lar_testing

This repository contains an illustration of the numerical experiments performed in the paper entitled

Multiple Testing and Variable Selection Along the Path of the Least Angle Regression, arXiv:1906.12072v5.

by Jean-Marc Azaïs and Yohann De Castro. The Python code can be downloaded at

Github repository lar_testing

and the code lar_testing-v2.0 used in the paper arXiv:1906.12072v5 has been posted on Zenodo:

Comparison with Knockoff, FCD and SLOPE on HIV dataset

The first notebook called Multiple Spacing Tests presents the numerical experiments of the paper entitled

Multiple Testing and Variable Selection Along a Path of the Least Angle Regression, arXiv:1906.12072v5.

We present the following points:

• A comparison of the power and FDR control on simulated data for GtST, FCD and Knockoff in Section I;
• Presentation of HIV dataset in Section II;
• A comparison of the power and FDR control on HIV dataset for GtST, FCD, Knockoff and Slope in Section III;
• A new formulation of LARS algorithm in Section IV;

The methods considered are:

• [Knockoff] Knockoff filters for FDR control and we use the implementation presented on the webpage https://web.stanford.edu/group/candes/knockoffs/ based on the paper:

  Controlling the False Discovery Rate via Knockoffs, arXiv:1404.5609;

• [FCD] False Discovery Control via Debiasing and we use the implementation of debiased lasso presented on the webpage https://web.stanford.edu/~montanar/sslasso/ and as presented in the paper:

  False Discovery Rate Control via Debiased Lasso, arXiv:1803.04464;

• [Slope] Slope for FDR control, as presented in the paper:

  SLOPE - Adaptive variable selection via convex optimization arXiv:1407.3824;

• [GtSt-BH] Generalized t-Spacing tests on successive entries of the LARS path comibined with a Benjamini–Hochberg procedure presented in the paper:

  Multiple Testing and Variable Selection along Least Angle Regression’s path, arXiv:1906.12072v5.

Numerical joint law

The second notebook gives an empirical evidence of the joint law shown in the paper

Multiple Testing and Variable Selection along Least Angle Regression’s path, arXiv:1906.12072v5.

Thank you for your time!