Fit an AddiVortes regression model

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 = 25,
  InitialSigma = "Linear",
  thinning = 1,
  metric = "E",
  members = NULL,
  catScaling = 1,
  showProgress = interactive()
)

Arguments

y

A vector of the output values.

x

A matrix or data frame of the covariates. Character and factor columns are treated as categorical variables and automatically converted to d-1 binary indicator variables via one-hot encoding (with the first level as reference).

m

The number of tessellations.

totalMCMCIter

The number of iterations.

mcmcBurnIn

The number of burn in iterations.

nu

The degrees of freedom.

q

The quantile.

k

The number of centres.

sd

The standard deviation used in centre proposals.

Omega

Omega/(number of covariates) is the prior probability of adding a dimension.

LambdaRate

The rate of the Poisson distribution for the number of centres.

InitialSigma

The method used to calculate the initial variance.

thinning

The thinning rate.

metric

Either "E" (Euclidean, default), "S" (Spherical), or "C" (Categorical).

members

If needed, indicates membership of covariates into different subspaces (needed if using multiple spheres in covariate space). Default NULL.

catScaling

Numeric scalar controlling the scale of binary indicator variables created from categorical covariates. Each binary indicator takes values 0 (reference level) or catScaling (non-reference level). The default value of 1 matches the range of continuous covariates, which are normalised to [-0.5, 0.5] (range = 1) during fitting, so categorical differences receive comparable weight to continuous differences in the distance calculations. Increase above 1 to give categorical differences more weight; decrease below 1 to give them less weight. Binary indicator columns are named <colname>_<level> (e.g. a column grp with levels "A", "B", "C" produces columns grp_B and grp_C, with "A" as the reference level).

showProgress

Logical; if TRUE, progress bars and messages are shown during fitting.

Value

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

Examples

# \donttest{
# 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))
# }