Learning to Recover Causal Relationship from Indefinite Data in the Presence of Latent Confounders

In Causal Discovery with latent variables, We define two data paradigms: definite data: a single-skeleton structure with observed nodes single-value, and indefinite data: a set of multi-skeleton structures with observed nodes multi-value. Multi,skeletons induce low sample utilization and multi values induce incapability of the distribution assumption, both leading that recovering causal relations from indefinite data is, as of yet, largely unexplored. We design the causal strength variational model to settle down these two problems. Specifically, we leverage the causal strength instead of independent noise as latent variable to mediate evidence lower bound. By this design ethos, The causal strength of different skeletons is regarded as a distribution and can be expressed as a single-valued causal graph matrix. Moreover, considering the latent confounders, we disentangle the causal graph G into two relatisubgraphs O and C. O contains pure relations between observed nodes, while C represents the relations from latent variables to observed nodes. We summarize the above designs as Confounding Disentanglement Causal Discovery (biCD), which is tailored to learn causal representation from indefinite data under the latent confounding. Finally, we conduct comprehensive experiments on synthetic and real-world data to demonstrate the effectiveness of our method.