An Adaptive Test of Independence with Analytic Kernel Embeddings
This work addresses the need for computationally efficient independence tests in statistics and machine learning, offering a linear-time alternative with competitive performance, though it is incremental in improving existing methods.
The authors tackled the problem of testing statistical independence efficiently by proposing a new linear-time dependence measure and adaptive test that selects features to maximize test power. In benchmarks, their method performed comparably to the state-of-the-art quadratic-time HSIC test and outperformed other efficient tests.
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the marginals, evaluated at a finite set of locations (features). These features are chosen so as to maximize a lower bound on the test power, resulting in a test that is data-efficient, and that runs in linear time (with respect to the sample size n). The optimized features can be interpreted as evidence to reject the null hypothesis, indicating regions in the joint domain where the joint distribution and the product of the marginals differ most. Consistency of the independence test is established, for an appropriate choice of features. In real-world benchmarks, independence tests using the optimized features perform comparably to the state-of-the-art quadratic-time HSIC test, and outperform competing O(n) and O(n log n) tests.