Estimating the parameters of a probabilistic directed graphical model from incomplete data remains a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without further 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 black-box variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the flexibility and versatility of our approach. Across experiments, we show that not only can our method recover the ground-truth parameters but it also performs comparably or better on downstream applications, notably the non-trivial task of discrete representation learning.

翻译：从非完整数据中估计概率有向图模型的参数始终是一个长期存在的挑战。这是因为在存在隐变量的情况下，似然函数和后验分布若不对结构依赖关系或模型类别做额外假设则难以处理。现有学习方法基本基于似然最大化，而本文通过最优传输的视角为参数学习问题提供了全新思路。该视角催生了一个通用框架，可适用于任意有向图，无需对隐变量后验分布做出不切实际的假设，也无需依赖黑箱变分近似。我们建立了理论框架，并通过大量实验证据证明了该方法的灵活性与普适性。跨实验结果表明，我们的方法不仅能恢复真实参数，在下游应用（尤其是非平凡的离散表示学习任务）中表现也相当或更优。