  Testing the independence between two random variables $x$ and $y$ is an
important problem in statistics and machine learning, where the kernel-based
tests of independence is focused to address the study of dependence recently.
The advantage of the kernel framework rests on its flexibility in choice of
kernel. The Hilbert-Schmidt Independence Criterion (HSIC) was shown to be
equivalent to a class of tests, where the tests are based on different
distance-induced kernel pairs. In this work, we propose to select the optimal
kernel pair by considering local alternatives, and evaluate the efficiency
using the quadratic time estimator of HSIC. The local alternative offers the
advantage that the measure of efficiency do not depend on a particular
alternative, and only requires the knowledge of the asymptotic null
distribution of the test. We show in our experiments that the proposed strategy
results in higher power than other existing kernel selection approaches.
