Extensions to the Proximal Distance Method of Constrained Optimization
Authors: Alfonso Landeros, Oscar Hernan Madrid Padilla, Hua Zhou, Kenneth Lange
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our extensive numerical tests include problems on metric projection, convex regression, convex clustering, total variation image denoising, and projection of a matrix to a good condition number. These experiments demonstrate the superior speed and acceptable accuracy of our steepest variant on high-dimensional problems. Julia code to replicate all of our experiments can be found at https://github.com/alanderos91/Proximal Distance Algorithms.jl |
| Researcher Affiliation | Academia | Alfonso Landeros EMAIL Department of Computational Medicine University of California, Los Angeles CA 90095-1596, USA Oscar Hernan Madrid Padilla EMAIL Department of Statistics University of California, Los Angeles CA 90095-1554, USA Hua Zhou EMAIL Departments of Biostatistics and Computational Medicine University of California, Los Angeles CA 90095-1596, USA Kenneth Lange EMAIL Departments of Computational Medicine, Human Genetics, and Statistics University of California, Los Angeles CA 90095-1596, USA |
| Pseudocode | Yes | Algorithm 1 Proximal Distance Iteration (Summary) Algorithm 2 Proximal Distance Iteration Algorithm 3 Search Heuristic |
| Open Source Code | Yes | Julia code to replicate all of our experiments can be found at https://github.com/alanderos91/Proximal Distance Algorithms.jl |
| Open Datasets | Yes | To evaluate the performance of the different methods on convex clustering, we consider a mixture of simulated data and discriminant analysis data from the UCI Machine Learning Repository (Dua and Graff, 2019). The simulated data in gaussian300 consists of 3 Gaussian clusters... The data in iris and zoo are representative of clustering with purely continuous or purely discrete data, respectively. |
| Dataset Splits | No | The paper describes how various synthetic datasets (e.g., gaussian300, input matrices Y, observed functional values yi) were generated or their characteristics (e.g., class sizes n1 = 150, n2 = 50, n3 = 100 for gaussian300; White noise with σ = 0.2 applied to an image). However, it does not provide explicit training/test/validation splits for any of the datasets used in the empirical evaluations. |
| Hardware Specification | Yes | Numerical experiments were carried out on a Manjaro Linux 5.10.89-1 desktop environment using 8 cores on an Intel 10900KF at 4.9 GHz and 32 GB RAM. |
| Software Dependencies | Yes | Code for our implementations and numerical experiments is available at https://github. com/alanderos91/Proximal Distance Algorithms.jl and is based on the Julia language (Bezanson et al., 2017). Additional packages used include Plots.jl (Breloff, 2021), GR.jl (Heinen et al., 2021), and (Udell et al., 2014). |
| Experiment Setup | Yes | Table 1: Summary of control parameters used in each example. Metric Projection 10 3 10 2 10 6 min{108, 1.2t 1} Each algorithm is allotted a maximum of 200 outer and 105 inner iterations, respectively, to achieve a gradient norm of δh = 10 3 and distance to feasibility of δd = 10 2. The relative change parameter is set to δq = 0 and the annealing schedule is set to ρ(t) = min{108, 1.2t 1} for the proximal distance methods. |