A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration
Authors: Yuetian Luo, Garvesh Raskutti, Ming Yuan, Anru R. Zhang
JMLR 2021 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We support our theoretical results by extensive numerical studies. Finally, we apply the novel perturbation bounds of HOOI on two applications, tensor denoising and tensor co-clustering, from machine learning and statistics, which demonstrates the superiority of the new perturbation results. In Section 7, we corroborate our theoretical results by extensive numerical studies. |
| Researcher Affiliation | Academia | Yuetian Luo EMAIL Department of Statistics University of Wisconsin-Madison Madison, WI 53706, USA; Garvesh Raskutti EMAIL Department of Statistics University of Wisconsin-Madison Madison, WI 53706, USA; Ming Yuan EMAIL Department of Statistics Columbia University New York, NY 10027, USA; Anru R. Zhang EMAIL Department of Statistics University of Wisconsin-Madison Madison, WI 53706, USA |
| Pseudocode | Yes | Algorithm 1 Higher-Order Orthogonal Iteration for Tensor Decomposition; Algorithm 2 Higher-Order Orthogonal Iteration for Tensor Decomposition (d 3); Algorithm 3 Power Iteration for Tensor Decomposition in Partial Multilinear Low-Rank Setting (25); Algorithm 4 HOOI for Tensor Co-clustering/Block Model |
| Open Source Code | No | The paper states: 'Nowadays, HOOI has become a prevalent choice to compute the low-rank tensor approximation in many applications and been coded in common tensor software such as Matlab Tensor Toolbox (Bader and Kolda, 2012), Tensorlab (Sorber et al., 2014) and R r Tensor package (Li et al., 2018).' This refers to existing third-party software, not code provided by the authors for the methodology described in this paper. No other explicit statement or link to open-source code by the authors is found. |
| Open Datasets | No | The paper discusses numerical studies using simulated data based on models like tensor denoising and tensor co-clustering: 'In tensor denoising, we assume T has the following structure...' and 'In the tensor coclustering/block model, we assume T has the following structure...'. There is no mention of any specific publicly available datasets, nor any links or citations to external datasets. |
| Dataset Splits | No | The numerical studies use synthetically generated data and simulations are repeated multiple times ('All simulations are repeated 100 times and the average statistics are reported.'). The paper does not mention any training/test/validation splits, cross-validation, or specific data partitioning methodologies, as it does not appear to use pre-existing datasets that would typically have such splits. |
| Hardware Specification | No | The paper does not provide any specific details regarding the hardware used for running the experiments. There are no mentions of GPU or CPU models, memory specifications, or other computing resource details. |
| Software Dependencies | No | The paper mentions 'Matlab Tensor Toolbox (Bader and Kolda, 2012), Tensorlab (Sorber et al., 2014) and R r Tensor package (Li et al., 2018)' as common tensor software. However, it does not specify which of these (if any) were used for the authors' experiments, nor does it provide specific version numbers for these or any other software components. |
| Experiment Setup | Yes | The 'Numerical Studies' section details various parameters for the synthetic data generation and experiment execution: 'p P t20, 30, . . . , 100u, r 5, σ P t1, 2, 3, 4u and λ 5?prσ'; 'p1 10, p2 100, p3 500, r P t3, 5u, σ 1 and λ α p3?r ?p1 with varying α'; 'p P t50, 80u, r P t3, 5, 8u, σ 1, λ α r3{2 p3{4 σ'; 'All simulations are repeated 100 times and the average statistics are reported.' |