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#' Calculates the confidence interval for the dataset.
#'
#' @description Calculates # of samples needed to ensure learning with,
#' a certain confidence interval simulated.
#'
#' @param rpart.tree rpart.tree. A Decision tree generated by rpart package.
#' @param epsilon float. The epsilon to be used in the delta calculation.
#' @param max_confidence int. The maximum confidence to achieve in 0.01 steps length.
#'
#' @usage confidence_interval(rpart.tree, epsilon, max_confidence)
#'
#' @return No return value, the function plot the confidence interval values.
#'
#' @export confidence_interval
confidence_interval <- function(rpart.tree, epsilon=.05, max_confidence=.2){
delta_confidence = NULL
n_confidence_samples = NULL
shattering_confidence = NULL
for (epsilon in seq(0.05, max_confidence, by=0.01)){
n_samples = 1
delta = epsilon+0.01
ret = search_delta_n_samples(rpart.tree, n_samples, delta, epsilon)
delta = ret$delta
n_samples = ret$n_samples
delta_confidence <- c(delta_confidence, 1-epsilon)
n_confidence_samples <- c(n_confidence_samples, n_samples)
}
plot(delta_confidence, n_confidence_samples, ylab="# of samples", xlab="Confidence interval (%)",
main="Number of samples needed to ensure learning given a confidence interval value", type="l")
}
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