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.

Publication:

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE

http://dx.doi.org/10.1109/TPAMI.2026.3658839

Author:

Yan, Jinling

Northwestern Polytech Univ, Sch Automat, MOE Key Lab Informat Fus Technol, Xian 710072, Peoples R China

Email：haust_yjl@163.com

Zhang, Shao-Wu(corresponding author)

Northwestern Polytech Univ, Sch Automat, MOE Key Lab Informat Fus Technol, Xian 710072, Peoples R China

Email：zhangsw@nwpu.edu.cn

Zhang, Chihao

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China

Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

Email：zhangchihao@amss.ac.cn

Huang, Weitian

South China Univ Technol, Sch Future Technol, Guangzhou 510006, Peoples R China

Guangdong Inst Intelligence Sci & Technol, Zhuhai 519031, Peoples R China

Email：cs_wthuang@mail.scut.edu.cn

Shi, Jifan

Fudan Univ, Res Inst Intelligent Complex Syst, Shanghai 200433, Peoples R China

Fudan Univ, Inst Brain Sci, State Key Lab Med Neurobiol, Shanghai 200032, Peoples R China

Fudan Univ, Inst Brain Sci, MOE Frontiers Ctr Brain Sci, Shanghai 200032, Peoples R China

Shanghai Artificial Intelligence Lab, Shanghai 200232, Peoples R China

Email：jfshi@fudan.edu.cn

Chen, Luonan

Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

Shanghai Jiao Tong Univ, Sch AI, Shanghai 200240, Peoples R China

Chinese Acad Sci, Univ Chinese Acad Sci, Sch Life Sci,Hangzhou Inst Adv Study, Key Lab Syst Hlth Sci Zhejiang Prov, Hangzhou 310024, Peoples R China

Tianfu Jincheng Lab, Chengdu 610212, Peoples R China

Email：lnchen@sjtu.edu.cn