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of 24
pro vyhledávání: '"Putterman, Eli"'
It is well known that Empirical Risk Minimization (ERM) with squared loss may attain minimax suboptimal error rates (Birg\'e and Massart, 1993). The key message of this paper is that, under mild assumptions, the suboptimality of ERM must be due to la
Externí odkaz:
http://arxiv.org/abs/2305.18508
Publikováno v:
Journal of Functional Analysis, 2024, ISSN 0022-1236
Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and pr
Externí odkaz:
http://arxiv.org/abs/2305.17468
For a convex body $K$ in $\mathbb R^n$, the inequalities of Rogers-Shephard and Zhang, written succinctly, are $$\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_n(n\text{vol}_n(K)\Pi^\circ K).$$ Here, $DK=\{x\in\mathbb R^n:K\cap(K+
Externí odkaz:
http://arxiv.org/abs/2305.00479
In 1970, Schneider generalized the difference body of a convex body to higher-order, and also established the higher-order analogue of the Rogers-Shephard inequality. In this paper, we extend this idea to the projection body, centroid body, and radia
Externí odkaz:
http://arxiv.org/abs/2304.07859
Autor:
Langharst, Dylan, Putterman, Eli
The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions with respect
Externí odkaz:
http://arxiv.org/abs/2210.04438
Autor:
Kur, Gil, Putterman, Eli
We study the computational aspects of the task of multivariate convex regression in dimension $d \geq 5$. We present the first computationally efficient minimax optimal (up to logarithmic factors) estimators for the tasks of (i) $L$-Lipschitz convex
Externí odkaz:
http://arxiv.org/abs/2205.03368
Publikováno v:
In Journal of Functional Analysis 15 January 2025 288(2)
Autor:
Artstein-Avidan, Shiri, Putterman, Eli
In this paper, we extend and generalize several previous works on maximal-volume positions of convex bodies. First, we analyze the maximal positive-definite image of one convex body inside another, and the resulting decomposition of the identity. We
Externí odkaz:
http://arxiv.org/abs/2112.02525
Autor:
Klartag, Bo'az, Putterman, Eli
We show that the Poincar\'e constant of a log-concave measure in Euclidean space is monotone increasing along the heat flow. In fact, the entire spectrum of the associated Laplace operator is monotone decreasing. Two proofs of these results are given
Externí odkaz:
http://arxiv.org/abs/2107.09496
Autor:
Putterman, Eli
We study a problem in the theory of cubature formulas on the sphere: given $\theta \in (0, 1)$, determine the infimum of $\|\nu\|_\theta = \sum_{i = 1}^n \nu_i^\theta$ over cubature formulas $\nu$ of strength $t$, where $\nu_i$ are the weights of the
Externí odkaz:
http://arxiv.org/abs/2012.08109