Throwing Vines at the Wall: Structure Learning via Random Search

TL;DR

This paper introduces random search algorithms and a statistical framework for vine copula structure learning, offering theoretical guarantees and improved performance over existing methods in real-world data applications.

Contribution

It proposes novel random search techniques and a statistical framework for vine copula structure learning, enhancing accuracy and providing theoretical guarantees.

Findings

Our methods outperform state-of-the-art approaches on real-world datasets.

The proposed framework offers theoretical guarantees on selection probabilities.

Random search algorithms improve structure learning over traditional heuristics.

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, such as Dissmann's greedy algorithm, are still considered the gold standard but are often suboptimal. We propose random search algorithms and a statistical framework based on model confidence sets, to improve structure selection, provide theoretical guarantees on selection probabilities and excess risk, as well as serve as a foundation for ensembling. Empirical results on real-world data sets show that our methods consistently outperform state-of-the-art approaches.