Dynamical Causality Under Latent Confounders for Biological Network Reconstruction

Causal interaction inference is prone to spurious causal interactions, due to the substantial confounders in a biological system. While many existing methods attempt to address misidentification challenges, there remains a notable lack of effective methods to infer causal interaction under latent/unobserved confounders. In this work, we propose a method to overcome such challenges to infer dynamical causality under invisible confounders (CIC) and further reconstruct the latent confounders from time-series data by developing an orthogonal decomposition theorem in a delay embedding space. This theoretical foundation ensures the causal detection for any high-dimensional system even with only two observed variables under many latent confounders, which is a long-standing problem in the field. In addition to the latent confounder problem, such a decomposition makes the coupled variables separable in the embedding space, thus also solving the non-separability problem of causal inference. Extensive validation of the CIC method is carried out using various real datasets, which all demonstrates its effectiveness to reconstruct real biological networks and unobserved confounders.