Construct Prior Parameters for the DKP Model

Computes prior Dirichlet distribution parameters alpha0 at each input location for the Dirichlet Kernel Process model, based on the specified prior type: noninformative, fixed, or adaptive.

Usage

get_prior_dkp(
  prior = c("noninformative", "fixed", "adaptive"),
  r0 = 2,
  p0 = NULL,
  Y = NULL,
  K = NULL
)

Arguments

prior: Character string specifying the type of prior to use. One of "noninformative", "fixed", or "adaptive".
r0: Positive scalar indicating the global precision parameter. Used when prior is "fixed" or "adaptive".
p0: Numeric vector specifying the global prior mean for each class (must sum to 1). Only used when prior = "fixed". Should be of length equal to the number of classes.
Y: Numeric matrix of observed class counts of size n × q, where n is the number of observations and q the number of classes.
K: A precomputed kernel matrix of size n × n, typically obtained from kernel_matrix.

Value

A list containing:

alpha0: A numeric matrix of prior Dirichlet parameters at each input location; dimension n × q.

Details

When prior = "noninformative", all entries in alpha0 are set to 1 (flat Dirichlet).
When prior = "fixed", all rows of alpha0 are set to r0 * p0.
When prior = "adaptive", each row of alpha0 is computed by kernel-weighted smoothing of the observed relative frequencies in Y, scaled by r0.

Examples

# Simulated multi-class data
set.seed(123)
n <- 15           # number of training points
q <- 3            # number of classes
X <- matrix(runif(n * 2), ncol = 2)

# Simulate class probabilities and draw multinomial counts
true_pi <- t(apply(X, 1, function(x) {
  raw <- c(
    exp(-sum((x - 0.2)^2)),
    exp(-sum((x - 0.5)^2)),
    exp(-sum((x - 0.8)^2))
  )
  raw / sum(raw)
}))
m <- sample(10:20, n, replace = TRUE)
Y <- t(sapply(1:n, function(i) rmultinom(1, size = m[i], prob = true_pi[i, ])))

# Compute kernel matrix (Gaussian)
K <- kernel_matrix(X, theta = rep(0.2, 2), kernel = "gaussian")

# Construct adaptive prior
prior_dkp <- get_prior_dkp(prior = "adaptive", r0 = 2, Y = Y, K = K)