Efficient kernel-based variable selection with sparsistency

Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable algorithm shall be flexible, scalable, with theoretical guarantee, yet most existing cannot attain these properties at the same time. In this article, three-step developed, involving kernel-based estimation of regression function its gradient functions as well hard thresholding. Its key advantage that it assumes no explicit model assumption, admits general predictor effects, allows for scalable computation, attains desirable asymptotic sparsistency. The proposed can adapted any reproducing kernel Hilbert space (RKHS) different functions, extended interaction slight modification. computational cost only linear in dimension, further improved through parallel computing. sparsistency established RKHS under mild conditions, including Gaussian kernels special cases. effectiveness also supported by variety simulated real examples.