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.