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Title: A general framework for sparse learning in reproducing kernel Hilbert space Authors:  Xin He - Shanghai University of Finance and Economics (China) [presenting]
Junhui Wang - City University of Hong Kong (Hong Kong)
Abstract: Sparse learning aims to learn the sparse structure of the true target function in various scenarios, which plays a crucial role in high-dimensional data analysis. A general framework is proposed for learning sparsity in M-estimators in a reproducing kernel Hilbert space (RKHS). The M-estimator 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. The proposed framework is motivated by the properties of RKHS, and its asymptotic estimation and selection consistencies are established {without any explicit model specification}. Its key advantages are that it works for a general loss function, admits general dependence structure, with theoretical guarantee, and allows for efficient computation. The superior performance of the proposed framework is also supported by a variety of simulated examples and a real application in the human breast cancer study (GSE20194).