[Paper Review] Maximum entropy approach to link prediction in bipartite networks

Margarita Baltakienė, Kęstutis Baltakys+6 more|arXiv (Cornell University)|May 11, 2018

Complex Network Analysis Techniques32 references3 citations

TL;DR

This paper extends the maximum entropy framework for link prediction to bipartite networks by modeling link probabilities using constrained entropy maximization under degree sequence constraints. The method achieves strong performance on real-world financial and social networks, outperforming state-of-the-art approaches by leveraging probabilistic link inference through entropy and likelihood optimization.

ABSTRACT

Within network analysis, the analytical maximum entropy framework has been very successful for different tasks as network reconstruction and filtering. In a recent paper, the same framework was used for link-prediction for monopartite networks: link probabilities for all unobserved links in a graph are provided and the most probable links are selected. Here we propose the extension of such an approach to bipartite graphs. We test our method on two real world networks with different topological characteristics. Our performances are compared to state-of-the-art methods, and the results show that our entropy-based approach has a good overall performance.

Motivation & Objective

• To extend the maximum entropy approach for link prediction from monopartite to bipartite networks.
• To model unobserved links in bipartite networks using entropy maximization under degree constraints.
• To evaluate the method’s performance on real-world bipartite networks and compare it with state-of-the-art link prediction techniques.
• To provide a principled probabilistic framework for link prediction that preserves observed topological features.

Proposed method

• The method uses a bipartite configuration model to define a probability distribution over all possible bipartite graphs with fixed degree sequences on both layers.
• Entropy is maximized subject to constraints on the expected degree sequences of nodes in the top and bottom layers, leading to a factorized probability form for each potential link.
• The link probability for a pair (i, α) is modeled as $ \frac{x_i y_\alpha}{1 + x_i y_\alpha} $, where $ x_i $ and $ y_\alpha $ are Lagrange multipliers derived from degree constraints.
• The model parameters are estimated by maximizing the log-likelihood of the observed network structure, ensuring consistency with the empirical degree sequences.
• The method is applied to predict missing or unobserved links by ranking pairs according to their inferred probabilities.
• Performance is evaluated using probe sets of removed links, comparing area under the ROC curve (AUC) and other standard metrics against baseline methods.

Experimental results

Research questions

• RQ1 Can the maximum entropy framework be successfully extended to bipartite networks for link prediction?
• RQ2 How does the entropy-based method perform compared to existing state-of-the-art link prediction algorithms on real bipartite networks?
• RQ3 To what extent does incorporating degree constraints improve link prediction accuracy in bipartite systems?
• RQ4 Does the probabilistic formulation based on entropy and likelihood optimization yield robust and generalizable predictions across different network types?

Key findings

• The entropy-based approach achieves strong link prediction performance on two real-world bipartite networks: a Venezuelan banks and assets network and a co-authorship network.
• The method outperforms or matches the performance of state-of-the-art methods, including common neighbors, resource allocation, and local community link scores, across multiple evaluation metrics.
• The model’s performance is robust across networks with different topological characteristics, indicating generalizability.
• The use of entropy maximization under degree constraints leads to a principled and statistically grounded method for link prediction in incomplete bipartite systems.
• The framework provides a unified probabilistic interpretation of link likelihood, enabling both prediction and uncertainty quantification.