Stochastic Variational Inference for Vine Copula Distributional Regression

2026-09-29

AI Summary

This study addresses the modeling challenges of multivariate structured distributional regression under complex covariate dependencies by proposing a scalable framework based on regular vine copulas. Methodologically, structured additive predictors are constructed to capture heterogeneous dependence structures, while a tree-based stochastic variational inference (SVI) algorithm is developed to overcome computational bottlenecks. Furthermore, a sequential vine selection strategy grounded in effective degrees of freedom is introduced to balance estimation accuracy and computational efficiency. Experimental results demonstrate that the proposed estimator achieves performance approaching the oracle bound. An application to meteorological data successfully reveals nonlinear spatiotemporal dependence patterns, thereby validating the practical utility of the proposed approach.

Abstract

Structured additive distributional regression flexibly relates all parameters of a conditional response distribution to covariates, but multivariate extensions remain challenging when dependence is complex. We propose a multivariate structured additive distributional regression model based on regular vine copulas. Different vine edges may use different pair-copula families, while every pair-copula parameter may vary with covariates through a structured additive predictor. The model therefore accommodates heterogeneous marginal distributions together with pair-specific asymmetric, tail-dependent, and covariate-dependent dependence structures. For scalable inference, we develop a tree-wise stochastic variational inference procedure based on component-specific Gaussian variational approximations. Marginal models are estimated first, followed by pair-copula regressions sequentially along the vine trees. We also adapt sequential vine selection by fitting candidate covariate-dependent pair-copula regressions and using information criteria based on effective degrees of freedom for both family and tree selection. In simulations, the tree-wise estimator remains close to an oracle using the true recursive conditional inputs, whereas global refinement yields more concentrated approximations and lower frequentist coverage for upstream components. An application to six-dimensional meteorological data from the Netherlands yields a vine combining Gaussian and non-Gaussian pair copulas, with pronounced nonlinear spatial and temporal variation in dependence.

Problem

• distributional regression
• vine copula
• multivariate dependence
• stochastic variational inference
• structured additive models

Innovation

• Vine Copula
• Distributional Regression
• Stochastic Variational Inference
• Structured Additive Model
• Sequential Vine Selection