A generalization of the randomized singular value decomposition
Authors: Nicolas Boulle, Alex Townsend
ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical examples on matrices and HS operators demonstrate the applicability of the algorithm. |
| Researcher Affiliation | Academia | Nicolas Boull e Mathematical Institute University of Oxford Oxford, OX2 6GG, UK boulle@maths.ox.ac.uk Alex Townsend Department of Mathematics Cornell University Ithaca, NY 14853, USA townsend@cornell.edu |
| Pseudocode | Yes | Algorithm 1 Randomized SVD for HS operators |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. |
| Open Datasets | No | The paper uses synthetic problem setups (e.g., discretized matrix of a differential operator, defined kernels) rather than publicly available datasets with concrete access information. |
| Dataset Splits | No | The paper does not provide specific dataset split information (e.g., train/validation/test percentages or counts) needed to reproduce the data partitioning. |
| Hardware Specification | Yes | Timings were performed on an Intel Xeon CPU E5-2667 v2 @ 3.30GHz using MATLAB R2020b without explicit parallelization. |
| Software Dependencies | Yes | Timings were performed on an Intel Xeon CPU E5-2667 v2 @ 3.30GHz using MATLAB R2020b without explicit parallelization. The algorithm is implemented in the Chebfun software system (Driscoll et al., 2014), which is a MATLAB package for computing with functions. The continuous Cholesky factorization is implemented in Chebfun2 (Townsend & Trefethen, 2013), which is the extension of Chebfun for computing with two-dimensional functions. |
| Experiment Setup | Yes | We vary the number of columns (i.e. samples from the GP) in the input matrix Ωfrom 1 to 2000. We employ the squared-exponential covariance kernel KSE with parameter ℓ= 0.01 and k = 100 samples (see Equation (3)) to sample random functions from the associated GP. [...] K(2,2) Jac with eigenvalues λj = 1/j3, for j ≥ 1. |