Stepdown SLOPE for Controlled Feature Selection

Sorted L-One Penalized Estimation (SLOPE) has shown the nice theoretical property as well empirical behavior recently on false discovery rate (FDR) control of high-dimensional feature selection by adaptively imposing non-increasing sequence tuning parameters sorted L1 penalties. This paper goes beyond previous concern limited to FDR considering stepdown-based SLOPE in order probability k or more rejections (k-FWER) and proportion (FDP). Two new SLOPEs, called k-SLOPE F-SLOPE, are proposed realize k-FWER FDP respectively, where stepdown procedure is injected into scheme. For we establish their guarantees controlling under orthogonal design setting, also provide an intuitive guideline for choice regularization parameter much general setting. Empirical evaluations simulated data validate effectiveness our approaches controlled support findings.