  Estimating the parameters of a probabilistic directed graphical model from
incomplete data is a long-standing challenge. This is because, in the presence
of latent variables, both the likelihood function and posterior distribution
are intractable without assumptions about structural dependencies or model
classes. While existing learning methods are fundamentally based on likelihood
maximization, here we offer a new view of the parameter learning problem
through the lens of optimal transport. This perspective licenses a general
framework that operates on any directed graphs without making unrealistic
assumptions on the posterior over the latent variables or resorting to
variational approximations. We develop a theoretical framework and support it
with extensive empirical evidence demonstrating the versatility and robustness
of our approach. Across experiments, we show that not only can our method
effectively recover the ground-truth parameters but it also performs comparably
or better than competing baselines on downstream applications.
