Dependence model assessment and selection with DecoupleNets

TL;DR

DecoupleNets are neural network-based transformations that assess and select dependence models by simplifying the dependence structure to a 2D space, enabling both numerical and graphical evaluation, especially useful for complex multivariate data.

Contribution

This paper introduces DecoupleNets, a novel neural network approach for dependence model assessment and selection, capable of handling high-dimensional data and providing graphical diagnostics.

Findings

DecoupleNets effectively transform complex dependence structures into 2D for analysis.

The approach is validated through simulations with various copulas.

Applications demonstrate practical usefulness in real-world data analysis.

Abstract

Neural networks are suggested for learning a map from $d$-dimensional samples with any underlying dependence structure to multivariate uniformity in $d'$ dimensions. This map, termed DecoupleNet, is used for dependence model assessment and selection. If the data-generating dependence model was known, and if it was among the few analytically tractable ones, one such transformation for $d'=d$ is Rosenblatt's transform. DecoupleNets have multiple advantages. For example, they only require an available sample and are applicable to $d'<d$, in particular $d'=2$. This allows for simpler model assessment and selection, both numerically and, because $d'=2$, especially graphically. A graphical assessment method has the advantage of being able to identify why, or in which region of the domain, a candidate model does not provide an adequate fit, thus leading to model selection in particular regions of interest or improved model building strategies in such regions. Through simulation studies with data from various copulas, the feasibility and validity of this novel DecoupleNet approach is demonstrated. Applications to real world data illustrate its usefulness for model assessment and selection.