Causal Scissor: root cause discovery via the measure of edge cuts in graphs

We propose a novel causal discovery, Causal Scissor, which captures the causal flows in graphs through the lens of the mechanism of edges to elucidate root causes. Causal discovery from observed data provides interpretable relationships between the variables, with latent causal structures playing a pivotal role in explaining practical downstream tasks such as finance, industry, climate, society, and genomics. Recently generative models are studied for causal representation learning towards disentanglement and identifiability on latent causal structures to uncover the hidden information like causal discovery via perturbation conditions on biological cells. However the interdependency of causal flows in conjunction with intervention is less explored. This paper presents the identifiability of root causes through Causal Edge Cut (CEC) from causal graphs. The key to identifying root causes lies in the Barycenter Subtrees (BS) via permutations and Cholesky decomposition. To measure the causal edge cut, we utilize BS and Gromov-Wasserstein distance as a support to ensure high expressiveness on local Ollivier-Ricci curvature. Causal Scissor, the causal walk or flow in a strongly perturbed subtree with its knock-on edges and a root cause, clarifies how the causal structures by perturbation have knock-on effect due to the root cause on biological datasets such as flow cytometry and fMRI9.