Convergence Guarantees for a Class of Non-convex and Non-smooth Optimization Problems
Authors: Koulik Khamaru, Martin J. Wainwright
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We illustrate our methods and theory via applications to the problems of best subset selection, robust estimation, mixture density estimation, and shape-from-shading reconstruction. ... Some reconstruction experiments: In order to illustrate the behavior of our method for this problem, we considered two synthetic images for simulated experiments. ...Figure 2 shows the performances of the prox-type method and CCCP for synthetic data simulated as above, with problem parameters (n, p) = (190, 300) and (n, p) = (380, 600) and different choices of sparsity s. |
| Researcher Affiliation | Collaboration | Koulik Khamaru EMAIL Martin J. Wainwright , , EMAIL Department of Statistics Department of Electrical Engineering & Computer Sciences University of California Berkeley Berkeley, CA 94720-1776, USA Voleon Group Berkeley, CA |
| Pseudocode | Yes | Algorithm 1 Subgradient-type method Algorithm 2 Proximal-type algorithm Algorithm 3 Frank-Wolfe type method Algorithm 4 Gradient descent with backtracking |
| Open Source Code | No | The paper does not provide any explicit statements about releasing code or links to source code repositories. |
| Open Datasets | Yes | The first one is a 256 256 image of Mozart (Zhang et al., 1999), and the second one is a 128 128 image of Vase. |
| Dataset Splits | No | The paper describes the generation of synthetic data but does not specify how this data was split into training, validation, or test sets for experiments. |
| Hardware Specification | No | The paper mentions runtimes for experiments ("The runtime for Mozart-example was 87 seconds, whereas the runtime for Vase-example was 39 seconds") but does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used. |
| Software Dependencies | No | The paper describes various algorithms and their theoretical properties. While it discusses implementation aspects, it does not specify any software libraries, frameworks, or their version numbers used for the experiments. |
| Experiment Setup | Yes | For both the algorithms, the tolerance level η was set to η = 10 8, whereas the maximum number of iterations was 1000. In all our simulations we used same initializations for both the algorithms. |