vorob_dev

moocore.vorob_dev(x, /, ref, *, ve=None)

Compute Vorob’ev deviation.

Parameters:

• x (ArrayLike) – Numpy array of numerical values and set numbers, containing multiple sets. For example the output of the read_datasets() function.

• ref (ArrayLike) – Reference point set as a numpy array or list. Must be same length as a single point in the dataset.

• ve (ArrayLike | None, default: None) – Vorob’ev expectation, e.g., as returned by vorob_t(). If not provided, it is calculated as vorob_t(x, ref).

Returns:

float – Vorob’ev deviation.

See also

vorob_t

Compute Vorob’ev threshold and expectation.

Notes

For more background, see Binois et al.[1], Molchanov[2], Chevalier et al.[3].

References

[1]

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

[2]

Ilya Molchanov. Theory of Random Sets. Springer, 2005. [BibTeX].

[3]

Clément Chevalier, David Ginsbourger, Julien Bect, and Ilya Molchanov. Estimating and quantifying uncertainties on level sets using the Vorob’ev expectation and deviation with Gaussian process models. In Dariusz Ucinski, Anthony C. Atkinson, and Maciej Patan, editors, mODa 10–Advances in Model-Oriented Design and Analysis, pages 35–43. Springer International Publishing, Heidelberg, Germany, 2013. doi:10.1007/978-3-319-00218-7_5, [BibTeX].

Examples

>>> CPFs = moocore.get_dataset("CPFs.txt")
>>> vd = moocore.vorob_dev(CPFs, ref=(2, 200))
>>> vd
3017.12989402326