2019/01/03 by Xin He, He, Xin, Yeheng Ge +3
Engineering · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1901.00615
openalex publication_date 2019/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some specific settings under certain model assumptions, this paper proposes a general and novel framework for recovering true structures of target functions by using unstructured M-regression in a reproducing kernel Hilbert space (RKHS). The proposed framework is inspired by the fact that gradient functions can be employed as a valid tool to learn underlying structures, including sparse learning, interaction selection and model identification, and it is easy to implement by taking advantage of the nice properties of the RKHS. More importantly, it admits a wide range of loss functions, and thus includes many commonly used methods, such as mean regression, quantile regression, likelihood-based classification, and margin-based classification, which is also computationally efficient by solving convex optimization tasks. The asymptotic results of the proposed framework are established within a rich family of loss functions without any explicit model specifications. The superior performance of the proposed framework is also demonstrated by a variety of simulated examples and a real case study.