Efficient Dictionary Learning with Gradient Descent
Authors: Dar Gilboa, Sam Buchanan, John Wright
ICML 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The main results of this work is a convergence rate for randomly initialized gradient descent for complete orthogonal dictionary learning to the neighborhood of a global minimum of the objective. Our results are probabilistic since they rely on initialization in certain regions of the parameter space, yet they allow one to flexibly trade off between the maximal number of iterations in the bound and the probabil-ity of the bound holding. The sample complexity required for the concentration results in the paper to hold with high probability is p O(n4) up to polylog(n) factors, where p is the number of samples and n is the dimensionality of the space. |
| Researcher Affiliation | Academia | 1Department of Neuroscience, Columbia University 2Data Science Institute, Columbia University 3Department of Electrical Engineering, Columbia University. |
| Pseudocode | No | The paper focuses on theoretical analysis and mathematical proofs. It does not include any structured pseudocode blocks or algorithms. |
| Open Source Code | No | The paper does not provide any statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper discusses theoretical models of data (e.g., 'sparse matrix X0 is random, with entries i.i.d. Bernoulli Gaussian') rather than using or providing access information for a specific public dataset for empirical training or evaluation. |
| Dataset Splits | No | The paper is theoretical and does not describe empirical experiments with data splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe empirical experiments that would require hardware specifications. |
| Software Dependencies | No | The paper is theoretical and does not describe empirical experiments that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and focuses on mathematical analysis of algorithms. It does not describe an empirical experimental setup with hyperparameters or system-level training settings. |