Fetching the paper…
Reading the bibliography…
We show that under minimal assumptions on a random vector $X\in\mathbb{R}^d$ and with high probability, given $m$ independent copies of $X$, the coordinate distribution of each vector $(\langle X_i,\theta \rangle)_{i=1}^m$ is dictated by the distribution of the true marginal $\langle X,\theta \rangle$.
The speed of mean Glivenko-Cantelli convergence
R. M. Dudley · 1969
Earlier work this paper cites.
The Wasserstein distance and approximation theorems
L. Rüschendorf · 1985
Earlier work this paper cites.
The distribution of Rademacher sums
S. J. Montgomery-Smith · 1990
Earlier work this paper cites.
Probability in Banach Spaces: isoperimetry and processes
M. Ledoux and M. Talagrand · 1991
Earlier work this paper cites.
Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
Z.-D. Bai and Y.-Q. Yin · 1993
Earlier work this paper cites.
Sharper bounds for Gaussian and empirical processes
M. Talagrand · 1994
Earlier work this paper cites.
Isoperimetric problems for convex bodies and a localization lemma
R. Kannan, L. Lovász, and M. Simonovits · 1995
Earlier work this paper cites.
Extremal properties of half-spaces for log-concave distributions
S. Bobkov · 1996
Earlier work this paper cites.
Weak convergence and empirical processes
A. W. Vaart and J. A. Wellner · 1996
Earlier work this paper cites.
Isoperimetric and analytic inequalities for log-concave probability measures
S. Bobkov · 1999
Earlier work this paper cites.
The volume of convex bodies and Banach space geometry
G. Pisier · 1999
Earlier work this paper cites.
The concentration of measure phenomenon
M. Ledoux · 2001
Earlier work this paper cites.
Concentration around the mean for maxima of empirical processes
T. Klein and E. Rio · 2005
Earlier work this paper cites.
Concentration of mass on convex bodies
G. Paouris · 2006
Earlier work this paper cites.
L p L_{p} -moments of random vectors via majorizing measures
O. Guédon and M. Rudelson · 2007
Cited alongside, same era.
A subgaussian embedding theorem
S. Mendelson and N. Tomczak-Jaegermann · 2008
Cited alongside, same era.
Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
R. Adamczak, A. Litvak, A. Pajor, and N. Tomczak-Jaegermann · 2010
Cited alongside, same era.
Challenging the empirical mean and empirical variance: a deviation study
O. Catoni · 2012
Cited alongside, same era.
Decoupling: from dependence to independence
V. De la Pena and E. Giné · 2012
Cited alongside, same era.
Concentration inequalities: A nonasymptotic theory of independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Approximating the covariance ellipsoid
S. Mendelson · 2020
Later among the works it cites.
Robust covariance estimation under L 4 − L 2 L_{4}-L_{2} norm equivalence
S. Mendelson and N. Zhivotovskiy · 2020
Later among the works it cites.
An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
A. Figalli and F. Glaudo · 2021
Later among the works it cites.
On projection robust optimal transport: Sample complexity and model misspecification
T. Lin, Z. Zheng, E. Chen, M. Cuturi, and M. I. Jordan · 2021
Later among the works it cites.
Approximating L p L_{p} unit balls via random sampling
S. Mendelson · 2021
Later among the works it cites.
Topics in optimal transportation
C. Villani · 2021
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
On the singular values of random matrices
S. Mendelson and G. Paouris · 2014
Cited alongside, same era.
Asymptotic Geometric Analysis, Part I
S. Artstein-Avidan, A. Giannopoulos, and V. D. Milman · 2015
Cited alongside, same era.
Sample covariance matrices of heavy-tailed distributions
K. Tikhomirov · 2018
Cited alongside, same era.
One-dimensional empirical measures, order statistics, and Kantorovich transport distances
S. Bobkov and M. Ledoux · 2019
Cited alongside, same era.
Max-sliced Wasserstein distance and its use for gans
I. Deshpande, Y.-T. Hu, R. Sun, A. Pyrros, N. Siddiqui, S. Koyejo, Z. Zhao, D. Forsyth, and A. G. Schwing · 2019
Cited alongside, same era.
Mean estimation and regression under heavy-tailed distributions: A survey,
G. Lugosi and S. Mendelson · 2019
Cited alongside, same era.
Later among the works it cites.
Random embeddings with an almost Gaussian distortion
D. Bartl and S. Mendelson · 2022
Closest in time.
Optimal non-gaussian Dvoretzky-Milman embeddings
D. Bartl and S. Mendelson · 2022
Closest in time.
Minimax confidence intervals for the sliced Wasserstein distance
T. Manole, S. Balakrishnan, and L. Wasserman · 2022
Closest in time.
Statistical, robustness, and computational guarantees for sliced wasserstein distances,
S. Nietert, R. Sadhu, Z. Goldfeld, and K. Kato · 2022
Closest in time.
The out-of-sample prediction error of the square-root-LASSO and related estimators
J. Olea, C. Rush, A. Velez, and J. Wiesel · 2022
Closest in time.
Upper and lower bounds for stochastic processes: decomposition theorems
M. Talagrand · 2022
Closest in time.
On dimension-dependent concentration for convex lipschitz functions in product spaces
H. Huang and K. Tikhomirov · 2023
Closest in time.