[Paper Review] Active Learning for Hidden Attributes in Networks

Xiaoran Yan, Yaojia Zhu+2 more|arXiv (Cornell University)|May 5, 2010

Machine Learning and Algorithms19 references4 citations

TL;DR

This paper proposes active learning methods for inferring hidden vertex attributes in networks using a stochastic block model, where attributes are correlated with network topology. It introduces two query strategies—maximizing mutual information and maximizing average agreement in Gibbs sampling—that significantly outperform simple heuristics like degree or betweenness centrality in identifying informative vertices early, especially in complex networks like food webs.

ABSTRACT

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing which vertex to query in order to learn as much as possible about the attributes of the other vertices. We assume the network is generated by a stochastic block model, but we make no assumptions about its assortativity or disassortativity. We choose which vertex to query using two methods: 1) maximizing the mutual information between its attributes and those of the others (a well-known approach in active learning) and 2) maximizing the average agreement between two independent samples of the conditional Gibbs distribution. Experimental results show that both these methods do much better than simple heuristics. They also consistently identify certain vertices as important by querying them early on.

Motivation & Objective

• To address the challenge of inferring hidden vertex attributes in networks when querying is costly and topology is known.
• To develop active learning strategies that select the most informative vertices to query, minimizing the number of queries needed for accurate attribute prediction.
• To evaluate whether information-theoretic and sampling-based criteria can outperform standard centrality heuristics in vertex selection.
• To assess the robustness and consistency of query order across different hidden attributes in real-world networks.
• To explore the scalability and generalization of the proposed methods beyond standard stochastic block models.

Proposed method

• The method assumes a stochastic block model where edge probabilities depend on vertex types, and uses Bayesian inference with uniform priors over edge probabilities to compute the likelihood of a type assignment.
• It employs Gibbs sampling to approximate the posterior distribution over vertex types, enabling estimation of mutual information and average agreement for query selection.
• The first query strategy maximizes the mutual information between a vertex's type and the types of unqueried vertices, based on the posterior distribution.
• The second strategy maximizes the average agreement between two independent samples from the conditional Gibbs distribution of unqueried vertices.
• Both methods are applied iteratively, with the network topology and partial type assignments updated after each query.
• Performance is evaluated using accuracy thresholds and correlation metrics between query orders and actual attribute types.

Experimental results

Research questions

• RQ1 Can mutual information and average agreement criteria effectively identify the most informative vertices to query in a network with hidden attributes?
• RQ2 How do the proposed active learning methods compare to simple centrality heuristics (degree, betweenness) in terms of query efficiency and accuracy?
• RQ3 To what extent do the query orders for different hidden attributes (e.g., feeding type and habitat) correlate, and what does this imply about the underlying network structure?
• RQ4 Does the performance of the active learning methods depend on network structure, such as sparsity or degree heterogeneity?
• RQ5 Can these methods be generalized to more complex models, such as degree-corrected stochastic block models?

Key findings

• The mutual information (MI) and average agreement (AA) methods significantly outperformed degree, betweenness, and random heuristics in reducing the number of queries needed to reach 90% accuracy on Zachary’s Karate Club network.
• On the Weddell Sea food web, MI and AA achieved high performance despite the network's complexity, with query orders for different attributes showing a 0.553 Pearson correlation, indicating shared structural importance.
• The two attributes—feeding type and habitat—had low intrinsic correlation (Adjusted Mutual Information = 0.357), suggesting that the query order correlation stems from network topology rather than attribute similarity.
• MI and AA required a burn-in phase; their performance improved over time, while random querying performed surprisingly well early on, indicating that early-stage predictions are sensitive to unqueried low-degree vertices.
• The methods consistently identified the same vertices as important across multiple runs, demonstrating robustness in query order selection.
• The study suggests that information-theoretic and sampling-based criteria are more effective than standard centrality measures for active learning in attributed networks.