用稀疏多项式构建图上扩散过程的代理模型，提升计算效率。
Surrogate models for diffusion on graphs via sparse polynomials
- 基于稀疏多项式构造图扩散过程的代理模型
- 理论证明最小二乘与压缩感知方法收敛性
- 适用于具有社区结构的图数据，适合大规模模拟
图上的扩散核在多种应用中被广泛使用，因其能准确建模节点和边间的信息流动。然而，图上扩散过程的代理模型研究仍存在明显空白。本文提出基于稀疏多项式的参数化图扩散方程代理模型，并针对具有社区结构的图进行设计。同时，通过证明参数解的解析正则性，给出了最小二乘和压缩感知方法的收敛性保证。一系列数值实验在合成与真实世界图数据上验证了该方法的有效性。
原文摘要 · Abstract (English)
Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature regarding the development of surrogate models for diffusion processes on graphs. In this work, we fill this gap by proposing sparse polynomial-based surrogate models for parametric diffusion equations on graphs with community structure. In tandem, we provide convergence guarantees for both least squares and compressed sensing-based approximations by showing the holomorphic regularity of parametric solutions to these diffusion equations. Our theoretical findings are accompanied by a series of numerical experiments conducted on both synthetic and real-world graphs that demonstrate the applicability of our methodology.
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