Matrix Norm Estimation from a Few Entries
Authors: Ashish Khetan, Sewoong Oh
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments suggest that we significantly improve upon a competing approach of using matrix completion methods. and Numerical experiments confirm that the proposed estimator significantly outperforms simple heuristics of using singular values of the sampled matrices directly or applying state-of-the-art matrix completion methods (see Figure 4). |
| Researcher Affiliation | Academia | Ashish Khetan Department of ISE University of Illinois Urbana-Champaign khetan2@illinois.edu and Sewoong Oh Department of ISE University of Illinois Urbana-Champaign swoh@illinois.edu |
| Pseudocode | Yes | Algorithm 1 Schatten k-norm estimator |
| Open Source Code | Yes | A MATLAB implementation of the estimator (3), that includes as its sub-routines the computation of the weights of all k-cyclic pseudographs, is available for download at https://github.com/khetan2/Schatten_norm_estimation. |
| Open Datasets | No | The paper generates its own data based on specific matrix properties and random distributions, rather than using a publicly available dataset. For example, 'Singular vectors U of M = UΣU , are generated by QR decomposition of N(0, Id d) and Σi,i is uniformly distributed over [1, 2].' |
| Dataset Splits | No | The paper generates its own data and discusses sampling probabilities, but it does not specify explicit training, validation, or test dataset splits. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., CPU, GPU, or cloud instance types) used for running the experiments. |
| Software Dependencies | No | The paper mentions 'A MATLAB implementation' but does not provide specific version numbers for MATLAB or any other software dependencies or libraries. |
| Experiment Setup | Yes | M is a symmetric positive semi-definite matrix of size d = 500, and rank r = 100 (left panel) and r = 500 (right panel). Singular vectors U of M = UΣU , are generated by QR decomposition of N(0, Id d) and Σi,i is uniformly distributed over [1, 2]. and All the three estimators are evaluated 20 times for each value of p. and Empirical probabilities are computed by averaging over 100 instances. |