Title:	(Bayesian) Additive Voronoi Tessellations
Version:	0.4.8
Date:	2026-01-14
Description:	Implements the Bayesian Additive Voronoi Tessellation model for non-parametric regression and machine learning as introduced in Stone and Gosling (2025) <doi:10.1080/10618600.2024.2414104>. This package provides a flexible alternative to BART (Bayesian Additive Regression Trees) using Voronoi tessellations instead of trees. Users can fit Bayesian regression models, estimate posterior distributions, and visualise the resulting tessellations. It is particularly useful for spatial data analysis, machine learning regression, complex function approximation and Bayesian modeling where the underlying structure is unknown. The method is well-suited to capturing spatial patterns and non-linear relationships.
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.3.2
Depends:	R (≥ 3.5.0)
Imports:	parallel (≥ 4.0.0), pbapply (≥ 1.6)
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0), xml2
Config/testthat/edition:	3
URL:	https://johnpaulgosling.github.io/AddiVortes/
VignetteBuilder:	knitr
BugReports:	https://github.com/johnpaulgosling/AddiVortes/issues
NeedsCompilation:	yes
Packaged:	2026-01-14 11:21:54 UTC; rwzr85
Author:	Adam Stone [aut], John Paul Gosling [aut, cre]
Maintainer:	John Paul Gosling <john-paul.gosling@durham.ac.uk>
Repository:	CRAN
Date/Publication:	2026-01-14 12:10:01 UTC

AddiVortes: Bayesian Additive Voronoi Tessellations for Machine Learning

Description

AddiVortes implements Bayesian Additive Voronoi Tessellation models for machine learning regression and non-parametric statistical modeling. This package provides a flexible alternative to BART (Bayesian Additive Regression Trees), using Voronoi tessellations instead of trees for spatial partitioning. The method is particularly effective for spatial data analysis, complex function approximation, and Bayesian regression modeling.

Details

Key features include:

• Machine learning regression with Bayesian inference

• Alternative to BART using Voronoi tessellations

• Spatial data analysis and modeling

• Non-parametric regression capabilities

• Complex function approximation

• Uncertainty quantification through posterior inference

Author(s)

Maintainer: John Paul Gosling john-paul.gosling@durham.ac.uk (ORCID)

Authors:

• Adam Stone adam.stone2@durham.ac.uk (ORCID)

References

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

See Also

https://johnpaulgosling.github.io/AddiVortes/

AddiVortes

Description

The AddiVortes function is a Bayesian nonparametric regression model that uses a tessellation to model the relationship between the covariates and the output values. The model uses a backfitting algorithm to sample from the posterior distribution of the output values for each tessellation. The function returns the RMSE value for the test samples.

Usage

AddiVortes(
  y,
  x,
  m = 200,
  totalMCMCIter = 1200,
  mcmcBurnIn = 200,
  nu = 6,
  q = 0.85,
  k = 3,
  sd = 0.8,
  Omega = min(3, ncol(x)),
  LambdaRate = 25,
  IntialSigma = "Linear",
  thinning = 1,
  showProgress = TRUE
)

Arguments

Value

An AddiVortesFit object containing the posterior samples of the tessellations, dimensions and predictions.

Examples

# Simple example with simulated data
set.seed(123)
x <- matrix(rnorm(50), 10, 5)
y <- rnorm(10)
# Fit model with reduced iterations for quick example
fit <- AddiVortes(y, x, m = 5, totalMCMCIter = 50, mcmcBurnIn = 10)

Create an AddiVortesFit Object

Description

A constructor for the AddiVortesFit class.

Usage

new_AddiVortesFit(
  posteriorTess,
  posteriorDim,
  posteriorSigma,
  posteriorPred,
  xCentres,
  xRanges,
  yCentre,
  yRange,
  inSampleRmse
)

Arguments

Value

An object of class AddiVortesFit.

Plot Method for AddiVortesFit

Description

Generates comprehensive diagnostic plots for a fitted AddiVortesFit object. This function creates multiple diagnostic plots including residuals, MCMC traces for sigma, and tessellation complexity over iterations.

