Benchmark repository for SLOPE

BenchOpt is a package to simplify and make more transparent and reproducible the comparisons of optimization algorithms. Regression with the Sorted L-One Penalized Estimation (SLOPE) estimator which consists in solving the following program:

$$ \min_{\beta} \, \tfrac{1}{2n} \Vert y - X\beta \Vert^2_2 + J(\beta, \lambda) $$

where

$$ J(\beta, \lambda) = \sum_{j=1}^p \lambda_j | \beta_{(j)}| $$

with $\lambda_1 \geq \lambda_2 \geq ... \geq \lambda_p$ and $|\beta_{(1)}| \geq |\beta_{(2)}| \geq ... \geq |\beta_{(p)}|$.

We note $n$ (or n_samples) the number of samples and $p$ (or n_features) the number of features. We also have that $X\in \mathbb{R}^{n\times p}$ and $y\in \mathbb{R}^n$.

Install

This benchmark can be run using the following commands:

$ pip install -U benchopt
$ git clone https://github.com/benchopt/benchmark_slope
$ benchopt run ./benchmark_slope

Apart from the problem, options can be passed to benchopt run, to restrict the benchmarks to some solvers or datasets, e.g.:

$ benchopt run ./benchmark_slope -s cd -d simulated --max-runs 10 --n-repetitions 5

Use benchopt run -h for more details about these options, or visit https://benchopt.github.io/cli.html.