds, showing that for any estimator $\hat \mu$ which achieves an optimal $\ell_2$-error bound of $O(\sqrt{d/n})$, the empirical sensitivity is at least $\Omega(\eta +\sqrt{\eta d/n})$. The two terms arise due to obstructions on the mean and variance (via an Efron-Stein argument) of such an estimator. We show that this bound is tight up to logarithmic factors, by employing recent results for robust empirical mean estimation.

Based on joint work with Valentio Iverson, Gautam Kamath, and Adam Smith. The work is currently under submission, and available on arXiv.

Bio: Argyris Mouzakis joined UT-Austin as an IFML Postdoctoral Fellow in September 2026. Before that, he completed his PhD at the University of Waterloo under Gautam Kamath. His work focuses on machine learning theory, algorithmic statistics, and differential privacy. He has been awarded the David R. Cheriton and the Onassis Foundation fellowships for the support of his doctoral studies.