High-Dimensional Tensor Regression With Oracle Properties
Authors: Wenbin Wang, Yu Shi, Ziping Zhao
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Extensive experiments conducted on both synthetic and real-world datasets validate the effectiveness of the proposed regression model and showcase the practical utility of the theoretical findings. Extensive numerical experiments on both synthetic data and real-world datasets validate the theoretical results and demonstrate the practical advantages and breadth of the proposed methods. |
| Researcher Affiliation | Academia | 1School of Information Science and Technology, Shanghai Tech University, Shanghai 201210, China. Correspondence to: Ziping Zhao <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Accelerated Proximal Gradient Algorithm |
| Open Source Code | No | The paper discusses the optimization algorithm and numerical experiments but does not provide any explicit statement or link to an open-source code repository for the methodology described in the paper. |
| Open Datasets | Yes | We validate our method on Image Net 2012 dataset (Russakovsky et al., 2015) for image denoising using a 3rd-order tensor A R64 64 3 with n = 4000 samples. The experimental data employed in this study were sourced from the University of Southern California s Viterbi School of Engineering repository and the UCI Machine Learning Repository s EEG Database. Specifically, the datasets can be accessed via the following links: https://archive.ics.uci.edu/dataset/121/eeg+database, https: //viterbi-web.usc.edu/~liu32/data.html. |
| Dataset Splits | Yes | The tuning parameter λ and the hyperparameter within the SCAD penalty are selected via ten-fold cross-validation, aiming to minimize the estimation error. |
| Hardware Specification | No | The paper describes the experimental setup and datasets used but does not provide specific details about the hardware (e.g., GPU models, CPU types, memory) on which the experiments were conducted. |
| Software Dependencies | No | The paper mentions "MATLAB CVX solver" in Table 6 but does not specify its version number. No other software dependencies are listed with specific version numbers. |
| Experiment Setup | Yes | The tuning parameter λ and the hyperparameter within the SCAD penalty are selected via ten-fold cross-validation, aiming to minimize the estimation error. All the reported results are averaged on 100 Monte Carlo realizations to ensure statistical robustness. For Figures 1 and 2, the noise parameter η is set to 0.1. In our experiments, we adopt q = 5 to balance the convergence speed and stability. For sparsity, we set the η = 0.1, and for low-rankness, η = 1. |