Probabilistic graphical models are powerful tools which allow us to formalise our knowledge about the world and reason about its inherent uncertainty. There exist a considerable number of methods for performing inference in probabilistic graphical models; however, they can be computationally costly due to significant time burden and/or storage requirements; or they lack theoretical guarantees of convergence and accuracy when applied to large scale graphical models. To this end, we propose the Universal Marginaliser Importance Sampler (UM-IS) -- a hybrid inference scheme that combines the flexibility of a deep neural network trained on samples from the model and inherits the asymptotic guarantees of importance sampling. We show how combining samples drawn from the graphical model with an appropriate masking function allows us to train a single neural network to approximate any of the corresponding conditional marginal distributions, and thus amortise the cost of inference. We also show that the graph embeddings can be applied for tasks such as: clustering, classification and interpretation of relationships between the nodes. Finally, we benchmark the method on a large graph (>1000 nodes), showing that UM-IS outperforms sampling-based methods by a large margin while being computationally efficient.
翻译:概率性图形模型是强大的工具,使我们能够正式确定我们对世界及其内在不确定性的认识和原因。在概率性图形模型中存在着大量方法进行推断;然而,由于时间负担和/或储存要求巨大,这些模型在计算上成本很高;或者在应用大型图形模型时缺乏理论的趋同性和准确性保障。为此,我们提议通用边际效应重要取样器(UM-IS) -- -- 一种混合推论办法,它结合了从模型样本中训练的深神经网络的灵活性,并继承了重要性抽样的无症状保证。我们展示了如何将图形模型中的样品与适当的遮罩功能相结合,使我们能够训练一个单一的神经网络,以接近任何相应的附带条件边际分布,从而将推断成本重新分类。我们还表明,图形嵌入可适用于诸如以下任务:组合、分类和解释节点之间的关系。最后,我们用一个大图表(>1000个节点)作为方法的基准,显示从大图表中提取的样本方法,显示在进行高效的边际间进行计算。