Model-free Knockoffs for SLOPE-Adaptive Variable Selection with Controlled False Discovery Rate

Automatic selection of true explanatory variables and controlling fraction of false discovery rate (FDR) in the linear model has received considerable attention in machine learning. The ordered regularization is an important component of the linear model and plays a key role in solving such kind of problems. Although there have been some models proposed for determining relevant features in either low-dimensional or high-dimensional space. However, there exists no single sorted model that can work in both low-high dimensions cases. This paper introduces a model called mSLOPE (model-free SLOPE) which is a mixed methodology based on model-free (MF) knockoffs and sorted Lone penalized estimation (SLOPE). mSLOPE uses original design matrix augmented with MF knockoffs matrix. The original feature matrix and MF matrix have the same covariance structure. Advantages of mSLOPE include, (i) it identifies true regressors in any dimension, (ii) it is an adaptive and computationally tractable and (iii) it gains power relative to its competitors through an exact control of FDR in any dimensions. Experimental results on both synthetic and real data show that mSLOPE gains superior power and accurate FDR control than state-of-the-art baselines.