On Sampling Complexity of the Semidefinite Affine Rank Feasibility Problem
Authors: Igor Molybog, Javad Lavaei1568-1575
AAAI 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This is followed by a heuristic algorithm based on semidefinite relaxation and an experimental proof of its performance on a large sample of synthetic data. Numerical results In this section, we present and study a randomized algorithm for solving the SARF problem via an SDP relaxation that is based on the theoretical results of this paper. Algorithm 1 iteratively solves SDP relaxations of the problem with randomly sampled objective matrices. Under the assumption that no prior information is available about the unknown solution, we sample N uniformly since it belongs to the compact set T + n;k that is isomorphic to the Grassmann manifold Gn;k. We present experimental results on the performance of Algorithm 1 on a large set of synthetic data. |
| Researcher Affiliation | Academia | Igor Molybog,1 Javad Lavaei1 1University of California at Berkeley igormolybog@berkeley.edu, lavaei@berkeley.edu |
| Pseudocode | Yes | Algorithm 1: Heuristic algorithm for solving the Semidefinite Affine Rank Feasibility problem (1) |
| Open Source Code | No | The paper does not provide any explicit statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper uses 'synthetic data' generated by the authors following a described procedure, rather than a pre-existing, publicly available dataset. |
| Dataset Splits | No | The paper discusses synthetic data generation and experimental setup but does not specify explicit training, validation, or test dataset splits with percentages or sample counts. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments (e.g., GPU/CPU models, memory). |
| Software Dependencies | No | The paper states: 'The experiments have been scripted in Python with the use of CVXOPT as the mathematical optimization library.' However, it does not provide version numbers for Python or CVXOPT. |
| Experiment Setup | Yes | The 'Implementation' section details how the data for the experiments is generated (e.g., random sampling of Mr and X, Haar distributions, specific indices), how the objective matrix N is sampled, and how parameters like n, k, and m are used in the generation process. This constitutes a specific experimental setup description. |