Coordinate Descent for SLOPE


Johan Larsson

Quentin Klopfenstein

Mathurin Massias

Jonas Wallin


26 October 2022


arXiv, arXiv:2210.14780




BibTeX citation:
  author = {Johan Larsson and Quentin Klopfenstein and Mathurin Massias
    and Jonas Wallin},
  publisher = {arXiv},
  title = {Coordinate Descent for {SLOPE}},
  number = {arXiv:2210.14780},
  date = {2022-10-26},
  url = {},
  doi = {10.48550/arXiv.2210.14780},
  langid = {en},
  abstract = {The lasso is the most famous sparse regression and feature
    selection method. One reason for its popularity is the speed at
    which the underlying optimization problem can be solved. Sorted
    L-One Penalized Estimation (SLOPE) is a generalization of the lasso
    with appealing statistical properties. In spite of this, the method
    has not yet reached widespread interest. A major reason for this is
    that current software packages that fit SLOPE rely on algorithms
    that perform poorly in high dimensions. To tackle this issue, we
    propose a new fast algorithm to solve the SLOPE optimization
    problem, which combines proximal gradient descent and proximal
    coordinate descent steps. We provide new results on the directional
    derivative of the SLOPE penalty and its related SLOPE thresholding
    operator, as well as provide convergence guarantees for our proposed
    solver. In extensive benchmarks on simulated and real data, we show
    that our method outperforms a long list of competing algorithms.}
For attribution, please cite this work as:
Johan Larsson, Quentin Klopfenstein, Mathurin Massias, and Jonas Wallin. 2022. “Coordinate Descent for SLOPE.” arXiv.