Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares
Authors: Christian Kümmerle, Johannes Maly
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The numerical simulations in Section 4 support our theoretical findings and provide empirical evidence for the efficacy of the proposed method. |
| Researcher Affiliation | Academia | Christian Kümmerle Department of Computer Science University of North Carolina at Charlotte Charlotte, NC 28223, USA kuemmerle@uncc.edu Johannes Maly Department of Mathematics Ludwig-Maximilians-Universität München 80799 Munich, Germany and Munich Center for Machine Learning (MCML) maly@math.lmu.de |
| Pseudocode | Yes | Algorithm 1 IRLS for simultaneously low-rank rand row-sparse matrices |
| Open Source Code | Yes | We refer to the MATLAB implementation available in the repository https://github.com/ckuemmerle/simirls for further details. |
| Open Datasets | No | In the experiments, we chose random ground truths X Rn1 n2 of rank r and row-sparsity s such that X = X / X F , where X = U diag(d )V , and where U Rn1 r is a matrix with s non-zero rows whose location is chosen uniformly at random and whose entries are drawn from i.i.d. standard Gaussian random variables, d has i.i.d. standard Gaussian entries and V Rn2 r has likewise i.i.d. standard Gaussian entries. |
| Dataset Splits | No | The paper describes experiments like 'phase transition experiments' and averaging over '64 random trials' but does not specify train/validation/test dataset splits. |
| Hardware Specification | Yes | The CPU models used in the simulations are Dual 18-Core Intel Xeon Gold 6154, Dual 24-Core Intel Xeon Gold 6248R, Dual 8-Core Intel Xeon E5-2667, 28-Core Intel Xeon E5-2690 v3, 64-Core Intel Xeon Phi KNL 7210-F. |
| Software Dependencies | Yes | The experiments of Section 4 were conducted using MATLAB implementations of the three algorithms on different Linux machines using MATLAB versions R2019b or R2022b. |
| Experiment Setup | Yes | In all phase transition experiments, we define successful recovery such that the relative Frobenius error X(K) X F / X F of the iterate X(K) returned by the algorithm relative to the simultaneously low-rank and row-sparse ground truth matrix X is smaller than the threshold 10 4. As stopping criteria, we used the criterion that the relative change of Frobenius norm satisfies X(k) X(k 1) F / X(k) F < tol for IRLS, the change in the matrix factors norms satisfy Uk Uk 1 < tol and Vk Vk 1 < tol for SPF, and the norm of the Riemannian gradient in Riem Ada IHT being smaller than tol for tol = 10 10, or if a maximal number of iterations is reached. This iteration threshold was chosen as max_iter = 250 for IRLS and SPF and as max_iter = 2000 for Riem Ada IHT. |