vorob_t

moocore.vorob_t(data, /, ref)

Compute Vorob’ev threshold and expectation.

Parameters:

• data (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 as a 1D vector. Must be same length as a single point in the data.

Returns:

dict – A dictionary with elements threshold, ve, and avg_hyp (average hypervolume).

See also

vorob_dev

Compute Vorob’ev deviation.

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")
>>> res = moocore.vorob_t(CPFs, ref=(2, 200))
>>> res["threshold"]
44.140625
>>> res["avg_hyp"]
8943.333191728081
>>> res["ve"].shape
(213, 2)