Causal Discovery by Kernel Deviance Measures with Heterogeneous
  Transforms
Tim Tse Zhitang Chen Shengyu Zhu Yue Liu
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.