A Nullspace Property for Subspace-Preserving Recovery
Authors: Mustafa D Kaba, Chong You, Daniel P Robinson, Enrique Mallada, Rene Vidal
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper derives a necessary and sufficient condition for subspace-preserving recovery that is inspired by the classical nullspace property. Based on this novel condition, called here the subspace nullspace property, we derive equivalent characterizations that either admit a clear geometric interpretation that relates data distribution and subspace separation to the recovery success, or can be verified using a finite set of extreme points of a properly defined set. We further exploit these characterizations to derive new sufficient conditions, based on inner-radius and outer-radius measures and dual bounds, that generalize existing conditions and preserve the geometric interpretations. Our primary goal is to present an in-depth theoretical analysis of subspace-preserving recovery through a nullspace-propertylike condition, and not necessarily to construct computationally efficient tools. |
| Researcher Affiliation | Collaboration | 1e Bay Inc., San Jose, CA, USA. 2Dept. of Elect. Eng. & Comp. Sci., University of California at Berkeley, Berkeley, CA, USA. 3Dept. of Ind. & Sys. Eng., Lehigh University, Bethlehem, PA, USA. 4Dept. of Elect. & Comp. Eng., Johns Hopkins University, Baltimore, MD, USA. 5MINDS & Dept. of Biom. Eng., Johns Hopkins University, Baltimore, MD, USA. |
| Pseudocode | No | The paper presents theorems, proofs, definitions, and mathematical formulations, but it does not include pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not mention or provide any link to open-source code for the methodology described. |
| Open Datasets | No | The paper is theoretical and does not conduct empirical experiments using datasets. It discusses theoretical conditions and properties but does not mention any specific dataset for training or evaluation. |
| Dataset Splits | No | The paper is theoretical and does not conduct empirical experiments, thus it does not mention dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical conditions and characterizations rather than experimental implementation. Therefore, it does not mention any hardware specifications used for experiments. |
| Software Dependencies | No | The paper is theoretical and presents mathematical conditions and proofs. It does not describe any experimental implementation or list software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on deriving mathematical conditions. It does not describe an experimental setup, hyperparameters, or training configurations. |