Separating Co-expression from Regulation in Cyclic Causal Discovery with Latent Confounders

Perturbational genomics enables causal inference from systematic genetic perturbations, but shared variation from unmeasured factors and feedback can complicate the attribution of co-expression to direct regulation. DCCD-CONF accommodates cyclic dependencies and latent confounding, but its covariance estimation can become numerically unstable, undermining the recovery of latent confounding. We introduce DCCD-J, which incorporates latent covariance learning into the causal model through a differentiable Cholesky parameterization. This formulation keeps the latent covariance positive definite by construction, preventing near-singular estimates during training. Joint covariance learning under the interventional likelihood improves the separation of latent confounding from directed regulation. Across real perturbation datasets and synthetic cyclic SCMs with known latent covariance, DCCD-J achieves lower held-out negative log-likelihood, avoids covariance-collapse failures, and substantially improves recovery of latent confounding structure while also improving directed-structure recovery.