Recursively learning causal structures using regression-based conditional independence test

Abstract

This paper addresses two important issues in causality inference. One is how to reduce redundant conditional independence (CI) tests, which heavily impact the efficiency and accuracy of existing constraint-based methods. Another is how to construct the true causal graph from a set of Markov equivalence classes returned by these methods. For the first issue, we design a recursive decomposition approach where the original data (a set of variables) is first decomposed into three small subsets, each of which is then recursively decomposed into three smaller subsets until none of subsets can be decomposed further. Consequently, redundant CI tests can be reduced by inferring causality from these subsets. Advantage of this decomposition scheme lies in two aspects: 1) it requires only low-order CI tests, and 2) it does not violate d-separation. Thus, the complete causality can be reconstructed by merging all the partial results of the subsets. For the second issue, we employ regression-based conditional independence test to check CIs in linear non-Gaussian additive noise cases, which can identify more causal directions by x-E(x|Z)z (or y-E(y|Z)z). Therefore, causal direction learning is no longer limited by the number of returned Vstructures and the consistent propagation. Extensive experiments show that the proposed method can not only substantially reduce redundant CI tests but also effectively distinguish the equivalence classes, thus is superior to the state of the art constraint-based methods in causality inference.