Bayesian Node-Level Outlier Detection for Graph Signals

TL;DR

This paper introduces a Bayesian method for detecting node-level outliers in graph signals, leveraging graph structure and probabilistic modeling to improve detection and uncertainty quantification.

Contribution

It presents a novel Bayesian framework combining Gaussian Markov random fields and spike-and-slab priors for outlier detection in graph signals, with efficient inference via Gibbs sampling.

Findings

Effective outlier detection demonstrated on simulated graph data.

Successful application to real PM2.5 data in California.

Provides probabilistic outlier scores with uncertainty estimates.

Abstract

This paper proposes a fully Bayesian framework for node-level outlier detection in graph signals, where measurements are observed on the nodes of an underlying graph. Unlike traditional outlier detection methods, our approach accounts for the relational dependencies induced by the graph, identifying outliers that disrupt the underlying smoothness. We model the observed signal as a combination of a graph-smooth component, captured via an intrinsic Gaussian Markov random field (IGMRF) prior, and a sparse outlier component modeled by a spike-and-slab prior. A key advantage of the proposed method is its ability to provide principled uncertainty quantification by estimating the posterior probability that each node is an outlier, rather than enforcing a deterministic binary decision. To facilitate posterior inference, we develop an efficient Gibbs sampling algorithm. We demonstrate the effectiveness of the proposed method through simulation studies on various graph structures, as well as a real data analysis of PM2.5 levels in California, exploring their relationship with wildfire occurrences.