Measuring Hilbert-Schmidt Independence Criterion with Different Kernels

Hilbert-Schmidt independence criterion (HSIC) which is a kernel-based method for testing statistical dependence between two random variables. It is widely applied in a variety of areas. However, this approach comes with a question of the selection of kernel functions. In this paper, we conduct an experiment using the forest fire data from UCI in the context of independence test, contrasting four commonly used kernel functions: Linear kernels, Gaussian kernels, Brownian kernels, Matern kernels. Through comparing p-value and rejection rate of hypothesis test we constructed; it is shown that the different choices in associated kernel function of HSIC give comparable performance on results.