Strong rules for nonconvex penalties and their implications for efficient algorithms in high-dimensional regression

Patrick Breheny &
We consider approaches for improving the efficiency of algorithms for fitting nonconvex penalized regression models such as SCAD and MCP in high dimensions. In particular, we develop rules for discarding variables during cyclic coordinate descent. This dimension reduction leads to an improvement in the speed of these algorithms for high-dimensional problems. The rules we propose here eliminate a substantial fraction of the variables from the coordinate descent algorithm. Violations are quite rare, especially in the...
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