Daniel Bartl

collaborators

5 papers

math.PR2026

On the structure of marginals in high dimensions

Daniel Bartl, Shahar Mendelson

Let $G, G_{1}, \dots, G_{N}$ be independent copies of a standard gaussian random vector in $R^{d}$ and denote by $I^ = \sum_{i = 1}^{N} ⟨ G_{i}, \cdot ⟩ e_{i}$ the standard gauss…

math.PR2026

Uniform mean estimation via generic chaining

Daniel Bartl, Shahar Mendelson

We introduce an empirical functional $I^¨$ that is an optimal uniform mean estimator: Let $F \subset L_{2} (I^¼)$ be a class of mean zero functions, $u$ is a real valued function, and $X…

math.ST2025

Robust, sub-Gaussian mean estimators in metric spaces

Daniel Bartl, Gabor Lugosi, Roberto Imbuzeiro Oliveira +1

Estimating the mean of a random vector from i.i.d. data has received considerable attention, and the optimal accuracy one may achieve with a given confidence is fairly well underst…

math.PR2025

A uniform Dvoretzky-Kiefer-Wolfowitz inequality

Daniel Bartl, Shahar Mendelson

We show that under minimal assumptions on a class of functions $H$ defined on a probability space $(X, I^¼)$ , there is a threshold $I^_{0}$ satisfying the following…

math.ST2025

Do we really need the Rademacher complexities?

Daniel Bartl, Shahar Mendelson

We study the fundamental problem of learning with respect to the squared loss in a convex class. The state-of-the-art sample complexity estimates in this setting rely on Rademacher…