Permutation tests for conditional independence
Speaker: Yuchen Chen
Abstract: We look at a couple ways to test for conditional independence, whether X is independent of Y conditional on a variable Z, using permutations. We first consider the case under the model X framework where the conditional distribution of X given Z is known. In this case, by putting a distribution over possible permutations, we can form exchangeable test statistics for a valid finite sample test. In the case where the distribution of X given Z is unknown, we will look at local permutation tests which involves binning the variable Z and shuffling within the bins. This procedure relies on the condition that the distribution of X and y conditioned on Z cannot change much with respect to small perturbations in Z. This is characterized through smoothness assumptions. We will discuss the validity of this procedure under these smoothness assumptions. https://arxiv.org/pdf/1807.05405.pdf, https://arxiv.org/pdf/2112.11666.pdf