vorobT {moocore}

Vorob'ev computations

Description

Compute Vorob'ev threshold, expectation and deviation. Also, displaying the symmetric deviation function is possible. 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

vorobT(x, sets, reference, maximise = FALSE)

vorobDev(x, sets, reference, VE = NULL, maximise = FALSE)

Arguments

x

matrix|data.frame
Matrix or data frame of numerical values, where each row gives the coordinates of a point. If sets is missing, the last column of x gives the sets.

sets

integer()
A vector that indicates the set of each point in x. If missing, the last column of x is used instead.

reference

numeric()
Reference point as a vector of numerical values.

maximise

logical()
Whether the objectives must be maximised instead of minimised. Either a single logical value that applies to all objectives or a vector of logical values, with one value per objective.

VE

matrix()
Vorob'ev expectation, e.g., as returned by vorobT().

Value

vorobT returns a list with elements threshold, VE, and avg_hyp (average hypervolume)

vorobDev returns the Vorob'ev deviation.

Author(s)

Mickael Binois

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.

Examples

data(CPFs)
res <- vorobT(CPFs, reference = c(2, 200))
res$threshold
res$avg_hyp
# Now print Vorob'ev deviation
VD <- vorobDev(CPFs, VE = res$VE, reference = c(2, 200))
VD