AddiVortes: (Bayesian) Additive Voronoi Tessellations

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 nonparallel 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 use 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 datasets 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.