mlsanityData to 7 Oct 2026

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

arXiv 2511.02430 ↗First posted 4 Nov 2025stat.CO cs.MS cs.SEcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 19 of its 81 references that are in the map. First posted on arXiv 4 Nov 2025.

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19 of 81 references.

References · 19

  1. 2015Coordinate Descent Algorithmscited by 218
  2. 2014SLOPE - Adaptive variable selection via convex optimizationcited by 33
  3. 2015Mind the duality gap: safer rules for the Lassocited by 31
  4. 2018Celer: a Fast Solver for the Lasso with Dual Extrapolationcited by 31
  5. 2022Benchopt: Reproducible, efficient and collaborative optimization benchmarkscited by 27
  6. 2018Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterationscited by 24
  7. 2022Beyond L1: Faster and Better Sparse Models with skglmcited by 16
  8. 2016Group SLOPE - adaptive selection of groups of predictorscited by 13
  9. 2020The Strong Screening Rule for SLOPEcited by 8
  10. 2017The biglasso Package: A Memory- and Computation-Efficient Solver for Lasso Model Fitting with Big Data in Rcited by 6
  11. 2021Safe rules for the identification of zeros in the solutions of the SLOPE problemcited by 6
  12. 2023Sparse-group SLOPE: adaptive bi-level selection with FDR-controlcited by 5
7 more
  1. 2018Solving the OSCAR and SLOPE Models Using a Semismooth Newton-Based Augmented Lagrangian Methodcited by 4
  2. 2022Coordinate Descent for SLOPEcited by 4
  3. 2014Sparse Estimation with Strongly Correlated Variables using Ordered Weighted L1 Regularizationcited by 3
  4. 2021The Hessian Screening Rulecited by 3
  5. 2021Look-Ahead Screening Rules for the Lassocited by 3
  6. 2014Decreasing Weighted Sorted ℓ1 Regularizationcited by 1
  7. 2025The Choice of Normalization Influences Shrinkage in Regularized Regressioncited by 1

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