Fetching the paper…
Reading the bibliography…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported distribution with a continuous density.
An extremal property of the hypersphere
Alexander Murray Macbeath · 1951
Earlier work this paper cites.
ε \varepsilon -entropy of convex sets and functions
EM Bronshtein · 1976
Earlier work this paper cites.
Log-concave and unimodal sequences in algebra, combinatorics, and geometry
Richard P Stanley · 1989
Earlier work this paper cites.
The convex hull of random points with spherically symmetric distributions
F Affentranger · 1991
Earlier work this paper cites.
Random polytopes in smooth convex bodies
Imre Bárány · 1992
Earlier work this paper cites.
Rates of convergence for minimum contrast estimators
Lucien Birgé and Pascal Massart · 1993
Earlier work this paper cites.
Weak convergence
Aad W van der Vaart and Jon A Wellner · 1996
Earlier work this paper cites.
Log-concave probability distributions: Theory and statistical testing
Mark Yuying An · 1997
Earlier work this paper cites.
Uniform central limit theorems
Richard M Dudley · 1999
Earlier work this paper cites.
Information-theoretic determination of minimax rates of convergence
Yuhong Yang and Andrew Barron · 1999
Earlier work this paper cites.
Empirical Processes in M-estimation , volume 6
Sara A van de Geer · 2000
Earlier work this paper cites.
Asymptotic statistics , volume 3
Aad W van der Vaart · 2000
Earlier work this paper cites.
Concentration inequalities and empirical processes theory applied to the analysis of learning algorithms
Olivier Bousquet · 2002
Earlier work this paper cites.
Introduction to Nonparametric Estimation
Alexandre B. Tsybakov · 2003
Earlier work this paper cites.
Log-concave probability and its applications
Mark Bagnoli and Ted Bergstrom · 2005
Earlier work this paper cites.
Convergence of algorithms for reconstructing convex bodies and directional measures
Richard J Gardner, Markus Kiderlen, Peyman Milanfar, et al · 2006
Earlier work this paper cites.
The geometry of logconcave functions and sampling algorithms
László Lovász and Santosh Vempala · 2007
Earlier work this paper cites.
Stochastic and integral geometry
Rolf Schneider and Wolfgang Weil · 2008
Earlier work this paper cites.
Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency
Lutz Dümbgen and Kaspar Rufibach · 2009
Cited alongside, same era.
Learning convex bodies is hard
Luis Rademacher and Navin Goyal · 2009
Cited alongside, same era.
Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
Madeleine Cule and Richard Samworth · 2010
Cited alongside, same era.
Consistency of multivariate log-concave density estimators
Dominic Schuhmacher and Lutz Dümbgen · 2010
Cited alongside, same era.
Approximation by log-concave distributions, with applications to regression
Lutz Dümbgen, Richard Samworth, and Dominic Schuhmacher · 2011
Cited alongside, same era.
Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems: Ecole d’Eté de Probabilités de Saint-Flour XXXVIII-2008 , volume 2033
Efficient robust proper learning of log-concave distributions
Ilias Diakonikolas, Daniel M Kane, and Alistair Stewart · 2016
Later among the works it cites.
Global rates of convergence of the mles of log-concave and s-concave densities
Charles R Doss and Jon A Wellner · 2016
Later among the works it cites.
Global rates of convergence in log-concave density estimation
Arlene KH Kim and Richard J Samworth · 2016
Later among the works it cites.
Learning multivariate log-concave distributions
Ilias Diakonikolas, Daniel M Kane, and Alistair Stewart · 2017
Later among the works it cites.
Entropy of convex functions on ℝ d \mathbb{R}^{d}
Fuchang Gao and Jon A Wellner · 2017
Later among the works it cites.
On univariate convex regression
Promit Ghosal and Bodhisattva Sen · 2017
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Vladimir Koltchinskii · 2011
Cited alongside, same era.
Combinatorial methods in density estimation
Luc Devroye and Gábor Lugosi · 2012
Cited alongside, same era.
Optimal rates of convergence for convex set estimation from support functions
Adityanand Guntuboyina · 2012
Cited alongside, same era.
Active and passive learning of linear separators under log-concave distributions
Maria-Florina Balcan and Phil Long · 2013
Cited alongside, same era.
Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
Cited alongside, same era.
Adaptive estimation of convex polytopes and convex sets from noisy data
Victor-Emmanuel Brunel · 2013
Cited alongside, same era.
Learning mixtures of structured distributions over discrete domains
Siu-On Chan, Ilias Diakonikolas, Rocco A Servedio, and Xiaorui Sun · 2013
Cited alongside, same era.
Later among the works it cites.
Empirical entropy, minimax regret and minimax risk
Alexander Rakhlin, Karthik Sridharan, Alexandre B Tsybakov, et al · 2017
Later among the works it cites.
Sharp oracle inequalities for least squares estimators in shape restricted regression
Pierre C Bellec · 2018
Later among the works it cites.
Near-optimal sample complexity bounds for maximum likelihood estimation of multivariate log-concave densities
Timothy Carpenter, Ilias Diakonikolas, Anastasios Sidiropoulos, and Alistair Stewart · 2018
Later among the works it cites.
Adaptation in multivariate log-concave density estimation
Oliver Y Feng, Adityanand Guntuboyina, Arlene KH Kim, and Richard J Samworth · 2018
Later among the works it cites.
Adaptation in log-concave density estimation
Arlene KH Kim, Adityanand Guntuboyina, Richard J Samworth, et al · 2018
Later among the works it cites.
Stochastic localization+ stieltjes barrier= tight bound for log-sobolev
Yin Tat Lee and Santosh S Vempala · 2018
Later among the works it cites.
Recent progress in log-concave density estimation
Richard J Samworth · 2018
Later among the works it cites.
A polynomial time algorithm for log-concave maximum likelihood via locally exponential families
Brian Axelrod, Ilias Diakonikolas, Anastasios Sidiropoulos, Alistair Stewart, and Gregory Valiant · 2019
Closest in time.
Global empirical risk minimizers with” shape constraints” are rate optimal in general dimensions
Qiyang Han · 2019
Closest in time.
Convergence rates of least squares regression estimators with heavy-tailed errors
Qiyang Han, Jon A Wellner, et al · 2019
Closest in time.
Approximation of the euclidean ball by polytopes with a restricted number of facets
Gil Kur · 2019
Closest in time.