IC2: interventional dynamical causality under latent confounders.

Understanding causality is central to scientific discovery, importantly enabling the elucidation of mechanisms within complex systems. However, current methods of causal inference face significant challenges in uncovering interventional causal interactions within non-interventional systems, in particular under latent confounders, as they either focus solely on associations or require additional interventional manipulation. To overcome these limitations, here we introduce a novel method of Interventional Dynamical Causality under Invisible/Latent confounders (named ICIC or IC2) to decipher interventional dynamical causality based solely on non-interventional data even under latent confounders. IC2 is theoretically grounded in the dual orthogonal decomposition theorem in the delay embedding space and is computationally implemented with the constructed interventional data from observed non-interventional data by deep neural networks. Comprehensive benchmarking demonstrates that IC2 outperforms alternative methods in recovering causal structures in various biological applications. In particular, IC2 was not only validated by true interventional effects with knockout experiments, but also reconstructed biological networks from real-world data, and predicted the perturbation effects of single-cell CRISPR perturbation experiments. These results show the power of IC2 in estimating interventional effects where experimental intervention is not feasible.