arXiv subjects

Argyris Mouzakis

Publications and source records attributed to Argyris Mouzakis.

7 recordsLinked to original sources

arXiv2026

Robust Statistical Estimators with Bounded Empirical Sensitivity

We introduce a new measure of robustness for statistical estimators, which we call \emph{empirical sensitivity}. An estimator $\hat θ$ 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 $ηn$ points in $X$, we have that $\hat θ(Y)$ is close to $\hat θ(X)$. We study bounds on this quantity for the prototypical problem of Gaussian mean estimation. We prove new lower bounds, showing that for any estimator $\hat μ$ which achieves an optimal $\ell_2$-error bound of $O\left(\sqrt{d/n}\right)$, the empirical sensitivity is at least $Ω\left(η+ \sqrt{ηd/n}\right)$. 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.

math.ST↗

arXiv2026

Not All Learnable Distribution Classes are Privately Learnable

We give an example of a class of distributions that is learnable up to constant error in total variation distance with a finite number of samples, but not learnable under $(\varepsilon, δ)$-differential privacy with the same target error. This weakly refutes a conjecture of Ashtiani.

cs.DS↗

arXiv2025

Optimal Differentially Private Sampling of Unbounded Gaussians

We provide the first $\widetilde{\mathcal{O}}\left(d\right)$-sample algorithm for sampling from unbounded Gaussian distributions under the constraint of $\left(\varepsilon, δ\right)$-differential privacy. This is a quadratic improvement over previous results for the same problem, settling an open question of Ghazi, Hu, Kumar, and Manurangsi.

cs.DS↗

arXiv2024

A Bias-Accuracy-Privacy Trilemma for Statistical Estimation

Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their empirical mean. Clipping controls the sensitivity and, hence, the variance of the noise that we add for privacy. But clipping also introduces statistical bias. This tradeoff is inherent: we prove that no algorithm can simultaneously have low bias, low error, and low privacy loss for arbitrary distributions. Additionally, we show that under strong notions of DP (i.e., pure or concentrated DP), unbiased mean estimation is impossible, even if we assume that the data is sampled from a Gaussian. On the positive side, we show that unbiased mean estimation is possible under a more permissive notion of differential privacy (approximate DP) if we assume that the distribution is symmetric.

math.ST↗

arXiv2024

Private Mean Estimation with Person-Level Differential Privacy

We study person-level differentially private (DP) mean estimation in the case where each person holds multiple samples. DP here requires the usual notion of distributional stability when $\textit{all}$ of a person's datapoints can be modified. Informally, if $n$ people each have $m$ samples from an unknown $d$-dimensional distribution with bounded $k$-th moments, we show that \[n = \tilde Θ\left(\frac{d}{α^2 m} + \frac{d}{αm^{1/2} \varepsilon} + \frac{d}{α^{k/(k-1)} m \varepsilon} + \frac{d}{\varepsilon}\right)\] people are necessary and sufficient to estimate the mean up to distance $α$ in $\ell_2$-norm under $\varepsilon$-differential privacy (and its common relaxations). In the multivariate setting, we give computationally efficient algorithms under approximate-DP and computationally inefficient algorithms under pure DP, and our nearly matching lower bounds hold for the most permissive case of approximate DP. Our computationally efficient estimators are based on the standard clip-and-noise framework, but the analysis for our setting requires both new algorithmic techniques and new analyses. In particular, our new bounds on the tails of sums of independent, vector-valued, bounded-moments random variables may be of interest.

cs.DS↗

arXiv2023

New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma

We prove new lower bounds for statistical estimation tasks under the constraint of $(\varepsilon, δ)$-differential privacy. First, we provide tight lower bounds for private covariance estimation of Gaussian distributions. We show that estimating the covariance matrix in Frobenius norm requires $Ω(d^2)$ samples, and in spectral norm requires $Ω(d^{3/2})$ samples, both matching upper bounds up to logarithmic factors. The latter bound verifies the existence of a conjectured statistical gap between the private and the non-private sample complexities for spectral estimation of Gaussian covariances. We prove these bounds via our main technical contribution, a broad generalization of the fingerprinting method to exponential families. Additionally, using the private Assouad method of Acharya, Sun, and Zhang, we show a tight $Ω(d/(α^2 \varepsilon))$ lower bound for estimating the mean of a distribution with bounded covariance to $α$-error in $\ell_2$-distance. Prior known lower bounds for all these problems were either polynomially weaker or held under the stricter condition of $(\varepsilon, 0)$-differential privacy.

cs.DS↗

arXiv2022

A Private and Computationally-Efficient Estimator for Unbounded Gaussians

We give the first polynomial-time, polynomial-sample, differentially private estimator for the mean and covariance of an arbitrary Gaussian distribution $\mathcal{N}(μ,Σ)$ in $\mathbb{R}^d$. All previous estimators are either nonconstructive, with unbounded running time, or require the user to specify a priori bounds on the parameters $μ$ and $Σ$. The primary new technical tool in our algorithm is a new differentially private preconditioner that takes samples from an arbitrary Gaussian $\mathcal{N}(0,Σ)$ and returns a matrix $A$ such that $A ΣA^T$ has constant condition number.

stat.ML↗