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 framework that operates on many 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 competitively on downstream applications, notably the non-trivial task
of discrete representation learning.

使用最优传输的方法实现了一个面向许多有向图的参数学习框架，可以灵活地从不完整数据中推断概率有向图模型中的潜在变量。在多个实验中，该方法展示了恢复真实参数和离散表示学习等任务上的优异性能。

使用最优传输学习有向图模型

Learning Directed Graphical Models with Optimal Transport

This work initiates a systematic investigation of testing high-dimensional
structured distributions by focusing on testing Bayesian networks -- the
prototypical family of directed graphical models. A Bayesian network is defined
by a directed acyclic graph, where we associate a random variable with each
node. The value at any particular node is conditionally independent of all the
other non-descendant nodes once its parents are fixed. Specifically, we study
the properties of identity testing and closeness testing of Bayesian networks.
Our main contribution is the first non-trivial efficient testing algorithms for
these problems and corresponding information-theoretic lower bounds. For a wide
range of parameter settings, our testing algorithms have sample complexity
sublinear in the dimension and are sample-optimal, up to constant factors.

本文研究了 Bayesian 网络的身份测试和相似性测试的性质，提出了第一个非平凡的高效测试算法，并给出了相应的信息理论下界，其测试样本复杂度在维度上是亚线性的，适用于各种参数设置，是样本的最优解，直到常数因子。

测试贝叶斯网络

Testing Bayesian Networks

We introduce a new approach for amortizing inference in directed graphical
models by learning heuristic approximations to stochastic inverses, designed
specifically for use as proposal distributions in sequential Monte Carlo
methods. We describe a procedure for constructing and learning a structured
neural network which represents an inverse factorization of the graphical
model, resulting in a conditional density estimator that takes as input
particular values of the observed random variables, and returns an
approximation to the distribution of the latent variables. This recognition
model can be learned offline, independent from any particular dataset, prior to
performing inference. The output of these networks can be used as
automatically-learned high-quality proposal distributions to accelerate
sequential Monte Carlo across a diverse range of problem settings.

本研究介绍了一种利用学习启发式逼近随机反演的方法来摊销有向图模型中的推理，它专门设计用作顺序蒙特卡罗方法中的提议分布。我们描述了一种构建和学习结构神经网络的方法，该网络表示图形模型的逆因子分解，从而得到一个有条件密度估计器，该估计器以所观察到的随机变量的特定值作为输入，并返回潜变量的分布的近似值。可以在离线、独立于任何特定数据集、在执行推理之前学习这个识别模型。这些网络的输出可以用作自动学习的高质量提议分布，以加速在各种问题设置中进行顺序蒙特卡罗。