On the restrictions of Pair-Copula Bayesian Networks for integration-free computations

On the restrictions of Pair-Copula Bayesian Networks for integration-free computations

Horsman, Niels (TU Delft Electrical Engineering, Mathematics and Computer Science)

Kurowicka, D. (mentor)
Derumigny, Alexis (mentor)

Delft University of Technology

Applied Mathematics | Stochastics

2023-11-17

The pair-copula Bayesian network (PCBN) is a Bayesian network (BN) where the conditional probability functions are modeled using pair-copula constructions. By assigning bivariate conditional copulas to the arcs of the BN, one finds a proper joint density which can flexibly model all kinds of dependence structures. It is a known problem that the PCBN may require numerical integration to perform computations such as sampling and likelihood-inference. To address this issue we propose novel restrictions on the graphical structure and assignment of copulas such that integration will not be required. The resulting restricted PCBN offers significant computational benefits. We establish how to estimate and conduct a structure search for the restricted PCBN. A simulation study shows that a restricted PCBN is able to model non-Gaussian dependence structures more accurately than the widely used Gaussian Bayesian network.

Bayesian Network
copula
Structure Learning
Hill Climbing algorithm
Pair-copula Bayesian network
integration-free

http://resolver.tudelft.nl/uuid:f9a03cbd-0c61-4367-a4fc-976491fef4bc

Student theses

master thesis

© 2023 Niels Horsman