论文标题
深高斯马尔可夫随机字段
Deep Gaussian Markov Random Fields
论文作者
论文摘要
高斯马尔可夫随机场（GMRF）是概率图形模型，广泛用于空间统计和相关字段，用于模型对空间结构的依赖性。我们在GMRF和卷积神经网络（CNN）之间建立了正式的联系。常见的GMRF是生成模型的特殊情况，其中1层线性CNN给出了从数据到潜在变量的反映射。这种连接使我们能够将GMRFS推广到多层CNN体系结构，从而有效地增加了相应的GMRF的顺序，具有有利的计算缩放。我们描述了如何使用良好的工具，例如自动化和变异推理，用于简单有效的推理和深入研究深度GMRF。我们证明了所提出的模型的灵活性，并表明它在预测和预测不确定性方面优于卫星温度数据集上的最先进。
Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.
