The discovery of causal relationships in a set of random variables is a fundamental objective of science and has also recently been argued as being an essential component towards real machine intelligence. One class of causal discovery techniques are founded based on the argument that there are inherent structural asymmetries between the causal and anti-causal direction which could be leveraged in determining the direction of causation. To go about capturing these discrepancies between cause and effect remains to be a challenge and many current state-of-the-art algorithms propose to compare the norms of the kernel mean embeddings of the conditional distributions. In this work, we argue that such approaches based on RKHS embeddings are insufficient in capturing principal markers of cause-effect asymmetry involving higher-order structural variabilities of the conditional distributions. We propose Kernel Intrinsic Invariance Measure with Heterogeneous Transform (KIIM-HT) which introduces a novel score measure based on heterogeneous transformation of RKHS embeddings to extract relevant higher-order moments of the conditional densities for causal discovery. Inference is made via comparing the score of each hypothetical cause-effect direction. Tests and comparisons on a synthetic dataset, a two-dimensional synthetic dataset and the real-world benchmark dataset T\"ubingen Cause-Effect Pairs verify our approach. In addition, we conduct a sensitivity analysis to the regularization parameter to faithfully compare previous work to our method and an experiment with trials on varied hyperparameter values to showcase the robustness of our algorithm.

基于异构转换的内核固有不变量测量（KIIM-HT）提出了一种基于RKHS嵌入的新型评分测量方法，以提取条件密度的相关高阶矩以用于因果关系的发现。

依据核偏差度量的因果发现及异构变换