Predict Method for AddiVortes

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

object

An object of class AddiVortes, typically the result of a call to AddiVortes().

newdata

A matrix of covariates for the new test set. The number of columns must match the original training data.

type

The type of prediction required. The default "response" gives the mean prediction (class probabilities for classification). "quantile" returns the quantiles specified by quantiles. "class" returns predicted class labels (classification only). "link" returns the latent sum of tessellations \(G(x)\) on the model scale before any response unscaling.

quantiles

A numeric vector of probabilities to compute for the predictions when type = "quantile".

interval

The type of interval calculation. The default "credible" accounts only for uncertainty in the mean (similar to lm's confidence interval). The alternative "prediction" also includes the model's error variance, producing wider intervals (similar to lm's prediction interval). Not used for classification models.

showProgress

Logical; if TRUE, a progress bar is shown during prediction.

...

Further arguments passed to or from other methods (currently unused).

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.

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.

Examples

# \donttest{
# 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])
#> [1] TRUE
# }