fit.BKP {BKP} | R Documentation |
Fit a Beta Kernel Process (BKP) Model
Description
Fits a BKP model to binomial or binary response data via local kernel smoothing. The model constructs a flexible latent probability surface by updating Beta priors using kernel-weighted observations.
Usage
fit.BKP(
X,
y,
m,
Xbounds = NULL,
prior = c("noninformative", "fixed", "adaptive"),
r0 = 2,
p0 = 0.5,
kernel = c("gaussian", "matern52", "matern32"),
loss = c("brier", "log_loss"),
n_multi_start = NULL
)
Arguments
X |
A numeric input matrix of size |
y |
A numeric vector of observed successes (length |
m |
A numeric vector of total binomial trials (length |
Xbounds |
Optional |
prior |
Type of prior to use. One of |
r0 |
Global prior precision (only used when |
p0 |
Global prior mean (only used when |
kernel |
Kernel function for local weighting. Choose from
|
loss |
Loss function for kernel hyperparameter tuning. One of
|
n_multi_start |
Number of random initializations for multi-start
optimization. Default is |
Value
A list of class "BKP"
containing the fitted BKP model, with
the following elements:
theta_opt
Optimized kernel hyperparameters (lengthscales).
kernel
Kernel function used, as a string.
loss
Loss function used for hyperparameter tuning.
loss_min
Minimum loss value achieved during optimization.
X
Original (unnormalized) input matrix of size
n × d
.Xnorm
Normalized input matrix scaled to
[0,1]^d
.Xbounds
Matrix specifying normalization bounds for each input dimension.
y
Observed success counts.
m
Observed binomial trial counts.
prior
Type of prior used.
r0
Prior precision parameter.
p0
Prior mean (for fixed priors).
alpha0
Prior shape parameter
\alpha_0(\mathbf{x})
, either a scalar or vector.beta0
Prior shape parameter
\beta_0(\mathbf{x})
, either a scalar or vector.alpha_n
Posterior shape parameter
\alpha_n(\mathbf{x})
.beta_n
Posterior shape parameter
\beta_n(\mathbf{x})
.
See Also
fit.DKP
for modeling multinomial responses using the
Dirichlet Kernel Process. predict.BKP
,
plot.BKP
, simulate.BKP
for making predictions,
visualizing results, and generating simulations from a fitted BKP model.
summary.BKP
, print.BKP
for inspecting model
details.
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)
#-------------------------- 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)