Globally Q-linear Gauss-Newton Method for Overparameterized Non-convex Matrix Sensing
Authors: Xixi Jia, Fangchen FENG, Deyu Meng, Defeng Sun
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conduct experiments to demonstrate the effectiveness of the proposed AGN method for solving the over-parameterized non-convex matrix sensing problem. We set the ground truth matrix M = U ΣV , with U Rn r, V Rn r random orthogonal matrices and Σ is a diagonal matrix with condition number κ. We set n = 100, r = 5, d = 3r and the number of sensing matrices m = 50nr. All experiments were conducted using MATLAB on a Mac Book Pro with a 2.4 GHz quadcore Intel Core i5 CPU and 8 GB of memory. |
| Researcher Affiliation | Academia | Xixi Jia1 Fangchen Feng2 Deyu Meng3,4 Defeng Sun5 1School of Mathematics and Statistics, Xidian University 2L2TI Laboratory, University Sorbonne Paris Nord 3 School of Mathematics and Statistics, Xi an Jiaotong University 4 Macao Institute of Systems Engineering, Macau University of Science and Technology 5 Department of Applied Mathematics, The Hong Kong Polytechnic University |
| Pseudocode | Yes | A.1.2 The main AGN algorithm Algorithm 1: AGN for matrix sensing Data: A( ), b, η and the random Gauss initialization X0, t = 0. Result: The estimated solution X and the low-rank matrix ˆ M = PXX Q. while not end do t = t + 1; Update the approximated Gauss-Newton direction by Eq. (10); Update Xt and Xt+ 1 2 by Eq. (11); end |
| Open Source Code | Yes | The code for this paper is available at https://github.com/hsijiaxidian/AGN. |
| Open Datasets | No | We set the ground truth matrix M = U ΣV , with U Rn r, V Rn r random orthogonal matrices and Σ is a diagonal matrix with condition number κ. We set n = 100, r = 5, d = 3r and the number of sensing matrices m = 50nr. |
| Dataset Splits | No | The paper describes the generation of synthetic data and plots 'training curves' but does not specify explicit training, validation, or test dataset splits. |
| Hardware Specification | Yes | All experiments were conducted using MATLAB on a Mac Book Pro with a 2.4 GHz quadcore Intel Core i5 CPU and 8 GB of memory. |
| Software Dependencies | No | All experiments were conducted using MATLAB... (no specific version of MATLAB or other software libraries with version numbers are mentioned). |
| Experiment Setup | Yes | We set the ground truth matrix M = U ΣV , with U Rn r, V Rn r random orthogonal matrices and Σ is a diagonal matrix with condition number κ. We set n = 100, r = 5, d = 3r and the number of sensing matrices m = 50nr. All the competing methods are initialized with random Gaussian matrix with zero mean the variance 1/n. |