Usage

## S3 method for class 'AddiVortesFit'
plot(
  x,
  x_train,
  y_train,
  sigma_trace = NULL,
  which = c(1, 2, 3),
  ask = FALSE,
  ...
)

Arguments

Details

The function generates up to four diagnostic plots:

1. Residuals Plot: Residuals vs fitted values with smoothed trend line

2. Sigma Trace: MCMC trace plot for the error variance parameter

3. Tessellation Complexity: Trace of average tessellation size over iterations

4. Predicted vs Observed: Scatter plot with credible intervals

Value

This function is called for its side effect of creating plots and returns NULL invisibly.

Examples

## Not run: 
# Assuming 'fit' is a trained AddiVortesFit object
plot(fit, x_train = x_train_data, y_train = y_train_data)

# Show only specific plots
plot(fit, x_train = x_train_data, y_train = y_train_data, which = c(1, 3))

# With custom sigma trace
plot(fit, x_train = x_train_data, y_train = y_train_data, 
     sigma_trace = my_sigma_samples)

## End(Not run)

Predict Method for AddiVortesFit

Description

Predicts outcomes for new data using a fitted AddiVortesFit model object. It can return mean predictions, quantiles and optionally calculate the Root Mean Squared Error (RMSE) if true outcomes are provided.

Usage

## S3 method for class 'AddiVortesFit'
predict(
  object,
  newdata,
  type = c("response", "quantile"),
  quantiles = c(0.025, 0.975),
  interval = c("credible", "prediction"),
  showProgress = TRUE,
  parallel = TRUE,
  cores = NULL,
  ...
)

Arguments

Details

This function relies on the internal helper function applyScaling_internal being available in the environment, which is used by the main AddiVortes function.

When interval = "prediction" and type = "quantile", the function samples additional Gaussian noise with variance equal to the sampled sigma squared from the posterior. This accounts for the inherent variability in individual predictions, not just uncertainty in the mean function. The noise is added in the scaled space before unscaling predictions.

Value

If type = "response", a numeric vector of mean predictions. If type = "quantile", a matrix where each row corresponds to an observation in newdata and each column to a quantile.

Examples

# Fit a model
set.seed(123)
X <- matrix(rnorm(100), 20, 5)
Y <- rnorm(20)
fit <- AddiVortes(Y, X, m = 5, totalMCMCIter = 50, mcmcBurnIn = 10)

# New data for prediction
X_new <- matrix(rnorm(25), 5, 5)

# Mean predictions
pred_mean <- predict(fit, X_new, type = "response")

# Credible intervals (uncertainty in mean only)
pred_conf <- predict(fit, X_new, type = "quantile", 
                    interval = "credible",
                    quantiles = c(0.025, 0.975))

# Prediction intervals (includes error variance)
pred_pred <- predict(fit, X_new, type = "quantile",
                    interval = "prediction",
                    quantiles = c(0.025, 0.975))

# Prediction intervals are wider than credible intervals
mean(pred_pred[, 2] - pred_pred[, 1]) > mean(pred_conf[, 2] - pred_conf[, 1])

Print Method for AddiVortesFit

Description

Prints a summary of a fitted AddiVortesFit object, providing information about the model structure, dimensions, and fit quality similar to the output of a linear model summary.

Usage

## S3 method for class 'AddiVortesFit'
print(x, ...)

Arguments

Details

The print method displays:

• The model formula representation

• Number of covariates and posterior samples

• Number of tessellations used

• In-sample RMSE

• Covariate scaling information

Value

The function is called for its side effect of printing model information and returns the input object x invisibly.

Summary Method for AddiVortesFit

Description

Provides a detailed summary of a fitted AddiVortesFit object, including more comprehensive information than the print method.

Usage

## S3 method for class 'AddiVortesFit'
summary(object, ...)

Arguments

Value

The function is called for its side effect of printing detailed model information and returns the input object object invisibly.