Print Summary of a Fitted BKP or DKP Model

Displays a concise summary of a fitted BKP or DKP model. The output includes key characteristics such as sample size, input dimensionality, kernel type, loss function, optimized kernel hyperparameters, and minimum loss.

Usage

# S3 method for class 'BKP'
print(x, ...)

# S3 method for class 'DKP'
print(x, ...)

Arguments

x: An object of class "BKP" (from fit.BKP) or "DKP" (from fit.DKP).
...: Additional arguments passed to the generic print method (currently not used).

Value

Invisibly returns the input object (of class "BKP" or "DKP"). The function is called for its side effect of printing a summary to the console.

Examples

# ============================================================== #
# ========================= 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)
print(model1)
#> --------------------------------------------------
#>            Beta Kernel Process (BKP) Model        
#> --------------------------------------------------
#> Number of observations (n):  30
#> Input dimensionality (d):    1
#> Kernel type:                 gaussian
#> Loss function used:          brier
#> Optimized kernel parameters: 0.0386
#> Minimum achieved loss:       0.00012
#> 
#> Prior specification:
#>   Noninformative prior: Beta(1,1).
#> --------------------------------------------------


#-------------------------- 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)
print(model2)
#> --------------------------------------------------
#>            Beta Kernel Process (BKP) Model        
#> --------------------------------------------------
#> Number of observations (n):  100
#> Input dimensionality (d):    2
#> Kernel type:                 gaussian
#> Loss function used:          brier
#> Optimized kernel parameters: 0.1112, 0.0680
#> Minimum achieved loss:       0.00020
#> 
#> Prior specification:
#>   Noninformative prior: Beta(1,1).
#> --------------------------------------------------

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

#-------------------------- 1D Example ---------------------------
set.seed(123)

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

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)

# 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)
print(model1)
#> --------------------------------------------------
#>            Dirichlet Kernel Process (DKP) Model        
#> --------------------------------------------------
#> Number of observations (n):  30
#> Input dimensionality (d):    1
#> Output dimensionality (q):   3
#> Kernel type:                 gaussian
#> Loss function used:          brier
#> Optimized kernel parameters: 0.0407
#> Minimum achieved loss:       0.00058
#> 
#> Prior specification:
#>   Noninformative prior: Dirichlet(1,...,1).
#> --------------------------------------------------


#-------------------------- 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
  p <- pnorm(f)
  return(matrix(c(p/2, p/2, 1 - p), nrow = length(p)))
}

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)

# 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)
print(model2)
#> --------------------------------------------------
#>            Dirichlet Kernel Process (DKP) Model        
#> --------------------------------------------------
#> Number of observations (n):  100
#> Input dimensionality (d):    2
#> Output dimensionality (q):   3
#> Kernel type:                 gaussian
#> Loss function used:          brier
#> Optimized kernel parameters: 0.1245, 0.0706
#> Minimum achieved loss:       0.00061
#> 
#> Prior specification:
#>   Noninformative prior: Dirichlet(1,...,1).
#> --------------------------------------------------

Print Summary of a Fitted BKP or DKP Model

Usage

Arguments

Value

See also

Examples