  Most existing causal discovery methods rely on the assumption of no latent
confounders, limiting their applicability in solving real-life problems. In
this paper, we introduce a novel, versatile framework for causal discovery that
accommodates the presence of causally-related hidden variables almost
everywhere in the causal network (for instance, they can be effects of observed
variables), based on rank information of covariance matrix over observed
variables. We start by investigating the efficacy of rank in comparison to
conditional independence and, theoretically, establish necessary and sufficient
conditions for the identifiability of certain latent structural patterns.
Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD,
that can efficiently locate hidden variables, determine their cardinalities,
and discover the entire causal structure over both measured and hidden ones. We
also show that, under certain graphical conditions, RLCD correctly identifies
the Markov Equivalence Class of the whole latent causal graph asymptotically.
Experimental results on both synthetic and real-world personality data sets
demonstrate the efficacy of the proposed approach in finite-sample cases.
