Subquadratic Kronecker Regression with Applications to Tensor Decomposition
Authors: Matthew Fahrbach, Gang Fu, Mehrdad Ghadiri
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the speed and accuracy of this Kronecker regression algorithm on synthetic data and real-world image tensors. 6 Experiments All experiments were run using Num Py [26] with an Intel Xeon W-2135 processor (8.25MB cache, 3.70 GHz) and 128GB of RAM. The Fast Kronecker Regression-based ALS experiments for low-rank Tucker decomposition on image tensors are deferred to Appendix D.2. |
| Researcher Affiliation | Collaboration | Matthew Fahrbach Google Research fahrbach@google.com Gang Fu Google Research thomasfu@google.com Mehrdad Ghadiri Georgia Tech ghadiri@gatech.edu |
| Pseudocode | Yes | Algorithm 1 Tucker ALS, Algorithm 2 Fast Kronecker Regression, Algorithm 3 Fast Factor Matrix Update |
| Open Source Code | Yes | All of our code is available at https://github.com/fahrbach/subquadratic-kronecker-regression. |
| Open Datasets | Yes | We used two real-world image tensors to evaluate the performance of our ALS implementation with Fast Kronecker Regression: the Columbia Object Image Library (COIL-20) [51] and the Natural Scenes Dataset (NSD) [50]. |
| Dataset Splits | No | The paper mentions using synthetic data and specific image tensors (COIL-20, NSD) but does not provide details on how these datasets were split into training, validation, or test sets, or reference standard splits. |
| Hardware Specification | Yes | All experiments were run using Num Py [26] with an Intel Xeon W-2135 processor (8.25MB cache, 3.70 GHz) and 128GB of RAM. |
| Software Dependencies | No | The paper mentions using "Num Py [26]" for experiments but does not provide specific version numbers for NumPy or any other software dependencies. |
| Experiment Setup | Yes | For both sketching algorithms, we use " = 0.1 and δ = 0.01. We reduce the number of row samples in both algorithms by = 10 5 so that the algorithms are more practical and comparable to the earlier experiments in [17, 18]. Lastly, we set λ = 10 3. |