Geometric Analysis of Matrix Sensing over Graphs
Authors: Haixiang Zhang, Ying Chen, Javad Lavaei
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Besides the theoretical guarantees, we numerically illustrate the close relation between the Ω-RIP condition and the optimization complexity. In this section, we show how the optimization complexity is related to the Ω-RIP constant δ and the sampling rate p via a numerical example. |
| Researcher Affiliation | Academia | Haixiang Zhang Department of Mathematics University of California, Berkeley Berkeley, CA 94720 haixiang_zhang@berkeley.edu Ying Chen Department of IEOR University of California, Berkeley Berkeley, CA 94720 ying-chen@berkeley.edu Javad Lavaei Department of IEOR University of California, Berkeley Berkeley, CA 94720 lavaei@berkeley.edu |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not include any explicit statements about releasing source code for the methodology described, nor does it provide a direct link to a code repository. |
| Open Datasets | No | In this example, we choose a random orthogonal matrix V Rn n and define the loss function to be fc[MΩ; (V M V T )Ω] := 1 2[M (V M V T )]Ω: (c I + H) : [M (V M V T )]Ω, M Rn n, where c R is a hyper-parameter and the tensor H and the ground truth M are defined in Section 3.2. We generate 100 independent problem instances and compute the success rate of the gradient descent algorithm with random initialization. |
| Dataset Splits | No | The paper generates '100 independent problem instances' for numerical illustrations but does not describe any train/validation/test dataset splits, cross-validation, or other specific data partitioning methodology. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as CPU/GPU models, processor types, or memory used for running the experiments. |
| Software Dependencies | No | The paper mentions using 'Burer-Monterio factorization' and 'perturbed accelerated gradient descent algorithm [23]' but does not list specific software names with version numbers (e.g., library versions, solver versions). |
| Experiment Setup | Yes | We choose the problem size to be n = 10 and r = 5. The regularization parameters are α = 10 and λ = 100. The set of sampling rates and Ω-RIP2r,2r constants are p {0.7, 0.75, . . . , 0.95, 1.0}, δ {0.2, 0.25, . . . , 0.75, 0.8}. We solve each problem instance by the Burer-Monterio factorization and the perturbed accelerated gradient descent algorithm [23], where the constant step size is 0.007/c. |