Daniel Bartl

activity

20232026

collaborators

7 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 $Γ = \sum_{i = 1}^{N} ⟨ G_{i}, \cdot ⟩ e_{i}$ the standard gaussi…

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.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…

math.PR2025

Uniform mean estimation via generic chaining

Daniel Bartl, Shahar Mendelson

We introduce an empirical functional $Ψ$ that is an optimal uniform mean estimator: Let $F \subset L_{2} (μ)$ be a class of mean zero functions, $u$ is a real valued function, and $X_1…

math.PR2023

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 $(X, μ)$ , there is a threshold $Δ_{0}$ satisfying the following:…

math.FA2023

Optimal non-gaussian Dvoretzky-Milman embeddings

Daniel Bartl, Shahar Mendelson

We construct the first non-gaussian ensemble that yields the optimal estimate in the Dvoretzky-Milman Theorem: the ensemble exhibits almost Euclidean sections in arbitrary normed s…

math.PR2023

Empirical approximation of the gaussian distribution in $R^{d}$

Daniel Bartl, Shahar Mendelson

Let $G_{1}, \dots, G_{m}$ be independent copies of the standard gaussian random vector in $R^{d}$ . We show that there is an absolute constant $c$ such that for any $A \subset S^{d…

On the structure of marginals in high dimensions

Robust, sub-Gaussian mean estimators in metric spaces

Do we really need the Rademacher complexities?

Uniform mean estimation via generic chaining

A uniform Dvoretzky-Kiefer-Wolfowitz inequality

Optimal non-gaussian Dvoretzky-Milman embeddings

Empirical approximation of the gaussian distribution in Rd

Empirical approximation of the gaussian distribution in $R^{d}$