Package {AddiVortes}

Title:	(Bayesian) Additive Voronoi Tessellations
Version:	0.6.8
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 (estimating the associated posterior distributions and make predictions. 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
Depends:	R (≥ 4.0.0)
Imports:	parallel, pbapply (≥ 1.6)
Suggests:	knitr, rmarkdown, testthat (≥ 3.0.0), withr, xml2
SystemRequirements:	C++20
Config/testthat/edition:	3
URL:	https://johnpaulgosling.github.io/AddiVortes/
VignetteBuilder:	knitr
BugReports:	https://github.com/johnpaulgosling/AddiVortes/issues
LazyData:	true
Config/roxygen2/version:	8.0.0
RoxygenNote:	7.3.3
NeedsCompilation:	yes
Packaged:	2026-07-30 10:36:19 UTC; johnpaul
Author:	Adam Stone [aut], John Paul Gosling [aut, cre], Andrew Iskauskas [aut]
Maintainer:	John Paul Gosling <john-paul.gosling@durham.ac.uk>
Repository:	CRAN
Date/Publication:	2026-07-30 14:50:02 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)

• Andrew Iskauskas andrew.iskauskas@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/

Fit an AddiVortes regression model

Description

The AddiVortes model 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. Alongside fitting details and the posterior sample, the function returns the RMSE value for the test samples.

The function can handle multiple types of covariates, including continuous, spherical and categorical. Categorical covariates are automatically detected and one-hot encoded, with the first level of each categorical variable used as the reference category. The catScaling parameter allows control over the weight of categorical differences in distance calculations. For spherical covariates, the function assumes that the final spherical dimension corresponds to the polar angle, which has a range of 0 to 2*pi. The metric parameter can be used to specify the type of each covariate (Euclidean, Spherical, or Categorical), and the members parameter can indicate membership of covariates into different subspaces when using multiple spheres in covariate space.

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 = 5,
  InitialSigma = "Linear",
  thinning = 1,
  metric = "E",
  members = NULL,
  catScaling = 1,
  cat.onehot = TRUE,
  showProgress = interactive()
)

Arguments

Value

An AddiVortes object containing the posterior samples of the tessellations, dimensions and predictions, plus per-iteration trace statistics used by traceplots().

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)

# Larger example with categorical covariates (d=2 and d=3) and a test set
set.seed(456)
n_train <- 200
n_test <- 50
x_train <- data.frame(
  x1   = rnorm(n_train),
  x2   = runif(n_train),
  grp2 = sample(c("A", "B"), n_train, replace = TRUE),
  grp3 = sample(c("low", "mid", "high"), n_train, replace = TRUE)
)
y_train <- x_train$x1 + ifelse(x_train$grp2 == "B", 1, 0) + rnorm(n_train, sd = 0.5)

fit2 <- AddiVortes(y_train, x_train,
  m = 10, totalMCMCIter = 200, mcmcBurnIn = 50,
  catScaling = 1, showProgress = FALSE
)

x_test <- data.frame(
  x1   = rnorm(n_test),
  x2   = runif(n_test),
  grp2 = sample(c("A", "B"), n_test, replace = TRUE),
  grp3 = sample(c("low", "mid", "high"), n_test, replace = TRUE)
)
y_test <- x_test$x1 + ifelse(x_test$grp2 == "B", 1, 0) + rnorm(n_test, sd = 0.5)

preds <- predict(fit2, x_test, showProgress = FALSE)
test_rmse <- sqrt(mean((y_test - preds)^2))

Boston Dataset

Description

The Boston Housing Dataset, derived from information from the U.S. Census Service.

Usage

Boston

Format

Boston

A data.frame with 506 rows and 14 columns:

x1-x13

The covariates in the data

y

The response variable

Source

Harrison, D. and Rubinfeld, D.L. 'Hedonic prices and the demand for clean air', J. Environ. Economics & Management, vol. 5, 81-102, 1978

Cylindrical Dataset

Description

Synthetic data generated for cylindrical parameters. The response is given by the function f(z, theta) = sin(z)cos(theta) + z*sin(theta)^2, with added noise.

Usage

Cylinder

Format

Cylinder

A data.frame with 400 rows and 3 columns:

z

Height

theta

Polar angle

Y

Response

Weather Dataset

Description

A subset of data collected as part of the GES DISC datasets for calibrated brightness temperatures.

Usage

Weather

Format

Weather

A data.frame with 2000 rows and 3 columns:

theta

Polar angle

phi

Azimuthal angle

Y

Response variable

Source

https://disc.gsfc.nasa.gov/datasets/GPM_1CGPMGMI_07/summary?keywords=10.5067%2FGPM%2FGMI%2FGPM%2F1C%2F07

Assign Observations to Tessellation Cells

Description

For a given tessellation, this function identifies which cell (centre) each observation belongs to based on nearest neighbour classification.

Usage

cellIndices(x, tess, dim, metric = "E", members)

Arguments

Details

It finds the closest tessellation centre for each observation (row) in the covariate matrix, considering only the specified dimensions. This is achieved using the k-nearest neighbour algorithm where k=1.

Value

A numeric vector of integers where each element corresponds to a row in x and its value is the row index of the nearest centre in tess.

Create an AddiVortes Object

Description

A constructor for the AddiVortes class.

Usage

new_AddiVortes(
  posteriorTess,
  posteriorDim,
  posteriorSigma,
  posteriorPred,
  xCentres,
  xRanges,
  yCentre,
  yRange,
  inSampleRmse,
  metric = "E",
  members = rep(1, length(xCentres)),
  metric_aug = "E",
  member_aug = rep(1, length(xCentres)),
  catEncoding = NULL,
  traceStats = NULL
)

Arguments

Value

An object of class AddiVortes.

Plot Method for AddiVortes

Description

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

Usage

## S3 method for class 'AddiVortes'
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 standard deviation

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 AddiVortes 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 AddiVortes

Description

Predicts outcomes for new data using a fitted AddiVortes 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 'AddiVortes'
predict(
  object,
  newdata,
  type = c("response", "quantile"),
  quantiles = c(0.025, 0.975),
  interval = c("credible", "prediction"),
  showProgress = interactive(),
  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 AddiVortes

Description

Prints a summary of a fitted AddiVortes 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 'AddiVortes'
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 AddiVortes

Description

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

Usage

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

Arguments

Value

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

Trace Plot Diagnostics

Description

Creates trace plots for MCMC diagnostics of a fitted model.

Usage

traceplots(x, ...)

Arguments

Value

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

Trace Plot Diagnostics for AddiVortes

Description

Displays four MCMC trace plots for a fitted AddiVortes object: the average number of centres per tessellation, the standard deviation of the number of centres per tessellation, the average number of dimensions used per tessellation, and the retained-state log-likelihood component whose differences form the likelihood part of the acceptance ratio.

Usage

## S3 method for class 'AddiVortes'
traceplots(x, ask = FALSE, ...)

Arguments

Details

The four trace plots are:

1. Average Centres: Average number of centres per tessellation.

2. Centre Count Standard Deviation: Standard deviation of the number of centres per tessellation.

3. Average Dimensions: Average number of active dimensions used per tessellation.

4. Log Likelihood: Average retained-state log-likelihood component at the end of each MCMC iteration.

Value

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

Examples

## Not run: 
# Assuming 'fit' is a trained AddiVortes object
traceplots(fit)

## End(Not run)