Generative Diffusion Models of Stochastic Graph Signals

2016-09-06 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Graph Machine Learning · Depth: Expert, extended

Summary

A new framework, Generative Diffusion Models of Stochastic Graph Signals, introduces the U-Graph Neural Network (U-GNN) to address conditional graph signal generative modeling. This approach learns a reverse diffusion process using GNNs, specifically designed to sample stochastic signals on irregular graph domains. The U-GNN generalizes the U-Net architecture by implementing multi-resolution encoder–decoder processing where pooling and unpooling are realized through learned node selection via nested selection matrices and zero-padded lifting. Graph convolutions operate on the original graph with a stride, avoiding explicit graph coarsening. The method demonstrates strong performance in two generative tasks: S&P 500 stock price forecasting, where it reduces price CRPS by 22%, RMSE by 28%, and MAE by 21% compared to a geometric random walk baseline, and optimal wireless resource allocation for 400 transmitter–receiver pairs, matching an expert primal–dual policy's ergodic rates and feasibility. The U-GNN also exhibits size-transferability across networks from 200 to 1600 pairs without retraining.

Key takeaway

For Machine Learning Engineers developing generative models for stochastic graph signals, you should consider the U-Graph Neural Network (U-GNN) architecture. This framework provides a robust and scalable method for sampling from complex conditional graph signal distributions, outperforming traditional baselines in tasks like stock price forecasting and wireless resource allocation. Its novel learned node selection and strided graph convolutions effectively adapt U-Net principles to irregular graph domains, offering a powerful tool for generating high-fidelity, diverse samples.

Key insights

A U-GNN-based denoising diffusion framework generates stochastic graph signals by learning a reverse process with learned node selection.

Principles

• Conditional graph signal generation can be unified via denoising diffusion.
• Graph U-Nets require learned node selection for multi-resolution processing.
• Stochastic policies can achieve feasibility where deterministic ones fail.

Method

Learn a reverse diffusion process using a U-GNN, which employs learned node selection via nested selection matrices and zero-padded lifting for multi-resolution processing, bypassing explicit graph coarsening.

In practice

• Apply U-GNN for probabilistic stock price forecasting.
• Use U-GNN to generate optimal wireless resource allocations.
• Leverage learned node selection for scalable graph signal processing.

Topics

• Generative Diffusion Models
• Graph Neural Networks
• U-Graph Neural Network
• Stochastic Graph Signals
• Stock Price Forecasting
• Wireless Resource Allocation
• Learned Node Selection

Code references

• yigit-uslu/graph-signal-diffusion
• yigit-uslu/graph-signal-diffusion-modeling

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, AI Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.