summary: Summary of a Fitted BKP or DKP Model

Description

Provides a structured summary of a fitted Beta Kernel Process (BKP) or Dirichlet Kernel Process (DKP) model. This function reports the model configuration, prior specification, kernel settings, and key posterior quantities, giving users a concise overview of the fitting results.

Usage

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

Value

A list containing key summaries of the fitted model:

n_obs: Number of training observations.
input_dim: Input dimensionality (number of columns in X).
kernel: Kernel type used in the model.
theta_opt: Estimated kernel hyperparameters.
loss: Loss function type used in the model.
loss_min: Minimum value of the loss function achieved.
prior: Prior type used (e.g., "noninformative", "fixed", "adaptive").
r0: Prior precision parameter.
p0: Prior mean parameter.
post_mean: Posterior mean estimates. For BKP: posterior mean success probabilities at training points. For DKP: posterior mean class probabilities (\(n_\text{obs} \times q\)).
post_var: Posterior variance estimates. For BKP: variance of success probabilities. For DKP: variance for each class probability.
n_class: (Only for DKP) Number of classes in the response.

Arguments

object: An object of class "BKP" (from fit_BKP) or "DKP" (from fit_DKP).
...: Additional arguments passed to the generic summary method (currently not used).

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

Run this code

# ============================================================== #
# ========================= BKP Examples ======================= #
# ============================================================== #

#-------------------------- 1D Example ---------------------------
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
model1 <- fit_BKP(X, y, m, Xbounds=Xbounds)
summary(model1)


#-------------------------- 2D Example ---------------------------
set.seed(123)

# Define 2D latent function and probability transformation
true_pi_fun <- function(X) {
  if(is.null(nrow(X))) X <- matrix(X, nrow=1)
  m <- 8.6928
  s <- 2.4269
  x1 <- 4*X[,1]- 2
  x2 <- 4*X[,2]- 2
  a <- 1 + (x1 + x2 + 1)^2 *
    (19- 14*x1 + 3*x1^2- 14*x2 + 6*x1*x2 + 3*x2^2)
  b <- 30 + (2*x1- 3*x2)^2 *
    (18- 32*x1 + 12*x1^2 + 48*x2- 36*x1*x2 + 27*x2^2)
  f <- log(a*b)
  f <- (f- m)/s
  return(pnorm(f))  # Transform to probability
}

n <- 100
Xbounds <- matrix(c(0, 0, 1, 1), nrow = 2)
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
model2 <- fit_BKP(X, y, m, Xbounds=Xbounds)
summary(model2)

# ============================================================== #
# ========================= DKP Examples ======================= #
# ============================================================== #

#-------------------------- 1D Example ---------------------------
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
model1 <- fit_DKP(X, Y, Xbounds = Xbounds)
summary(model1)


#-------------------------- 2D Example ---------------------------
set.seed(123)

# Define latent function and transform to 3-class probabilities
true_pi_fun <- function(X) {
  if (is.null(nrow(X))) X <- matrix(X, nrow = 1)
  m <- 8.6928; s <- 2.4269
  x1 <- 4 * X[,1] - 2
  x2 <- 4 * X[,2] - 2
  a <- 1 + (x1 + x2 + 1)^2 *
    (19 - 14*x1 + 3*x1^2 - 14*x2 + 6*x1*x2 + 3*x2^2)
  b <- 30 + (2*x1 - 3*x2)^2 *
    (18 - 32*x1 + 12*x1^2 + 48*x2 - 36*x1*x2 + 27*x2^2)
  f <- (log(a*b)- m)/s
  p1 <- pnorm(f) # Transform to probability
  p2 <- sin(pi * X[,1]) * sin(pi * X[,2])
  return(matrix(c(p1/2, p2/2, 1 - (p1+p2)/2), nrow = length(p1)))
}

n <- 100
Xbounds <- matrix(c(0, 0, 1, 1), nrow = 2)
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
model2 <- fit_DKP(X, Y, Xbounds = Xbounds)
summary(model2)