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. |