  The recently proposed fixed-X knockoff is a powerful variable selection
procedure that controls the false discovery rate (FDR) in any finite-sample
setting, yet its theoretical insights are difficult to show beyond Gaussian
linear models. In this paper, we make the first attempt to extend the fixed-X
knockoff to partially linear models by using generalized knockoff features, and
propose a new stability generalized knockoff (Stab-GKnock) procedure by
incorporating selection probability as feature importance score. We provide FDR
control and power guarantee under some regularity conditions. In addition, we
propose a two-stage method under high dimensionality by introducing a new joint
feature screening procedure, with guaranteed sure screening property. Extensive
simulation studies are conducted to evaluate the finite-sample performance of
the proposed method. A real data example is also provided for illustration.
