BKP (version 0.2.3)

fitted: Extract BKP or DKP Model Fitted Values

Description

Compute the posterior fitted values from a fitted BKP or DKP object. For a BKP object, this returns the posterior mean probability of the positive class. For a DKP object, this returns the posterior mean probabilities for each class.

Usage

# S3 method for BKP
fitted(object, ...)
# S3 method for DKP
fitted(object, ...)

Value

A numeric vector (for BKP) or a numeric matrix (for DKP) containing posterior mean estimates at the training inputs.

Arguments

object

An object of class BKP or DKP, typically the result of a call to fit_BKP or fit_DKP.

...

Additional arguments (currently unused).

Details

For a BKP model, the fitted values correspond to the posterior mean probability of the positive class, computed from the Beta Kernel Process. For a DKP model, the fitted values correspond to the posterior mean probabilities for each class, derived from the posterior Dirichlet distribution of the class probabilities.

References

Zhao J, Qing K, Xu J (2025). BKP: An R Package for Beta Kernel Process Modeling. arXiv. https://doi.org/10.48550/arXiv.2508.10447.

Examples

# -------------------------- BKP ---------------------------
set.seed(123)

# Define true success probability function
true_pi_fun <- function(x) {
  (1 + exp(-x^2) * cos(10 * (1 - exp(-x)) / (1 + exp(-x)))) / 2
}

n <- 30
Xbounds <- matrix(c(-2, 2), nrow = 1)
X <- tgp::lhs(n = n, rect = Xbounds)
true_pi <- true_pi_fun(X)
m <- sample(100, n, replace = TRUE)
y <- rbinom(n, size = m, prob = true_pi)

# Fit BKP model
model <- fit_BKP(X, y, m, Xbounds = Xbounds)

# Extract fitted values
fitted(model)

# -------------------------- DKP ---------------------------
#' set.seed(123)

# Define true class probability function (3-class)
true_pi_fun <- function(X) {
  p1 <- 1/(1+exp(-3*X))
  p2 <- (1 + exp(-X^2) * cos(10 * (1 - exp(-X)) / (1 + exp(-X)))) / 2
  return(matrix(c(p1/2, p2/2, 1 - (p1+p2)/2), nrow = length(p1)))
}

n <- 30
Xbounds <- matrix(c(-2, 2), nrow = 1)
X <- tgp::lhs(n = n, rect = Xbounds)
true_pi <- true_pi_fun(X)
m <- sample(150, n, replace = TRUE)

# Generate multinomial responses
Y <- t(sapply(1:n, function(i) rmultinom(1, size = m[i], prob = true_pi[i, ])))

# Fit DKP model
model <- fit_DKP(X, Y, Xbounds = Xbounds)

# Extract fitted values
fitted(model)