AddiVortes: (Bayesian) Additive Voronoi Tessellations

Overview

AddiVortes implements the Bayesian Additive Voronoi Tessellation model for machine learning regression, classification and non-parametric statistical modelling. This R package provides a flexible alternative to BART (Bayesian Additive Regression Trees), using Voronoi tessellations instead of trees for spatial partitioning.

Key Features

• Machine Learning Regression: Advanced Bayesian regression modelling for complex datasets
• Classification: Binary and multi-category probit models, chosen automatically from the response
• Alternative to BART: Uses Voronoi tessellations instead of trees for more flexible spatial modelling
• Spatial Data Analysis: Excellent for geographic and spatial datasets
• Non-parametric Modelling: No assumptions about functional form
• Bayesian Framework: Full posterior inference with uncertainty quantification
• Complex Function Approximation: Captures non-linear relationships and interactions

Applications

AddiVortes is particularly well-suited for:

• Spatial regression and geographic data analysis
• Binary and multi-category classification with posterior class probabilities
• Machine learning tasks requiring interpretable models
• Non-parametric regression where the functional form is unknown
• Bayesian modelling with uncertainty quantification
• Complex surface modelling and function approximation
• Alternative to BART for researchers seeking different ensemble approaches

Installation

You can install the latest version of AddiVortes from GitHub with:

pak::pak("johnpaulgosling/AddiVortes")

Quick Start

library(AddiVortes)

# Load your data
# X <- your_predictors
# y <- your_response

# Fit the AddiVortes model (regression or classification, from y)
# model <- AddiVortes(y, X)

# Make predictions
# predictions <- predict(model, newdata = X_test)
# For classification, type = "response" gives probabilities
# and type = "class" gives labels

Documentation

Vignettes:

• Machine Learning with AddiVortes
• Bayesian Regression and Prediction
• Modelling Spherical Data with AddiVortes
• Using Categorical Covariates with AddiVortes
• Classification with AddiVortes

See also the function reference.

Comparison with BART

While BART (Bayesian Additive Regression Trees) uses tree-based partitioning, AddiVortes uses Voronoi tessellations, which can provide:

• More natural spatial partitioning
• Flexible geometric boundaries
• Alternative ensemble approach for machine learning
• Enhanced performance on spatial data

Cite Us

If you use this package in your research, please cite:

citation("AddiVortes")

References

Stone, A. and Gosling, J.P. (2025). AddiVortes: (Bayesian) additive Voronoi tessellations. Journal of Computational and Graphical Statistics, 34, 859–71. doi

Keywords

Bayesian machine learning, BART alternative, Voronoi tessellation, spatial regression, non-parametric regression, ensemble methods, statistical modelling, R package