Integral-based Knockoffs Inference for Partially Linear Models

Partial linear models (PLM) have attracted much attention for regression estimation and variable selection due to their feasibility on utilizing linear and nonlinear approximations jointly. However, theoretical understanding of how they control the false discovery rate (FDR) during variable selection remains limited. To address this issue, we formulate a new integral-based knockoffs (IKO) inference scheme for controlled variable selection in PLM, where integral-based knockoff statistics are used to measure the variable importance and B-splines (or random Fourier features) are employed for approximating nonlinear components. In theory, FDR control is guaranteed for both linear and nonlinear parts, and the statistical analysis for its power is established. Empirical evaluations validate the effectiveness of our proposed approach.