Statistical Dependence Test with Hilbert-Schmidt Independence Criterion

This paper studies an approach of nonlinear independence test between random variables. The method is Hilbert–Schmidt independence criterion (HSIC), one of the popular kernel methods for testing statistical dependence between random variables. There are several advantages of using HSIC method. It is easier compared with other kernel methods like the canonical correlation, because it requires no extra regularization terms for an appropriate finite sample behavior. Also, the learning rates of HSIC method is faster because there exists a well-defined population quantity in the estimate. The paper studies the detailed concepts and criterion associated with HSIC, its p-value and sensitivity maps. Results in the experiment about the wine data from UCI data set show the good performance of the approach.