AddiVortes: (Bayesian) Additive Voronoi Tessellations

Stone, Adam. J.; Gosling, John Paul

Abstract

The Additive Voronoi Tessellations (AddiVortes) model is a multivariate regression model that uses Voronoi tessellations to partition the covariate space in an additive ensemble model. Unlike other partition methods, such as decision trees, this has the benefit of allowing the boundaries of the partitions to be non-orthogonal and non-parallel to the covariate axes. The AddiVortes model uses a similar sum-of-tessellations approach and a Bayesian backfitting MCMC algorithm to the BART model. We utilize regularization priors to limit the strength of individual tessellations and accepts new models based on a likelihood. The performance of the AddiVortes model is illustrated through testing on several data sets and comparing the performance to other models along with a simulation study to verify some of the properties of the model. In many cases, the AddiVortes model outperforms random forests, BART and other leading black-box regression models when compared using a range of metrics. Supplementary materials for this article are available online.

Citation

Stone, A. J., & Gosling, J. P. (online). AddiVortes: (Bayesian) Additive Voronoi Tessellations. Journal of Computational and Graphical Statistics, https://doi.org/10.1080/10618600.2024.2414104

• Journal Article Type: Article
• Acceptance Date: Oct 2, 2024
• Online Publication Date: Nov 26, 2024
• Deposit Date: Nov 13, 2024
• Publicly Available Date: Nov 26, 2024
• Journal: Journal of Computational and Graphical Statistics
• Print ISSN: 1061-8600
• Electronic ISSN: 1537-2715
• Publisher: American Statistical Association
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1080/10618600.2024.2414104
• Public URL: https://durham-repository.worktribe.com/output/3093668