Low-Rank Matrix Estimation in the Presence of Change-Points
Authors: Lei Shi, Guanghui Wang, Changliang Zou
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical results demonstrate the validity and effectiveness of the proposed scheme. Keywords: High-dimensional data, low-rank estimation, multiple change-point detection, non-asymptotic bounds, rate-optimal estimators. In this section, we run several synthetic experiments to show the validity and effectiveness of the proposed scheme in change-point detection as well as low-rank matrix recovery. A real-data example is also investigated, which reveals the benefit of incorporating structural changes for matrix estimation. |
| Researcher Affiliation | Academia | Lei Shi EMAIL Department of Biostatistics University of California, Berkeley California 94704, United States; Guanghui Wang EMAIL School of Statistics and Data Science, LPMC, KLMDASR, and LEBPS Nankai University Tianjin 300071, China; Changliang Zou EMAIL NITFID, School of Statistics and Data Science, LPMC, KLMDASR, and LEBPS Nankai University Tianjin 300071, China |
| Pseudocode | Yes | Algorithm 1: Joint multiple change-point detection and matrix estimation; Algorithm 2: Joint single change-point detection and matrix estimation; Algorithm 3: Proximal gradient descent for (3) |
| Open Source Code | Yes | The algorithm is implemented in MATLAB and the source code can be accessed through the public Git Hub repository: https://github.com/ Lei Shi-rocks/Low Rank_Change Points. |
| Open Datasets | Yes | Our study is based on an hourly air pollutants dataset from 12 nationally controlled air-quality monitoring sites collected by the Beijing Municipal Environmental Monitoring Center. The time period is from March 1st, 2013 to February 28th, 2017. The original data file and descriptions are available at the UCI Machine Learning Repository: https://archive. ics.uci.edu/ml/datasets/Beijing+Multi-Site+Air-Quality+Data. |
| Dataset Splits | Yes | To study the performance of our method, we split the dataset into two parts: a test set {Ytest, Xtest} with 20% of the total observations (Ntest = 220) and a training set {Ytrain, Xtrain} with the remaining 80% (Ntrain = 880). Then the training set is further divided into 5 folds and we apply cross-validation to tune the number of change-points, with 4 folds for model training and 1 fold for validation. |
| Hardware Specification | No | The paper mentions running numerical studies and real-data analysis but does not provide any specific hardware details such as GPU/CPU models, processor types, or memory amounts used for these experiments. |
| Software Dependencies | No | The algorithm is implemented in MATLAB and the source code can be accessed through the public Git Hub repository: https://github.com/ Lei Shi-rocks/Low Rank_Change Points. The paper mentions MATLAB but does not specify its version number or any other software dependencies with their versions. |
| Experiment Setup | Yes | Algorithm 2: Joint single change-point detection and matrix estimation Input: Observed data (yi, Xi, ti), for i = 1, , n; regularization parameter λN; floor curvature L(0); ceiling curvature Lmax; updating rate η; convergence tolerance tol and maximal iteration T. Algorithm 3: Proximal gradient descent for (3) Input: Same input as Algorithm 2; testing break position τ. In practice, the regularization parameter λN is chosen through cross-validation. |