Learning Graph Structure from Convolutional Mixtures
Learning Graph Structure from Convolutional Mixtures
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DOI：
10.48550/arxiv.2205.09575
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Max Wasserman;Saurabh Sihag;G. Mateos;Alejandro Ribeiro
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文献类型：
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作者：
Max Wasserman;Saurabh Sihag;G. Mateos;Alejandro Ribeiro
图神经网络等机器学习框架通常依赖于给定的固定图来利用关系归纳偏差，从而有效地从网络数据中学习。然而，当所述图（部分）未被观察到、有噪声或动态时，从数据推断图结构的问题就变得相关了。在本文中，我们假设观察图和潜在图之间存在图卷积关系，并将图学习任务表述为网络逆（反卷积）问题。代替基于特征分解的谱方法或迭代优化解决方案，我们展开并截断近端梯度迭代，以得到一个参数化的神经网络架构，我们称之为图反卷积网络（GDN）。gdn可以以监督的方式学习图的分布，通过调整损失函数来执行链接预测或边权回归任务，并且它们本质上是归纳的。我们证实了GDN优越的图恢复性能及其在监督设置中使用合成数据的更大图的泛化。此外，我们展示了gdn在真实世界神经成像和社交网络数据集上的鲁棒性和表示能力。
Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive. We corroborate GDN's superior graph recovery performance and its generalization to larger graphs using synthetic data in supervised settings. Furthermore, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.