A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery

Authors: Xiao Zhang, Lingxiao Wang, Yaodong Yu, Quanquan Gu

ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental In this section, we provide simulation results of the primal-dual based method, as discussed in Section 5, for matrix completion and one-bit matrix completion.
Researcher Affiliation Academia 1Department of Computer Science, University of Virginia, Charlottesville, VA 22904, USA. 2Department of Computer Science, University of California, Los Angeles, Los Angeles, CA 90095, USA.
Pseudocode Yes Algorithm 1 Augmented Lagrangian Method
Open Source Code No The paper does not provide concrete access to source code for the methodology described.
Open Datasets No We generate the observed data matrix according to the uniform observation model (2.3). In particular, the unknown low-rank matrix X Rd1 d2 is generated via X = U V , where each entry of U Rd1 r and V Rd2 r is generated independently from standard Gaussian distribution, and we scale them to ensure max{ U 2, , V 2, } ", where " = 2.
Dataset Splits No The paper describes data generation and various experimental settings but does not provide specific dataset split information (e.g., percentages or counts for training, validation, and test sets) as required for reproduction.
Hardware Specification No The paper mentions that algorithms are implemented in Matlab but provides no specific details about the hardware (e.g., CPU, GPU models) used for experiments.
Software Dependencies No All of the aforementioned algorithms are implemented in Matlab
Experiment Setup Yes We generate the observed data matrix according to the uniform observation model (2.3). In particular, the unknown low-rank matrix X Rd1 d2 is generated via X = U V , where each entry of U Rd1 r and V Rd2 r is generated independently from standard Gaussian distribution, and we scale them to ensure max{ U 2, , V 2, } ", where " = 2. The noise matrix E is set as 0 in the noiseless case, while under the noisy setting, we generate each element of the noise matrix E from i.i.d. centered Gaussian distribution with variance ", " = 0.25.