Concentration inequalities under sub-Gaussian and sub-exponential conditions

Authors: Andreas Maurer, Massimiliano Pontil

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We prove analogues of the popular bounded difference inequality (also called Mc Diarmid s inequality) for functions of independent random variables under sub Gaussian and sub-exponential conditions.In this work we use the entropy method ([8], [2], [3]) to extend these inequalities from sums to general functions of independent variables, for which the centered conditional versions are sub-Gaussian or sub-exponential, respectively. These concentration inequalities, Theorem 3, 4 and 5, are stated in Section 3 below. Theorems 4 and 5, which apply to the heavier tailed sub-exponential distributions, are our principal contributions.
Researcher Affiliation Academia Andreas Maurer Istituto Italiano di Tecnologia am@andreas-maurer.eu Massimiliano Pontil Istituto Italiano di Tecnologia & University College London massimiliano.pontil@iit.it
Pseudocode No The paper focuses on mathematical proofs and theoretical derivations and does not include any pseudocode or algorithm blocks.
Open Source Code No The paper does not provide any information or links regarding the availability of open-source code.
Open Datasets No The paper is theoretical and discusses applications to learning theory problems abstractly, without referring to or using any specific publicly available datasets for training or evaluation.
Dataset Splits No The paper does not describe any experiments involving datasets, and therefore no dataset split information (training, validation, or test) is provided.
Hardware Specification No The paper is purely theoretical and does not describe any experiments requiring hardware specifications.
Software Dependencies No The paper is purely theoretical and does not describe any experiments that would require specific software dependencies or versions.
Experiment Setup No The paper is theoretical and does not describe any experimental setup or configurations.