Multi-Level Wavelet Mapping Correlation for Statistical Dependence Measurement: Methodology and Performance.

We propose a new criterion for measuring dependence between two real variables, namely, Multi-level Wavelet Mapping Correlation (MWMC). MWMC can capture the nonlinear dependencies between variables by measuring their correlation under different levels of wavelet mappings. We show that the empirical estimate of MWMC converges exponentially to its population quantity. To support independence test better with MWMC, we further design a permutation test based on MWMC and prove that our test can not only control the type I error rate (the rate of false positives) well but also ensure that the type II error rate (the rate of false negatives) is upper bounded by O(1/n) (n is the sample size) with finite permutations. By extensive experiments on (conditional) independence tests and causal discovery, we show that our method outperforms existing independence test methods.