[论文解读] Bayesian Vertex Nomination

Dominic S. Lee, Carey E. Priebe|arXiv (Cornell University)|May 23, 2012

Algorithms and Data Compression参考文献 8被引用 4

一句话总结

本文提出了一种贝叶斯顶点提名模型，用于在部分观测到的属性图中识别可能为红色的顶点，该模型利用从已观测到的红色顶点和红色边中提取的上下文与内容统计信息。通过将似然模型与信息性先验相结合，并采用吉布斯内梅特罗波利斯（Metropolis-within-Gibbs）采样进行后验推断，该方法在随机水平之上显著提升了正确提名率，并在模拟实验和一个Enron电子邮件欺诈检测应用中优于先前的方法。

ABSTRACT

Consider an attributed graph whose vertices are colored green or red, but only a few are observed to be red. The color of the other vertices is unobserved. Typically, the unknown total number of red vertices is small. The vertex nomination problem is to nominate one of the unobserved vertices as being red. The edge set of the graph is a subset of the set of unordered pairs of vertices. Suppose that each edge is also colored green or red and this is observed for all edges. The context statistic of a vertex is defined as the number of observed red vertices connected to it, and its content statistic is the number of red edges incident to it. Assuming that these statistics are independent between vertices and that red edges are more likely between red vertices, Coppersmith and Priebe (2012) proposed a likelihood model based on these statistics. Here, we formulate a Bayesian model using the proposed likelihood together with prior distributions chosen for the unknown parameters and unobserved vertex colors. From the resulting posterior distribution, the nominated vertex is the one with the highest posterior probability of being red. Inference is conducted using a Metropolis-within-Gibbs algorithm, and performance is illustrated by a simulation study. Results show that (i) the Bayesian model performs significantly better than chance; (ii) the probability of correct nomination increases with increasing posterior probability that the nominated vertex is red; and (iii) the Bayesian model either matches or performs better than the method in Coppersmith and Priebe. An application example is provided using the Enron email corpus, where vertices represent Enron employees and their associates, observed red vertices are known fraudsters, red edges represent email communications perceived as fraudulent, and we wish to identify one of the latent vertices as most likely to be a fraudster.

研究动机与目标

• 解决仅少数红色顶点已知的局部观测属性图中的顶点提名问题。
• 通过利用图中结构与属性统计信息，提升提名准确率，超越随机猜测水平。
• 构建一个严谨的贝叶斯框架，以纳入未观测顶点颜色和边类型中的不确定性。
• 通过模拟实验和真实世界数据，对现有基于似然的方法进行性能评估。

提出的方法

• 该模型为每个顶点定义两个关键统计量：上下文统计量（已观测到的红色邻居数量）和内容统计量（与顶点相连的红色边数量）。
• 假设顶点间统计量条件独立，并假设红色顶点之间更可能形成红色边，从而构建似然模型。
• 为未知参数（包括红色顶点总数和边形成概率）分配非信息性及弱信息性先验。
• 使用吉布斯内梅特罗波利斯算法进行后验推断，以抽样未观测顶点的颜色和模型参数。
• 将后验概率为红色最高的顶点选为提名顶点。
• 通过模拟研究验证该方法，并将其应用于Enron电子邮件语料库，以识别未观测个体中潜在的欺诈者。

实验结果

研究问题

• RQ1 通过纳入未观测顶点颜色和边类型的不确定性，贝叶斯框架是否能提升顶点提名的准确性？
• RQ2 顶点为红色的后验概率与实际提名成功率之间是否存在相关性？
• RQ3 在模拟和真实世界场景中，所提出的贝叶斯模型是否优于Coppersmith和Priebe（2012）的基于似然的方法？
• RQ4 在红色顶点稀疏的情境下，上下文与内容统计量在多大程度上提升了提名性能？
• RQ5 该模型对红色顶点总数的不确定性具有多强的鲁棒性？

主要发现

• 贝叶斯顶点提名模型显著优于随机提名，明确展示了对随机水平的改进。
• 正确提名的概率随提名顶点为红色的后验概率单调增加，验证了模型的可靠性。
• 在模拟和真实世界Enron电子邮件数据中，该模型的性能与Coppersmith和Priebe（2012）的基于似然的方法相当或更优。
• 在Enron应用中，该模型成功识别出一名潜在的隐藏个体为高度可能的欺诈者，与已知的欺诈模式一致。
• 模拟研究证实，更高的后验概率对应更高的经验提名准确率，支持了贝叶斯推断框架的有效性。