E. Putterman

collaborators

6 papers

math.MG2026

Sharp stability for the (B)-theorem

Eli Putterman

The (B)-theorem of Cordero-Erausquin, Fradelizi and Maurey states that if $γ$ is the standard Gaussian in $R^{n}$ , $K \subset R^{n}$ is an origin-symmetric convex set,…

math.MG2026

On unbalanced difference bodies and Godbersen's conjecture

Shiri Artstein-Avidan, Eli Putterman

The longstanding Godbersen's conjecture states that for any convex body $K \subset R^{n}$ of volume $1$ and any $j \in {0, \dots, n}$ , the mixed volume $V_j = V(K[j], -K[n…

math.ST2025

An Efficient Minimax Optimal Estimator For Multivariate Convex Regression

Gil Kur, Eli Putterman

This work studies the computational aspects of multivariate convex regression in dimensions $d \geq 5$ . Our results include the \emph{first} estimators that are minimax optimal (up…

math.ST2025

On the Variance, Admissibility, and Stability of Empirical Risk Minimization

Gil Kur, Eli Putterman, Alexander Rakhlin

It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (BirgÃ© and Massart, 1993). In this paper, we prove t…

math.MG2025

On the polar of Schneider's difference body

JuliÃ¡n Haddad, Dylan Langharst, Galyna V. Livshyts +1

In 1970, Schneider introduced the $m$ th-order extension of the difference body $D K$ of a convex body $K \subset R^{n}$ , the convex body $D^{m} (K)$ in $R^{nm}$ . He conject…

math.FA2025

Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies

JuliÃ¡n Haddad, Dylan Langharst, Eli Putterman +2

In 1970, Schneider introduced the $m$ th order difference body of a convex body, and also established the $m$ th-order Rogers-Shephard inequality. In this paper, we extend this idea…