gemseo_umdo / statistics / multilevel / mlmc_mlcv / pilots

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mean module

The mean-based pilot for the MLMC-MLCV algorithm.

class gemseo_umdo.statistics.multilevel.mlmc_mlcv.pilots.mean.Mean(sampling_ratios, costs)[source]

Bases: MLMCMLCVPilot

The mean-based pilot for the MLMC-MLCV algorithm.

See also

El Amri et al., Algo. 1, Multilevel Surrogate-based Control Variates, 2023.

  • sampling_ratios (NDArray[float]) – The sampling ratios $r_0,ldots,r_L$; the sampling ratio $r_ell$ is the factor by which $n_ell$ is increased between two sampling steps on the level $ell$.

  • costs (NDArray[float]) – The unit sampling costs of each level of the telescopic sum. Namely, $(mathcal{C}_{ell-1}+mathcal{C}_ell)_{ellin{0,ldots,L}}$ with $mathcal{C}_{-1}=0$.

compute_next_level_and_statistic(levels, total_n_samples, samples, *pilot_parameters)

Compute the next level $ell^*$ to sample and estimate the statistic.

  • levels (Iterable[int]) – The levels that have just been sampled.

  • total_n_samples (ndarray[Any, dtype[int]]) – The total number of samples of each level.

  • samples (Sequence[ndarray[Any, dtype[float]]]) – The samples of the different quantities of each level.

  • *pilot_parameters (Any) – The parameters of the pilot.


The next level $ell^*$ to sample and an estimation of the statistic.

Return type:

tuple[int, numpy.ndarray[Any, numpy.dtype[float]]]

V_l: ndarray[Any, dtype[float]]

The terms variances $mathcal{V}_0,ldots,mathcal{V}_L$.