Sub-Gaussian random variables

  title={Sub-Gaussian random variables},
  author={Valeriĭ V. Buldygin and Yurij Kozachenko},
  journal={Ukrainian Mathematical Journal},
Memoryless scalar quantization for random frames
This work rigorously establishes sharp non-asymptotic error bounds without using the WNH that explain the observed decay rate, and extends this approach to the compressed sensing setting, obtaining rigorous error bounds that agree with empirical observations. Expand
Weakly Sub-Gaussian Random Elements in Banach Spaces
We give a survey of properties of weakly sub-Gaussian random elements in infinite-dimensional spaces. Some new results and examples are also given.
Valid Statistical Inference on Automatically Matched Files
A statistical process for determining a confidence set for an unknown bipartite matching that permits efficient analysis of the matched data, e.g., using linear regression, while maintaining the proper degree of uncertainty about the linkage itself. Expand
Contextual Bandits with Random Projection
  • X. Yu
  • Mathematics, Computer Science
  • ArXiv
  • 2019
This paper develops an algorithm of Contextual Bandits via RAndom Projection in the setting of linear payoffs, which works especially for high-dimensional contextual data and provides a linear upper regret bound for the proposed algorithm, which is associated with reduced dimensions. Expand
Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data
This paper establishes an upper bound for the Kolmogorov distance between the maximum of a high-dimensional vector of smooth Wiener functionals and the maximum of a Gaussian random vector. As aExpand
Optimal estimation of Gaussian mixtures via denoised method of moments
The Method of Moments [Pea94] is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimatedExpand
Concentration of measure for block diagonal measurement matrices
This paper derives a concentration of measure bound for block diagonal matrices where the nonzero entries along the main diagonal blocks are i.i.d. subgaussian random variables and states that the concentration exponent, in the best case, scales as that for a fully dense matrix. Expand
A Good Representation Detects Noisy Labels
  • Zhaowei Zhu, Zihao Dong, Hao Cheng, Yang Liu
  • Computer Science
  • ArXiv
  • 2021
Given good representations that are commonly available in practice, given good representations, this paper proposes a universally applicable and training-free solution to detect noisy labels and theoretically analyze how they affect the local voting and provide guidelines for tuning neighborhood size. Expand
Adaptive function-on-scalar regression with a smoothing elastic net
A regularization method in the style of an adaptive Elastic Net penalty that involves mixing two types of functional norms, providing a fine tune control of both the smoothing and variable selection in the estimated model. Expand
Bounding Information Leakage in Machine Learning
This paper identifies and bound the success rate of the worst-case membership inference attack, connecting it to the generalization error of the target model, and derives bounds on the mutual information between the sensitive attributes and model parameters. Expand


Sub-Gaussian processes and convergence of random series in functional spaces
the random process which can be presented by this series can be chosen to be continuous with probability one. The Hunt condition, besides being simple, is also interesting in that it is invariantExpand
Inequalities for Ising models and field theories which obey the Lee-Yang Theorem
A series of inequalities for partition, correlation, and Ursell functions are derived as consequences of the Lee-Yang Theorem. In particular, then-point Schwinger functions ofeven φ4 models areExpand
Sums of Independent Random Variables
I. Probability Distributions and Characteristic Functions.- 1. Random variables and probability distributions.- 2. Characteristic functions.- 3. Inversion formulae.- 4. The convergence of sequencesExpand
The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes
The first two sections of this paper are introductory and correspond to the two halves of the title. As is well known, there is no complete analog of Lebesue or Haar measure in anExpand