$\ell_0$ Trend Filtering

This archive is distributed in association with the INFORMS Journal on Computing under the MIT License.

The software and R scripts in this repository are a snapshot of the software and code that were used in the research reported on in the paper $\ell_0$ Trend Filtering by C. Wen and X. Wang and A. Zhang.

Important: This code is being developed on an on-going basis at https://github.com/C2S2-HF/L0TF. Please go there if you would like to get a more recent version or would like support

Cite

To cite the contents of this repository, please cite both the paper and this repo, using their respective DOIs.

https://doi.org/10.1287/ijoc.2019.0000

https://doi.org/10.1287/ijoc.2019.0000.cd

Below is the BibTex for citing this snapshot of the respoitory.

@article{wenl0trend,
  author =        {Canhong Wen, Xueqin Wang, Aijun Zhang},
  publisher =     {INFORMS Journal on Computing},
  title =         {$\ell_0$ Trend Filtering},
  year =          {2023},
  doi =           {10.1287/ijoc.2019.0000.cd},
  url =           {https://github.com/INFORMSJoC/2021.0313},
}  

Description

The goal of this repository is to share softare and R scripts of our paper $\ell_0$ Trend Filtering. Our motivation is to present our code and results in a reproducible way and facilitate the coding effort of thos who want to run further experiments or improve our model.

Repository Structure

code folder contains the following files in R language:

• SimuL0TF.Rmd: generate Figures 2-7 and include some more illustrative simulated examples.
• AlgoAnalysis.Rmd: replicate the reuslts and generate Figures 8-11 in Section 4.1.
• utils.R and amiasutils.R: source codes used in AlgoAnalysis.Rmd.
• RealData.R: replicate the results and generate all the graphs in Section 4.3.
• AlgoAnalysis_APP.Rmd: replicate the reuslts and generate Figures B.1-B.7 in Appendix B.1.
• simu folder contains R scripts used in Appendix B.2:
  • nsimu.R and tsimu.R: replicate the results for all methods except for the l0-MIP with large sample size.
  • nsimul0tfc.R and tsimul0tfc.R: replicate the results of the l0-MIP method when sample size is large.
• simu_plots folder contains the R Scripts used to generate Figures B.9-B.20 in Appendix B.2.
  • post_plot.R: generate Figures B.9, B.11 and B.13.
  • pre_plot.R: generate Figures B.10, B.12 and B.14.
  • post_tplot.R: generate Figures B.15, B.17 and B.19.
  • pre_tplot.R: generate Figures B.16, B.18 and B.20.
  • combine_RData.R: combine the RData and needed to be run before generating all the figures.

data folder contains the data in the real data application in Section 4.2. Please see spreadsheet file to view the data.

AMIAS_1.0.3.tar.gz contains the source file of the R package for implementing the AMIAS algorithm proposed in our paper. After downloading it, you need to run the following code in R to install it.

install.packages("Your_download_path/AMIAS_1.0.3.tar.gz", repos = NULL)

Support

For support in using the scripts, you can reach the authors by email wench@ustc.edu.cn.