Abstract
Quantifying molecular regulations between genes/molecules causally from observed data is crucial for elucidating the molecular mechanisms underlying biological processes at the network level. Presently, most methods for inferring gene regulatory and biological networks rely on association studies or observational causal-analysis approaches. This study introduces a novel approach that combines intervention operations and diffusion models within a do-calculus framework by deep learning, i.e., Causal Diffusion Do-calculus (CDD) analysis, to infer causal networks between molecules. CDD can extract causal relations from observed data owing to its intervention operations, thereby significantly enhancing the accuracy and generalizability of causal network inference. Computationally, CDD has been applied to both simulated data and real omics data, which demonstrates that CDD outperforms existing methods in accurately inferring gene regulatory networks and identifying causal links from genes to disease phenotypes. Especially, compared with the Mendelian randomization algorithm and other existing methods, the CDD can reliably identify the disease genes or molecules for complex diseases with better performances. In addition, the causal analysis between various diseases and the potential factors in different populations from the UK Biobank database is also conducted, which further validated the effectiveness of CDD.