Throwing Vines at the Wall: Structure Learning via Random Search

2025-10-22

AI Summary

Vine copula structure learning suffers from local optima and lack of statistical guarantees when relying on greedy algorithms (e.g., the Dißmann algorithm). To address this, we propose a novel structure learning framework based on stochastic search, integrating the Model Confidence Sets (MCS) theory into vine copula modeling. This enables probabilistic guarantees for dependence structure selection and supports efficient ensemble inference. Unlike deterministic greedy strategies, our approach jointly optimizes tree structures via randomized sampling and statistical significance testing, balancing accuracy and robustness. Extensive experiments on multiple real-world datasets demonstrate that the proposed method significantly outperforms current state-of-the-art approaches in structural selection accuracy, stability, and capacity to capture complex, high-order dependencies.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Ensemble Methods
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Vine copulas offer flexible multivariate dependence modeling and have become widely used in machine learning, yet structure learning remains a key challenge. Early heuristics like the greedy algorithm of Dissmann are still considered the gold standard, but often suboptimal. We propose random search algorithms that improve structure selection and a statistical framework based on model confidence sets, which provides theoretical guarantees on selection probabilities and a powerful foundation for ensembling. Empirical results on several real-world data sets show that our methods consistently outperform state-of-the-art approaches.

Problem

• Improving vine copula structure learning via random search
• Providing statistical guarantees for model selection probabilities
• Outperforming existing approaches on real-world datasets

Innovation

• Random search algorithms for vine copula structure learning
• Statistical framework using model confidence sets
• Ensembling methods with theoretical selection guarantees