Entropy-Based Concentration Inequalities for Dependent Variables
Authors: Liva Ralaivola, Massih-Reza Amini
ICML 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We provide new concentration inequalities for functions of dependent variables. The work extends that of Janson (2004), which proposes concentration inequalities using a combination of the Laplace transform and the idea of fractional graph coloring, as well as many works that derive concentration inequalities using the entropy method (see, e.g., (Boucheron et al., 2003)). We give inequalities for fractionally sub-additive and fractionally self-bounding functions. In the way, we prove a new Talagrand concentration inequality for fractionally sub-additive functions of dependent variables. The results allow us to envision the derivation of generalization bounds for various applications where dependent variables naturally appear, such as in bipartite ranking. |
| Researcher Affiliation | Academia | Liva Ralaivola LIVA.RALAIVOLA@LIF.UNIV-MRS.FR QARMA, LIF, CNRS, Aix-Marseille University, F 13288 Marseille cedex 9, France Massih-Reza Amini MASSIH-REZA.AMINI@IMAG.FR AMA, LIG, CNRS, University Grenoble Alpes, Centre Equation 4, BP 53, F 38041 Grenoble Cedex 9, France |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found. |
| Open Source Code | No | The paper does not contain any statement or link indicating the release of source code for the described methodology. |
| Open Datasets | No | The paper discusses theoretical concepts related to training data (e.g., 'training set S = {(Ti, Yi)}n i=1') but does not specify a concrete, publicly available dataset with access information (link, DOI, citation) used for empirical evaluation. |
| Dataset Splits | No | The paper does not conduct empirical experiments, and therefore, no specific dataset split information for validation is provided. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not mention specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not provide details on experimental setup such as hyperparameter values or training configurations. |