Plot the symmetric deviation function.

The symmetric deviation function is the probability for a given target in the objective space to belong to the symmetric difference between the Vorob'ev expectation and a realization of the (random) attained set.

Usage

symdevplot(
  x,
  sets,
  VE,
  threshold,
  nlevels = 11,
  ve.col = "blue",
  xlim = NULL,
  ylim = NULL,
  legend.pos = "topright",
  main = "Symmetric deviation function",
  col.fun = function(n) gray(seq(0, 0.9, length.out = n)^2)
)

Arguments

x: Either a matrix of data values, or a data frame, or a list of data frames of exactly three columns. The third column gives the set (run, sample, ...) identifier.
sets: A vector that indicates the set of each point in x. If missing, the last column of x is used instead.
VE, threshold: Vorob'ev expectation and threshold, e.g., as returned by moocore::vorobT().
nlevels: number of levels in which is divided the range of the symmetric deviation.
ve.col: plotting parameters for the Vorob'ev expectation.
xlim, ylim, main: Graphical parameters, see plot.default().
legend.pos: the position of the legend, see legend(). A value of "none" hides the legend.
col.fun: function that creates a vector of n colors, see heat.colors().

References

M Binois, D Ginsbourger, O Roustant (2015). “Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations.” European Journal of Operational Research, 243(2), 386–394. doi:10.1016/j.ejor.2014.07.032 .

C. Chevalier (2013), Fast uncertainty reduction strategies relying on Gaussian process models, University of Bern, PhD thesis.

Ilya Molchanov (2005). Theory of Random Sets. Springer.

Author

Mickael Binois

Examples

data(CPFs, package = "moocore")
res <- moocore::vorobT(CPFs, reference = c(2, 200))
print(res$threshold)
#> [1] 44.14062

## Display Vorob'ev expectation and attainment function
# First style
eafplot(CPFs[,1:2], sets = CPFs[,3], percentiles = c(0, 25, 50, 75, 100, res$threshold),
        main = substitute(paste("Empirical attainment function, ",beta,"* = ", a, "%"),
                          list(a = formatC(res$threshold, digits = 2, format = "f"))))


# Second style
eafplot(CPFs[,1:2], sets = CPFs[,3], percentiles = c(0, 20, 40, 60, 80, 100),
        col = gray(seq(0.8, 0.1, length.out = 6)^0.5), type = "area",
        legend.pos = "bottomleft", extra.points = res$VE, extra.col = "cyan",
        extra.legend = "VE", extra.lty = "solid", extra.pch = NA, extra.lwd = 2,
        main = substitute(paste("Empirical attainment function, ",beta,"* = ", a, "%"),
                          list(a = formatC(res$threshold, digits = 2, format = "f"))))

# Vorob'ev deviation
VD <- moocore::vorobDev(CPFs, reference = c(2, 200), VE = res$VE)
# Display the symmetric deviation function.
symdevplot(CPFs, VE = res$VE, threshold = res$threshold, nlevels = 11)

# Levels are adjusted automatically if too large.
symdevplot(CPFs, VE = res$VE, threshold = res$threshold, nlevels = 200, legend.pos = "none")


# Use a different palette.
symdevplot(CPFs, VE = res$VE, threshold = res$threshold, nlevels = 11, col.fun = heat.colors)