Tensor Balancing on Statistical Manifold
Authors: Mahito Sugiyama, Hiroyuki Nakahara, Koji Tsuda
ICML 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | show in numerical experiments that the proposed algorithm is several orders of magnitude faster than existing ones. |
| Researcher Affiliation | Academia | 1National Institute of Informatics 2JST PRESTO 3RIKEN Brain Science Institute 4Graduate School of Frontier Sciences, The University of Tokyo 5RIKEN AIP 6NIMS. |
| Pseudocode | No | The paper describes the algorithms in prose and mathematical equations but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | An implementation of algorithms for matrices and third order tensors is available at: https://github.com/ mahito-sugiyama/newton-balancing |
| Open Datasets | Yes | Hessenberg Matrix. The first set of experiments used a Hessenberg matrix, which has been a standard benchmark for matrix balancing (Parlett & Landis, 1982; Knight & Ruiz, 2013). Next, we collected a set of Trefethen matrices from a collection website2, which are nonnegative diagonal matrices with primes. Footnote 2: http://www.cise.ufl.edu/research/sparse/ matrices/ |
| Dataset Splits | No | The paper evaluates algorithm efficiency and convergence on benchmark matrices but does not mention or specify any training, validation, or test dataset splits. |
| Hardware Specification | Yes | All experiments were conducted on Amazon Linux AMI release 2016.09 with a single core of 2.3 GHz Intel Xeon CPU E5-2686 v4 and 256 GB of memory. |
| Software Dependencies | Yes | All methods were implemented in C++ with the Eigen library and compiled with gcc 4.8.31. |
| Experiment Setup | Yes | We measured the residual of a matrix A = (a ij) by the squared norm (A 1 1, A T 1 1) 2, where each entry a ij is obtained as npij in our algorithm, and ran each of three algorithms until the residual is below the tolerance threshold 10 6. |