Fast Graph Laplacian Estimation using Effective Resistance

2026-09-20

AI Summary

本文提出了一种基于有效电阻的非迭代图拉普拉斯估计方法，以解决在样本数少于节点数时高斯马尔可夫随机场的图估计问题。

Abstract

Inferring network topology from noisy node observations is a central problem in graph signal processing. In this paper, we consider Laplacian-constrained graph estimation for Gaussian Markov random fields, focusing on the underdetermined regime in which the number of samples is smaller than the number of graph nodes. Existing approaches often formulate the problem as a sparsity-regularized maximum-likelihood estimation problem. While effective, such methods typically require iterative optimization and are often computationally demanding, particularly under Laplacian constraints. Instead, we propose a non-iterative estimator of graph Laplacians that uses effective resistance for regularization, and evaluate the method using a simple sparsification procedure. Experiments show that with some trade-off in edge and weight recovery on the considered dataset, computational cost for moderately sized graphs can be substantially reduced.

Problem

• Graph Laplacian
• Effective Resistance
• Gaussian Markov Random Fields
• Network Topology Inference

Innovation

• non-iterative estimator
• effective resistance
• Laplacian-constrained graph estimation
• sparsification