Jonas Wallin

Universitetslektor, Studierektor för forskarutbildningen, Statistiska institutionen

Coordinate Descent for SLOPE

Författare

Johan Larsson
Quentin Klopfenstein
Mathurin Massias
Jonas Wallin

Redaktör

Francisco Ruiz
Jennifer Dy
Jan-Willem van de Meent

Summary, in English

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 demonstrate our method's performance against a long list of competing algorithms.

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