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.