Abstract
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types of convex free energies. These approximations are efficient but can fail if the model is complex and highly interactive. In this work, we analyze two classes of approximations that include the above methods as special cases: first, if the model parameters are changed; and second, if the entropy approximation is changed. We discuss benefits and drawbacks of either approach, and deduce from this analysis how a free energy approximation should ideally be constructed. Based on our observations, we propose approximations that automatically adapt to a given model and demonstrate their effectiveness for a range of difficult problems.
Abstract (translated)
在概率图模型中的变分推理旨在近似基本量，如边缘分布和配分函数。流行的方法包括Bethe近似、树重新加权以及其它类型的凸自由能量。这些方法虽然高效，但在面对复杂且高度交互的模型时可能会失效。在这项工作中，我们分析了两类包含上述方法作为特例的近似：第一类是在改变模型参数的情况下；第二类是在更改熵近似的情况下。我们讨论了每种方法的优点和缺点，并由此推断出理想的自由能近似应如何构建。基于我们的观察结果，我们提出了一组能够自动适应给定模型的近似方法，并展示了这些方法在一系列难题中的有效性。
URL
https://arxiv.org/abs/2502.03341
