  Differentiable causal discovery has made significant advancements in the
learning of directed acyclic graphs. However, its application to real-world
datasets remains restricted due to the ubiquity of latent confounders and the
requirement to learn maximal ancestral graphs (MAGs). To date, existing
differentiable MAG learning algorithms have been limited to small datasets and
failed to scale to larger ones (e.g., with more than 50 variables).
  The key insight in this paper is that the causal skeleton, which is the
undirected version of the causal graph, has potential for improving accuracy
and reducing the search space of the optimization procedure, thereby enhancing
the performance of differentiable causal discovery. Therefore, we seek to
address a two-fold challenge to harness the potential of the causal skeleton
for differentiable causal discovery in the presence of latent confounders: (1)
scalable and accurate estimation of skeleton and (2) universal integration of
skeleton estimation with differentiable causal discovery.
  To this end, we propose SPOT (Skeleton Posterior-guided OpTimization), a
two-phase framework that harnesses skeleton posterior for differentiable causal
discovery in the presence of latent confounders. On the contrary to a
``point-estimation'', SPOT seeks to estimate the posterior distribution of
skeletons given the dataset. It first formulates the posterior inference as an
instance of amortized inference problem and concretizes it with a supervised
causal learning (SCL)-enabled solution to estimate the skeleton posterior. To
incorporate the skeleton posterior with differentiable causal discovery, SPOT
then features a skeleton posterior-guided stochastic optimization procedure to
guide the optimization of MAGs. [abridged due to length limit]
