Global Optimality of Local Search for Low Rank Matrix Recovery
Authors: Srinadh Bhojanapalli, Behnam Neyshabur, Nati Srebro
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 1: The plots in this figure compare the success probability of gradient descent between (left) random and (center) SVD initialization (suggested in [15]), for problem (2), with increasing number of samples m and various values of rank r. Right most plot is the first m for a given r, where the probability of success reaches the value 0.5. A run is considered success if k UU > X k F /k X k F 1e 2. White cells denote success and black cells denote failure of recovery. We set n to be 100. Measurements yi are inner product of entrywise i.i.d Gaussian matrix and a rank-r p.s.d matrix with random subspace. We notice no significant difference between the two initialization methods, suggesting absence of local minima as shown. Both methods have phase transition around m = 2 n r. |
| Researcher Affiliation | Academia | Srinadh Bhojanapalli srinadh@ttic.edu Behnam Neyshabur bneyshabur@ttic.edu Nathan Srebro nati@ttic.edu Toyota Technological Institute at Chicago |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described (e.g., no specific repository link, explicit code release statement, or mention of code in supplementary materials). |
| Open Datasets | No | The paper mentions "i.i.d. Gaussian measurements" and "random rank-k matrices" for experiments, but does not provide concrete access information (specific link, DOI, repository name, formal citation with authors/year) for a publicly available or open dataset. |
| Dataset Splits | No | The paper describes generating synthetic data for its experiments but does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types with speeds, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiment. |
| Experiment Setup | Yes | Figure 1: The plots in this figure compare the success probability of gradient descent between (left) random and (center) SVD initialization (suggested in [15]), for problem (2), with increasing number of samples m and various values of rank r. ... We set n to be 100. Measurements yi are inner product of entrywise i.i.d Gaussian matrix and a rank-r p.s.d matrix with random subspace. |