moocore.

vorob_dev

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

Compute Vorob’ev deviation.

Parameters:

• points (ArrayLike) – Array of numerical values, where each row gives the coordinates of a point in objective space. If the array is created by the read_datasets() function, remove the last column.

• sets (ArrayLike) – 1D vector or list of values that gives the set of each row of points.

• ref (ArrayLike) – Reference point as a 1D vector. Must be either a single value, which will be used for all coordinates, or the same length as a single point in points.

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

Mickaël Binois, David Ginsbourger, and Olivier 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.xz")
>>> vd = moocore.vorob_dev(CPFs[:, :-1], sets=CPFs[:, -1], ref=(2, 200))
>>> vd
3017.12989402326