Efficient Solvers for SLOPE in R, Python, Julia, and C++
Abstract
We present a suite of packages in R, Python, Julia, and C++ that efficiently solve the Sorted L-One Penalized Estimation (SLOPE) problem. The packages feature a highly efficient hybrid coordinate descent algorithm that fits generalized linear models (GLMs) and supports a variety of loss functions, including Gaussian, binomial, Poisson, and multinomial logistic regression. Our implementation is designed to be fast, memory-efficient, and flexible. The packages support a variety of data structures (dense, sparse, and out-of-memory matrices) and are designed to efficiently fit the full SLOPE path as well as handle cross-validation of SLOPE models, including the relaxed SLOPE. We present examples of how to use the packages and benchmarks that demonstrate the performance of the packages on both real and simulated data and show that our packages outperform existing implementations of SLOPE in terms of speed.
Keywords
Cite
@article{arxiv.2511.02430,
title = {Efficient Solvers for SLOPE in R, Python, Julia, and C++},
author = {Johan Larsson and Malgorzata Bogdan and Krystyna Grzesiak and Mathurin Massias and Jonas Wallin},
journal= {arXiv preprint arXiv:2511.02430},
year = {2025}
}
Comments
30 pages, 8 figures