research
∙
08/09/2023
On a variance dependent Dvoretzky-Kiefer-Wolfowitz inequality
Let X be a real-valued random variable with distribution function F. Set...
share
research
∙
07/03/2023
Fitting an ellipsoid to a quadratic number of random points
We consider the problem (P) of fitting n standard Gaussian random vector...
research
∙
09/15/2022
Structure preservation via the Wasserstein distance
We show that under minimal assumptions on a random vector X∈ℝ^d, and wit...
research
∙
04/08/2022
Fast metric embedding into the Hamming cube
We consider the problem of embedding a subset of ℝ^n into a low-dimensio...
research
∙
01/13/2022
Sharp estimates on random hyperplane tessellations
We study the problem of generating a hyperplane tessellation of an arbit...
research
∙
03/09/2021
Column randomization and almost-isometric embeddings
The matrix A:ℝ^n →ℝ^m is (δ,k)-regular if for any k-sparse vector x, ...
research
∙
01/19/2021
On Monte-Carlo methods in convex stochastic optimization
We develop a novel procedure for estimating the optimizer of general con...
research
∙
10/22/2020
Multivariate mean estimation with direction-dependent accuracy
We consider the problem of estimating the mean of a random vector based ...
research
∙
02/04/2020
Learning bounded subsets of L_p
We study learning problems in which the underlying class is a bounded su...
research
∙
07/26/2019
Robust multivariate mean estimation: the optimality of trimmed mean
We consider the problem of estimating the mean of a random vector based ...
research
∙
07/16/2019
On the geometry of polytopes generated by heavy-tailed random vectors
We study the geometry of centrally-symmetric random polytopes, generated...
research
∙
06/10/2019
Mean estimation and regression under heavy-tailed distributions--a survey
We survey some of the recent advances in mean estimation and regression ...
research
∙
04/17/2019
Stable recovery and the coordinate small-ball behaviour of random vectors
Recovery procedures in various application in Data Science are based on ...
research
∙
12/17/2018
Robust one-bit compressed sensing with partial circulant matrices
We present optimal sample complexity estimates for one-bit compressed se...
research
∙
09/27/2018
Robust covariance estimation under L_4-L_2 norm equivalence
Let X be a centered random vector taking values in R^d and let Σ= E(X⊗ X...
research
∙
06/16/2018
Near-optimal mean estimators with respect to general norms
We study the problem of estimating the mean of a random vector in R^d ba...
research
∙
05/23/2018
Robust one-bit compressed sensing with non-Gaussian measurements
We study memoryless one-bit compressed sensing with non-Gaussian measure...
research
∙
04/15/2018
Approximating the covariance ellipsoid
We explore ways in which the covariance ellipsoid B={v ∈R^d : E <X,v>^2...
research
∙
12/19/2017
A remark on "Robust machine learning by median-of-means"
We explore the recent results announced in "Robust machine learning by m...
research
∙
09/04/2017
Extending the small-ball method
The small-ball method was introduced as a way of obtaining a high probab...
research
∙
07/17/2017
An optimal unrestricted learning procedure
We study learning problems in the general setup, for arbitrary classes o...
research
∙
02/21/2017
Column normalization of a random measurement matrix
In this note we answer a question of G. Lecué, by showing that column no...
research
∙
02/01/2017
Sub-Gaussian estimators of the mean of a random vector
We study the problem of estimating the mean of a random vector X given a...
research
∙
01/15/2017
Regularization, sparse recovery, and median-of-means tournaments
A regularized risk minimization procedure for regression function estima...
research
∙
04/09/2015
`local' vs. `global' parameters -- breaking the gaussian complexity barrier
We show that if F is a convex class of functions that is L-subgaussian, ...
research
∙
02/25/2015
On aggregation for heavy-tailed classes
We introduce an alternative to the notion of `fast rate' in Learning The...
research
∙
10/13/2014
Learning without Concentration for General Loss Functions
We study prediction and estimation problems using empirical risk minimiz...
research
∙
01/01/2014