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.

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.

Deep sparse networks (DSNs) have demonstrated exceptional performance for nonlinear estimation and feature selection, which is crucial for enhancing predictive performance and interpretability. However, existing methods often overlook feature interactions and lack theoretical guarantees on false discovery rate (FDR), especially under interaction scenarios.To address the above issues, this paper develops a DSN-based knockoffs inference framework for feature interaction selection. Theoretical guarantee can be provided by knockoffs inference for controlling on FDR. Empirical evaluations on synthetic datasets demonstrate the capabilities of our proposal on FDR control and identification of informative interactions.