论文标题
一般图的可扩展高斯马尔可夫随机字段
Scalable Deep Gaussian Markov Random Fields for General Graphs
论文作者
论文摘要
由于能够处理一般结构化数据，因此在图形上的机器学习方法已被证明在许多应用程序中很有用。高斯马尔可夫随机场（GMRF）的框架通过利用其稀疏结构来定义图表上的高斯模型的原则方法。我们提出了一个灵活的GMRF模型，用于建立在Deep GMRF的多层结构上的通用图，最初仅针对晶格图提出。通过设计新型的图层，我们使模型可以扩展到大图。该层的构造是为了使用图形神经网络的变分推理和现有软件框架进行有效的培训。对于高斯的可能性，潜在领域接近确切的贝叶斯推理。这可以通过随附的不确定性估计进行预测。通过对许多合成和现实世界数据集的实验来验证所提出的模型的有用性，在该数据集中，它与其他贝叶斯和深度学习方法相比有利。
Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models on graphs by utilizing their sparsity structure. We propose a flexible GMRF model for general graphs built on the multi-layer structure of Deep GMRFs, originally proposed for lattice graphs only. By designing a new type of layer we enable the model to scale to large graphs. The layer is constructed to allow for efficient training using variational inference and existing software frameworks for Graph Neural Networks. For a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. This allows for making predictions with accompanying uncertainty estimates. The usefulness of the proposed model is verified by experiments on a number of synthetic and real world datasets, where it compares favorably to other both Bayesian and deep learning methods.
