Near-Optimal Weighted Matrix Completion
Authors: Oscar López
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments are presented that validate the theoretical behavior derived for several example weighted programs. |
| Researcher Affiliation | Academia | Oscar L opez EMAIL Harbor Branch Oceanographic Institute Florida Atlantic University Fort Pierce, FL 34946, USA |
| Pseudocode | No | The paper describes programs like (4), (1), and (5) using mathematical formulations and equations, but it does not contain a clearly labeled 'Pseudocode' or 'Algorithm' block with structured, step-by-step instructions. |
| Open Source Code | No | The paper mentions using 'LR-BPDN implementation introduced by Aravkin et al. 2014', which is a third-party tool. There is no explicit statement or link indicating that the authors' own code for the methodology described in this paper is publicly available. |
| Open Datasets | No | The paper states, 'Let D = UrΣr V r Rn1 n2, where Ur Rn1 r and V r Rn2 r are constructed by orthogonalizing the columns of a standard random Gaussian matrix with r columns and normalizing so that D F = 1.' This indicates the use of custom-generated synthetic data rather than a publicly available dataset. |
| Dataset Splits | No | The paper describes generating synthetic data and sampling observed entries: 'The set of observed matrix entries is selected uniformly at random from all subsets of the same cardinality |Ω| = λ(n1n2), where λ [0, 1] will be varied to specify a desired sampling percentage.' It does not specify traditional training, validation, or test dataset splits for a fixed dataset. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, or memory) used for running the numerical experiments. |
| Software Dependencies | No | The paper mentions using 'LR-BPDN implementation introduced by Aravkin et al. 2014' but does not specify its version or any other software dependencies with version numbers. |
| Experiment Setup | Yes | The setup of Eftekhari et al. 2018b is adopted to generate a data matrix and subspace information. Let D = UrΣr V r Rn1 n2, where Ur Rn1 r and V r Rn2 r are constructed by orthogonalizing the columns of a standard random Gaussian matrix with r columns and normalizing so that D F = 1. To obtain prior knowledge, a perturbed matrix is generated D = D + N where the entries of N Rn1 n2 are i.i.d. Gaussian random variables with variance σ2 that will be toggled to select a desired PABS. Then U Rn1 r and V Rn2 r are the leading r left and right singular vectors of D. The dimensions are set to n1 = n2 = 500 and r = 50. The set of observed matrix entries is selected uniformly at random from all subsets of the same cardinality |Ω| = λ(n1n2), where λ [0, 1] will be varied to specify a desired sampling percentage. In each experiment, D, N and Ωare generated independently and programs (4) and (5) are solved with ω = ω1ω2 varying in (0,1] (setting ω1 = ω2). The plots below present the average relative errors of 100 independent trials via trustworthy and relatively inaccurate subspace estimates. |