  We consider the task of learning a causal graph in the presence of latent
confounders given i.i.d.~samples from the model. While current algorithms for
causal structure discovery in the presence of latent confounders are
constraint-based, we here propose a score-based approach. We prove that under
assumptions weaker than faithfulness, any sparsest independence map (IMAP) of
the distribution belongs to the Markov equivalence class of the true model.
This motivates the \emph{Sparsest Poset} formulation - that posets can be
mapped to minimal IMAPs of the true model such that the sparsest of these IMAPs
is Markov equivalent to the true model. Motivated by this result, we propose a
greedy algorithm over the space of posets for causal structure discovery in the
presence of latent confounders and compare its performance to the current
state-of-the-art algorithms FCI and FCI+ on synthetic data.
