用统一框架生成图信号,能精准建模复杂关系。
Generative Diffusion Models of Stochastic Graph Signals

- 基于图神经网络设计反向扩散过程,直接从图结构和节点特征采样。
- 提出U-GNN架构,通过学习节点选择实现多分辨率处理。
- 在股票预测与无线资源分配中表现优异,适合图数据生成任务。
支持在图上的随机信号采样是推荐系统、金融市场预测和无线网络优化等图机器学习任务的核心。这些场景中的目标信号是未知条件分布的实现。然而,现有方法多依赖复杂的定制设计,常退化为条件均值回归而非从条件分布采样。本文将此类问题统一为条件图信号生成建模,并提出一种单一去噪扩散框架解决。我们学习一个由图神经网络(GNN)参数化的反向扩散过程,直接根据图拓扑和节点特征信息生成图信号。该反向过程通过一种新型架构——U-图神经网络(U-GNN)实现,其将图像卷积型U-Net推广至图结构信号。U-GNN执行多分辨率编码器-解码器处理,其中池化与上采样转化为由嵌套选择矩阵表示的学习节点选择,以及对粗粒度信号进行零填充后恢复到全节点集。图卷积在原始图上进行,步长决定其跳数范围,从而避免每层显式图降维。我们在两个生成任务上验证了该方法:股票价格预测和最优无线资源分配,展示了大量数值结果。
原文摘要 · Abstract (English)
Sampling stochastic signals supported on a graph underlies many graph machine learning tasks, including recommender systems, forecasting in financial markets, and wireless network optimization. In these settings, the target signals are realizations of unknown conditional distributions. However, prevailing approaches rely mostly on intricate, application-tailored designs that often regress to a conditional mean instead of sampling from the conditional law. This paper unifies such problems as conditional graph signal generative modeling and tackles them with a single denoising diffusion framework. We learn a reverse diffusion process, parametrized by graph neural networks (GNNs), that draws graph signals conditioned directly on the graph topology and on node-feature side information. The reverse process is realized by a novel architecture, the U-Graph Neural Network (U-GNN), which generalizes the image-convolutional U-Net to graph-structured signals. The U-GNN performs multi-resolution encoder--decoder processing in which pooling and unpooling reduce to a learned node selection, expressed by nested selection matrices, and a zero-padded lifting of coarse signals back to the full node set. The graph convolutions are carried out on the original graph, with a stride that sets their hop reach, so the U-GNN bypasses explicit graph coarsening at every resolution. We demonstrate our method on two generative tasks: stock price forecasting and optimal wireless resource allocation, with extensive numerical results in both domains.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。