Efficient Solvers for SLOPE in R, Python, Julia, and C++

TL;DR

This paper introduces efficient, multi-language software packages for solving the SLOPE problem, supporting various models and data types, with benchmarks showing superior speed over existing solutions.

Contribution

It provides a highly efficient, flexible suite of packages in R, Python, Julia, and C++ for solving SLOPE with a novel hybrid coordinate descent algorithm.

Findings

Packages outperform existing SLOPE implementations in speed

Support for multiple loss functions and data structures

Efficiently fits the full SLOPE path and handles cross-validation

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.