Package {AddiVortes}

Title:	(Bayesian) Additive Voronoi Tessellations
Version:	1.0.1
Description:	Implements the Bayesian Additive Voronoi Tessellation model for non-parametric regression, classification 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 and probit classification models, estimate the associated posterior distributions and make predictions. It is particularly useful for spatial data analysis, machine learning, complex function approximation and Bayesian modelling where the underlying structure is unknown.
License:	GPL (≥ 3)
Encoding:	UTF-8
Depends:	R (≥ 4.0.0)
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:	8.1.0
NeedsCompilation:	yes
Packaged:	2026-09-17 09:01:51 UTC; johnpaul
Author:	Adam Stone [aut], John Paul Gosling [aut, cre], Andrew Iskauskas [aut], Leo Thomson [aut]
Maintainer:	John Paul Gosling <john-paul.gosling@durham.ac.uk>
Repository:	CRAN
Date/Publication:	2026-09-17 10:30:15 UTC

AddiVortes: Bayesian Additive Voronoi Tessellations for Machine Learning

Description

AddiVortes implements Bayesian Additive Voronoi Tessellation models for machine learning regression, classification and non-parametric statistical modelling. 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 and classification.

Details

Key features include:

• Machine learning regression and classification with Bayesian inference

• Binary and multinomial probit models with latent-variable data augmentation

• Alternative to BART using Voronoi tessellations

• Spatial data analysis and modelling

• 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:

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

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

• Andrew Iskauskas andrew.iskauskas@durham.ac.uk (ORCID)

• Leo Thomson leo@feasibly.co.uk

References

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

Stone, A.J., Ogundimu, E. and Gosling, J.P. (2026). Binary AddiVortes: (Bayesian) Additive Voronoi Tessellations for Binary Classification with an application to Predicting Home Mortgage Application Outcomes.

Albert, J.H. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association.

Kindo, B.P., Wang, H. and Peña, E.A. (2016). Multinomial probit Bayesian additive regression trees. Stat.

See Also

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

Fit an AddiVortes regression or classification model

Description

The AddiVortes model is a Bayesian nonparametric model that uses additive Voronoi tessellations to relate covariates to a response. For a numeric response the model is Gaussian regression. For a classification response it uses a probit link with Albert-Chib latent variables (binary) or independent multinomial probit latents (three or more classes). The task is chosen automatically from y.

The function can handle multiple types of covariates, including continuous, spherical and categorical. Categorical covariates are automatically detected. By default (cat.onehot = TRUE) they are one-hot encoded, with the first level of each categorical variable used as the reference category; the catScaling parameter then controls the weight of categorical differences in distance calculations. Setting cat.onehot = FALSE instead keeps each categorical covariate as a single integer-coded column and uses Eskin distance (Eskin et al., 2002). 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 = 2000,
  mcmcBurnIn = 500,
  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(). Classification fits also store task, classLevels, nLatents and in-sample accuracy.

References

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

Stone, A.J., Ogundimu, E. and Gosling, J.P. (2026). Binary AddiVortes: (Bayesian) Additive Voronoi Tessellations for Binary Classification with an application to Predicting Home Mortgage Application Outcomes.

Albert, J.H. and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669–679.

Kindo, B.P., Wang, H. and Peña, E.A. (2016). Multinomial probit Bayesian additive regression trees. Stat, 5(1), 171–181.

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))

# Binary classification is selected automatically from a 0/1 or factor y
set.seed(789)
x_clf <- matrix(runif(80), 40, 2)
y_clf <- factor(ifelse(x_clf[, 1] + x_clf[, 2] > 1, "yes", "no"))
fit_clf <- AddiVortes(y_clf, x_clf, m = 8, totalMCMCIter = 80,
                      mcmcBurnIn = 20, showProgress = FALSE)
p_clf <- predict(fit_clf, x_clf, type = "response", showProgress = FALSE)
cls_clf <- predict(fit_clf, x_clf, type = "class", showProgress = FALSE)

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

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,
  task = "regression",
  classLevels = NULL,
  nLatents = 1L,
  mPerLatent = NA_integer_,
  inSampleAccuracy = NA_real_,
  inSampleBrier = NA_real_
)

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. Regression fits return means or quantiles of the response. Classification fits return class probabilities, class labels, latent-scale values, or quantiles of the class probabilities.

Usage

## S3 method for class 'AddiVortes'
predict(
  object,
  newdata,
  type = c("response", "quantile", "class", "link"),
  quantiles = c(0.025, 0.975),
  interval = c("credible", "prediction"),
  showProgress = interactive(),
  ...
)

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.

Predictions traverse all retained draws and tessellations in a single C++ call, avoiding repeated R/C++ boundary crossings per tessellation.

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. Classification uses a probit link with residual variance fixed at 1, so prediction intervals are not defined; use type = "quantile" for credible intervals on probabilities.

For regression, "response" unscales predictions back to the original response units, while "link" returns the posterior mean of the latent scaled function G(x).

For binary classification, "response" is the posterior mean of \Phi(G^{(s)}(x)). For multinomial classification, class probabilities are estimated from independent N(G, I) latents, with the first class as the reference.

Value

If type = "response", a numeric vector of mean predictions for regression or binary classification, or an n \times K probability matrix for multinomial classification. If type = "quantile", a matrix of quantiles (binary/regression) or a named list of such matrices (multinomial). If type = "class", a factor of predicted labels. If type = "link", the latent function G(x) on the model scale before response unscaling.

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 plots

Description

S3 generic for MCMC trace plots of fitted AddiVortes models. Users should call traceplots(fit); see traceplots.AddiVortes() for the method documentation.

Usage

traceplots(x, ...)

Arguments

See Also

traceplots.AddiVortes()

Trace Plot Method 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)