Causal discovery from time-series discrete data in the presence of latent confounders

Learning causal structures from discrete time series data presents significant challenges, particularly in the presence of unobserved variables, or latent confounders, which are frequently encountered in real-world scenarios. Such latent factors often lead existing algorithms to output incorrect causal structures. In this work, we consider a general setting in which certain observed variables are influenced by a discrete latent confounder. Under appropriate non-degeneracy conditions, we reveal a fundamental connection between the rank of probability tensors and d-separation patterns in discrete time series models, and we introduce a graphical criterion to characterize this relationship. Building on this insight, we develop an efficient constraint-based temporal causal discovery algorithm, Tensor Rank-based Temporal Causal Discovery (TRTCD), which first recovers the causal skeleton among observed variables and then infers causal relations involving latent variables. Theoretically, we show that TRTCD can recover the causal structure up to a Markov equivalence class, even in the presence of latent confounders. Empirical evaluations on both synthetic and real-world datasets demonstrate the effectiveness of the proposed approach.