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.

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