EFFICIENT KERNEL-BASED VARIABLE SELECTION WITH SPARSISTENCY

Sparse learning is central to high-dimensional data analysis, and various methods have been developed. Ideally, a sparse learning method should be methodologically flexible, computationally efficient, and provide a theoretical guarantee. However, most existing methods need to compromise some of these properties in order to attain the others. We develop a three-step sparse learning method, involving a kernel-based estimation of the regression function and its gradient functions, as well as a hard thresholding. Its key advantages are that it includes no explicit model assumption, admits general predictor effects, allows efficient computation, and attains desirable asymptotic sparsistency. The proposed method can be adapted to any reproducing kernel Hilbert space (RKHS) with different kernel functions, and its computational cost is only linear in the data dimension. The asymptotic sparsistency of the proposed method is established for general RKHS under mild conditions. The results of numerical experiments show that the proposed method compares favorably with its competitors in both simulated and real examples.