B1587
Title: Inference with non-differentiable surrogate loss in a general high-dimensional classification framework
Authors: Muxuan Liang - University of Florida (United States) [presenting]
Yingqi Zhao - Fred Hutchinson Cancer Research Center (United States)
Yang Ning - Cornell University (United States)
Maureen Smith - University of Wisconsin-Madison (United States)
Abstract: Penalized empirical risk minimization with a surrogate loss function is often used to derive a high-dimensional linear decision rule in classification problems. Although much literature focuses on the generalization error, there is a lack of valid inference procedures to identify the driving factors of the estimated decision rule, especially when the surrogate loss is non-differentiable. We propose a kernel-smoothed de-correlated score to construct hypothesis testings and interval estimations for the linear decision rule estimated using a piece-wise linear surrogate loss, which has a discontinuous gradient and non-regular Hessian. Specifically, we adopt kernel approximations to smooth the discontinuous gradient near discontinuity points and approximate the non-regular Hessian of the surrogate loss. In applications where additional nuisance parameters are involved, we propose a novel cross-fitted version to accommodate flexible nuisance estimates and kernel approximations. We establish the limiting distribution of the kernel-smoothed de-correlated score and its cross-fitted version in a high-dimensional setup. Simulation and real data analysis are conducted to demonstrate the validity and superiority of the proposed method.
