def_cstr_X_space: def_cstr_X_space

In alex-conanec/optisure:

Description

Find the space where points where observed. Send back a function to check if a/several point(s) belong to the space where the points where observed

Usage

def_cstr_X_space(
  X,
  alpha = 0.15,
  allowed_dependence = matrix(TRUE, nrow = NCOL(X), ncol = 1),
  path_tracking = NULL
)

Details

@param X matrix of dimension n x d observed points @param alpha probability to deal with the trade-off false positive false negatif. Alpha closed to 1 mean low false positive and vice versa @param path_tracking path where to write the step of the running function.

Examples

library(tidyverse)
library(optisure)

#parameters constraint
alpha = 0.05

#parameters data
n = 1000
d1 = 2
mini = rep(0, d1)
maxi = rep(10, d1)
b = matrix(c(0, 0, 5, 5), byrow = T, ncol = d1)
B = matrix(c(4, 4, 10, 10), byrow = T, ncol = d1)
p = NROW(B) #nombre de "foyer"


#generate data
X_U = sapply(seq_len(d1), function(i){
  sapply(seq_len(p), function(k){
    runif(n/p, b[k,i], B[k,i])
  })
}) %>% as.data.frame()

#Monte Carlo simulation of 5000 points to check the constraint
n_MC = 5000
X_MC = sapply(seq_len(d1), function(i){
  runif(n_MC, mini[i], maxi[i])
})

#visualisation
res = def_cstr_X_space(X=X_U, alpha = alpha)
feasible_X_MC = res$g(x = X_MC)

cols <- c("FALSE" = "red", "training" = "blue", "TRUE" = "green")
ggplot(data.frame(X_MC, feasible = feasible_X_MC)) +
  geom_point(aes(x = X1, y = X2, colour = feasible)) +
  geom_point(data = X_U, aes(x = V1, y = V2, colour = "training"),
             shape = 17, size = 1) +
  scale_colour_manual(values = cols)


# verification avec les aires de MC
# aire theorique de 95% de la surface
A_true_uni = (1-alpha) * sum(apply(B-b, 1, prod))
A_true_uni

# Aire estime par Monte Carlo
A_MC = prod(maxi - mini)
A_estime = A_MC*sum(feasible_X_MC)/n_MC
A_estime
(A_estime - A_true_uni)/A_true_uni #ratio

alex-conanec/optisure documentation built on Dec. 19, 2021, 12:27 a.m.