Random Quadratic Forms with Dependence: Applications to Restricted Isometry and Beyond
Authors: Arindam Banerjee, Qilong Gu, Vidyashankar Sivakumar, Steven Z. Wu
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we show that such independence is in fact not needed for such results which continue to hold under fairly general dependence structures. In particular, we present uniform bounds on random quadratic forms of stochastic processes which are conditionally independent and sub-Gaussian given another (latent) process. The technical analysis for our main result is a significant generalization of prior analysis on tail behavior of chaos processes [3, 28, 43] for random vectors with i.i.d. elements. |
| Researcher Affiliation | Academia | Arindam Banerjee Qilong Gu Vidyashankar Sivakumar Zhiwei Steven Wu Department of Computer Science & Engineering, University of Minnesota, Twin Cities Minneapolis, MN 55455, USA |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper only provides a link to its full version on arXiv (https://arxiv.org/abs/1910.04930) and does not state that source code for the methodology is openly available or provide a link to a code repository. |
| Open Datasets | No | The paper focuses on theoretical bounds and their implications, not on training models with specific datasets. No mention of a dataset used for training or its public availability for this paper's work was found. |
| Dataset Splits | No | The paper is theoretical and does not describe any experimental validation process or use of a validation dataset. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used for running experiments. |
| Software Dependencies | No | The paper is theoretical and does not list any specific software dependencies with version numbers required to replicate experimental results. |
| Experiment Setup | No | The paper is theoretical and does not describe specific experimental setup details, hyperparameters, or training configurations. |