S. Mendelson · wovepaper

collaborators

6 papers

Can we spot a fake?

Shahar Mendelson, Grigoris Paouris, Roman Vershynin

The problem of detecting fake data inspires the following seemingly simple mathematical question. Sample a data point $X$ from the standard normal distribution in $R^{n}$ . A…

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…

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…

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…

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…

Structure preservation via the Wasserstein distance

Daniel Bartl, Shahar Mendelson

We show that under minimal assumptions on a random vector $X \in R^{d}$ and with high probability, given $m$ independent copies of $X$ , the coordinate distribution of each vec…