Automated and Unbiased Coefficient Clustering with Non Convex SLOPE

TMLR Paper2551 Authors

Abstract:

This work studies the problem of sparse structured generalized linear models with sorted nonsmooth penalties, which are known to induce an automatic grouping of the features without a priori.
Generalizing the Sorted L1 Penalty (SLOPE), we introduce a family of nonconvex sorted penalties which not only promote clustering of variables, but are less biased than their popular convex counterpart.
For sorted weakly convex penalties (e.g. sorted MCP and SCAD), we provide an algorithm that exactly and efficiently computes their proximal operator.
Moreover, we show that a slight modification of this algorithm turns out to be remarkably efficient to tackle the computation of the proximal operator of sorted $\ell_q$ with $ q \in \left]0,1\right[$, which is not weakly convex and whose prox yields a challenging combinatorial problem.
We demonstrate the interest of using such penalties on several experiments.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Stephen_Becker1

Submission Number: 2551