Learning the Graph Structure of Regular Vine-Copulas from Dependence Lists

Abstract

Regular vine copulas (R-vines) provide a comprehensive framework for modeling high-dimensional dependencies using a hierarchy of trees and conditional pair-copulas. While the graphical structure of R-vines is traditionally derived from data, this work introduces a novel approach by utilizing a (conditional) pairwise dependence list. Our primary goal is to construct R-vine graphs that include the maximum possible number of dependence relationships specified in such lists. To tackle this optimization challenge, characterized by exponential growth in the search space and the structural constraints of R-vines, we propose two distinct methodologies: A 0-1 linear programming formulation and a Genetic Algorithm (GA). Additionally, the Randomized Constructive Technique (RCT) is employed to generate the initial population of the GA, serving as a baseline for our comparison. Experimental results reveal the superior performance of the GA over the RCT in terms of success rate, incorporating more relationships than RCT into the constructed R-vine graphs and achieving near-optimal or optimal graph structures.