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A0909
Title: GSLM: Structure learning via unstructured kernel-based M-regression Authors:  Yeheng Ge - Shanghai University of Finance and Economics (China) [presenting]
Xingdong Feng - Shanghai University of Finance and Economics (China)
Xin He - Shanghai University of Finance and Economics (China)
Abstract: In statistical learning, identifying underlying structures of true target functions based on observed data is crucial in facilitating subsequent modeling and analysis. Unlike most of those existing methods that focus on some specific settings under certain model assumptions, a general and novel framework is proposed for recovering true structures of target functions in a reproducing kernel Hilbert space (RKHS). The proposed framework is inspired by the fact that the gradient functions can be employed as a valid tool to learn underlying structures, including sparse learning, interaction selection and model identification. It is easy to be implemented by taking advantage of the nice properties of the RKHS. More importantly, it admits a wide range of loss functions, and thus includes many scenarios as its special cases, 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 supported by a variety of simulated examples and a real case study.