Conditional Independent Component Analysis for Estimating Causal Structure with Latent Variables

Identifying latent variables and their induced causal structure is fundamental in various scientific fields. Existing approaches often rely on restrictive structural assumptions (e.g., purity assumption) and may become invalid when these assumptions are violated. We introduce Conditional Independent Component Analysis (CICA), a new principle that extracts components that are conditionally independent given latent variables. Under mild conditions, CICA can be optimized using a tractable proxy such as rank-deficiency constraints. Building on CICA, we establish an identifiability theory for linear non-Gaussian acyclic models with latent variables: solving CICA and then applying an appropriate row permutation to the sparsest CICA solution enables recovery of the causal structure. Accordingly, we propose an estimation method based on the identifiability theory and substantiate the algorithm with experiments on both synthetic and real-world datasets.