Nonasymptotic Guarantees for Spiked Matrix Recovery with Generative Priors
Authors: Jorio Cocola, Paul Hand, Vlad Voroninski
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We further corroborate these findings by proposing a (sub)gradient algorithm which, as shown by our numerical experiments, is able to recover the sought spike with optimal sample complexity. |
| Researcher Affiliation | Collaboration | Jorio Cocola Department of Mathematics Northeastern University Boston, MA 02115 cocola.j@northeastern.edu Paul Hand Department of Mathematics and Khoury College of Computer Sciences, Northeastern University Boston, MA 02115 p.hand@northeastern.edu Vladislav Voroninski Helm.ai, Menlo Park, CA 94025 vlad@helm.ai |
| Pseudocode | Yes | Algorithm 1 Gradient method for the minizimization problem (4) |
| Open Source Code | No | The paper does not provide any specific links or explicit statements about releasing the source code for the methodology described. |
| Open Datasets | No | The paper describes generating 'synthetic generative priors' and 'randomly sample the weights of the matrix' and 'consider data Y according the spiked models (1) and (2)', rather than using a publicly available or open dataset. Therefore, no information on public dataset access is provided. |
| Dataset Splits | No | The paper performs numerical experiments on synthetically generated data, varying parameters like 'samples N' and 'noise level ν'. It does not describe standard training, validation, and testing splits from a fixed dataset, nor does it specify exact percentages or counts for such splits. |
| Hardware Specification | No | The paper mentions running 'numerical experiments' but does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used for these experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., Python, PyTorch, specific libraries). |
| Experiment Setup | Yes | We consider 2-layer generative networks with Relu activation functions, hidden layer of dimension n1 = 250, output dimension n = 1700 and varying number of latent dimension k [10, 30, 70]. We randomly sample the weights of the matrix independently from N(0, 2/ni), which removes that 2d dependence in Theorem 2. We then consider data Y according the spiked models (1) and (2), where x Rk is chosen so that y = G(x ) has unit norm. For the Wishart model we vary the samples N while for the Wigner model we vary the noise level ν so that the following quantities remain constant for the different networks (latent dimension k). |