Muxuan Liang, Ph.D.
Post-Doctoral Research Fellow
Public Health Sciences Division
Fred Hutchinson Cancer Research Center
Title: Statistical inference of decision rules under a non-differentiable surrogate loss in a general high-dimensional classification framework
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 many literature focus 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. In this work, 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. Specifically, we adopt kernel approximations to approximate the gradient and the 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 the superiority of the proposed method.
About Muxuan Liang, Ph.D.
Dr. Liang is currently a post-doctoral research fellow at Fred Hutchinson Cancer Research Center working on both biostatistics methodology and applications. He obtained his Ph.D. degree in statistics from the University of Wisconsin-Madison in 2018 and will join the Department of Biostatistics at University of Florida next spring. His research topics focus on treatment recommendations based on patient-level information, identifying signals from high-dimensional data, and other novel machine learning techniques with applications to biomarker identification, cancer surveillance, and the impact of digital health. He has published more than 10 papers including first author papers on top-tier statistical journals and been a reviewer for top journals including Journal of the American Statistical Association, Journal of Machine Learning Research, and Journal of the Royal Statistical Society: Series B.
Department of Industrial & Systems Engineering