This article addresses two important issues of causal inference in the high-dimensional situation. 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) are first decomposed into two small subsets, each of which is then recursively decomposed into two smaller subsets until none of these subsets can be decomposed further. Redundant CI tests can be reduced by inferring causalities from these subsets. The advantage of this decomposition scheme lies in two aspects: 1) it requires only low-order CI tests and 2) it does not violate dd -separation. The complete causality can be reconstructed by merging all the partial results of the subsets. For the second issue, we employ regression-based CI tests to check CIs in linear non-Gaussian additive noise cases, which can identify more causal directions by x_E(x|Z)__∥zx - E(x|Z) \_{}\!\!\_{}\!\!\!\!\!\shortparallel z (or y_E(y|Z)__∥zy - E(y|Z) \_{}\!\!\_{}\!\!\!\!\!\shortparallel z ). Consequently, causal direction learning is no longer limited by the number of returned VV -structures and consistent propagation. Extensive experiments show that the proposed method can not only substantially reduce redundant CI tests but also effectively distinguish the equivalence classes.

中文翻译：

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基于分而治之的因果结构学习


本文讨论了高维情况下因果推理的两个重要问题。一是如何减少冗余的条件独立（CI）测试，这严重影响了现有基于约束的方法的效率和准确性。另一个问题是如何从这些方法返回的一组马尔可夫等价类构造真正的因果图。对于第一个问题，我们设计了一种递归分解方法，其中原始数据（一组变量）首先被分解为两个小子集，然后每个子集递归地分解为两个较小的子集，直到这些子集都无法进一步分解为止。通过从这些子集中推断因果关系可以减少冗余 CI 测试。这种分解方案的优点在于两个方面：1）它只需要低阶 CI 测试，2）它不违反 dd 分离。完整的因果关系可以通过合并子集的所有部分结果来重建。对于第二个问题，我们采用基于回归的 CI 测试来检查线性非高斯加性噪声情况下的 CI，这可以通过 x_E(x|Z)__∥zx - E(x|Z) \_{ 识别更多因果方向}\!\!\_{}\!\!\!\!\!\shortparallel z (或 y_E(y|Z)__∥zy - E(y|Z) \_{}\!\!\_ {}\!\!\!\!\!\shortparallel z )。因此，因果方向学习不再受到返回的 VV 结构数量和一致传播的限制。大量实验表明，该方法不仅可以大幅减少冗余CI测试，而且可以有效地区分等价类。