Quantile Regression Benchmark

Benchopt is a package to simplify and make more transparent and reproducible the comparisons of optimization algorithms. This benchmark is dedicated to the the L1-regularized quantile regression problem:

$$\min_{\beta, \beta_0} \frac{1}{n} \sum_{i=1}^{n} \text{pinball}(y_i, x_i^\top \beta + \beta_0) + \lambda \lVert \beta \rVert_1$$

where

$$\text{pinball}(y, \hat{y}) = \alpha \max(y - \hat{y}, 0) + (1 - \alpha) \max(\hat{y} - y, 0)$$

where $n$ (or n_samples) stands for the number of samples, $p$ (or n_features) stands for the number of features and

$$X = [x_1^\top, \dots, x_n^\top]^\top \in \mathbb{R}^{n \times p}$$

Install

This benchmark can be run using the following commands:

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

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_quantile_regression -s scipy -d simulated --max-runs 10 --n-repetitions 10

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