Knockoffs Inference for Partially Linear Models with Automatic Structure Discovery

Partially linear models (PLM) have attracted much attention in the field of statistical machine learning. Specially, the ability of variable selection of PLM has been studied extensively due to the high requirement of model interpretability. However, few of the existing works concerns the false discovery rate (FDR) controllability of variable selection associated with PLM. To address this issue, we formulate a new Knockoffs Inference scheme for Linear And Nonlinear Discoverer (called KI-LAND), where FDR is controlled with respect to both linear and nonlinear variables for automatic structure discovery. For the proposed KI-LAND, theoretical guarantees are established for both FDR controllability and power, and experimental evaluations are provided to validate its effectiveness.