/High-dimensional-Linear-Bandits-with-Variable-Selection

Primary LanguageR

High-dimensional Linear Bandits with Variable Selection

Author Contributions Checklist Form

Data

Abstract

We implement simulation and real data experiments, i.e., Africa soil property data and Riboflavin production data, in this paper.

Availability

  1. Africa soil property data: training dataset in https://www.kaggle.com/c/afsis-soil-properties;
  2. Riboflavin production data: provided in the supplementary material (riboflavin.csv) of Bühlmann et al. (2014). (https://www.annualreviews.org/doi/abs/10.1146/annurev-statistics-022513-115545)

Description

We provide the data file:

  1. Africa soil data: trainging.csv contains the training dataset from (https://www.kaggle.com/competitions/afsis-soil-properties/data), including response variable Ca and covariate Depth that is used to partition the dataset into two groups for bandit experiment.
  2. Riboflavin data: riboflavin.csv contains the dataset https://www.annualreviews.org/doi/abs/10.1146/annurev-statistics-022513-115545.

Code

Abstract

All of the simulation and real data experiments are done in R. We provide R code that is necessary for the replication of our empirical results.

Description

Version of primary software used

R version 4.0.1

Libraries and dependencies used by the code

R packages: glmnet; MASS; ncvreg; picasso; foreach; doParallel

Parallelization used

Multi-core parallelization on a single machine/node: 22 cores used.

Instructions for use

Reproducibility

  • The simulation folder contains the R code for reproducing simulation results in the paper corresponding to $K=5, d=100, s_0=5$ scenario. The other two scenarios ($d=1000$ and $d=20$) can be reproduced by changing parameters in the R code. Below is the description of R code files for all compared methods.
    • mcp_ucb_vs_cv.R: our proposed UCB-VS algorithm with MCP
    • scad_ucb_vs_cv.R: our proposed UCB-VS algorithm with SCAD
    • mcp_ucb_cv.R: $\ell_1$-confidence ball based algorithm with MCP
    • scad_ucb_cv.R: $\ell_1$-confidence ball based algorithm with SCAD
  • The real_data folder contains the R-code for two real data experiments in the paper.
  • africa_soil folder contains R-code for Africa soil property data.
    • trainging.csv: the file contains the training dataset from (https://www.kaggle.com/competitions/afsis-soil-properties/data), including response variable Ca and covariate Depth that is used to partition the dataset into two groups for bandit experiment.
    • mcp_ucb_vs_ridge.R: UCB-VS algorithm with MCP and $\alpha=1$ for additional $\ell_2$-penalty.
    • mcp_ucb_vs_ridge_cv.R: UCB-VS algorithm with MCP and cross-validation.
    • mcp_ucb_ridge.R: $\ell_1$-confidence ball based algorithm with MCP and $\alpha=1$ for additional $\ell_2$-penalty.
    • scad_ucb_vs_ridge.R: UCB-VS algorithm with SCAD and $\alpha=1$ for additional $\ell_2$-penalty.
    • scad_ucb_vs_ridge_cv.R: UCB-VS algorithm with SCAD and cross-validation.
    • scad_ucb_ridge.R: $\ell_1$-confidence ball based algorithm with SCAD and $\alpha=1$ for additional $\ell_2$-penalty.
    • Other $\alpha$ values (e.g. $1$ and $1/9$) for $\ell_2$-penalty can also be set. More details can be found from the comments in R code.
  • riboflavin folder contains R-code for Riboflavin production data.
    • riboflavin.csv: the file contains the dataset