Causal Discovery from Markov Properties Under Latent Confounders

We address the problems of causal structure inference from conditional independence facts when latent confounders are admitted. The conditions that allow one to identify latent confounders and fully or partially recognize causal links are described. The updated implicative rules for orienting edges under confounding are suggested. We propose several new rules that are able to reveal bows and confounded causal edges. The rules rely on facts of absence of certain authentic edges (edge absence may be implied by Verma constraint or given in input as a priori requirement).