A Vector Bernstein Inequality for Self-Normalized Martingales
Authors: Ingvar Ziemann
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We prove a Bernstein inequality for vector-valued self-normalized martingales. We first give an alternative perspective of the corresponding sub-Gaussian bound due to Abbasi Yadkori et al. (2011) via a PAC-Bayesian argument with Gaussian priors. By instantiating this argument to priors drawn uniformly over well-chosen ellipsoids, we obtain a Bernstein bound. |
| Researcher Affiliation | Academia | Ingvar Ziemann EMAIL University of Pennsylvania |
| Pseudocode | No | The paper focuses on mathematical proofs and theoretical derivations and does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to any code repositories for the methodology described. |
| Open Datasets | No | The paper is theoretical, presenting mathematical proofs and inequalities. It does not describe or use any specific datasets for empirical evaluation, hence no information about public or open datasets is provided. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical experiments with datasets, thus no information regarding dataset splits (training, validation, test) is provided. |
| Hardware Specification | No | The paper presents theoretical work on a vector Bernstein inequality and does not describe any computational experiments that would require hardware specifications. |
| Software Dependencies | No | The paper is purely theoretical, focusing on mathematical derivations and proofs. It does not mention any software or libraries with version numbers used for experimental purposes. |
| Experiment Setup | No | The paper is purely theoretical, focusing on mathematical derivations and proofs. It does not describe any experimental setup details, hyperparameters, or training configurations. |