get_discrepancy_covariances_KL

pyapprox.control_variate_monte_carlo.get_discrepancy_covariances_KL(cov, nsample_ratios, K, L, pkg=<module 'numpy' from '/Users/jdjakem/opt/miniconda3/envs/pyapprox-dev/lib/python3.7/site-packages/numpy/__init__.py'>)

Get the covariances of the discrepancies \(\delta\) between each low-fidelity model and its estimated mean using the MFMC sampling strategy and the ACV KL estimator.

The ACV-KL estimator partitions all of the control variates into two groups; the first K variables form a K -level approximate control variate, and the last \(M-K\) variables are used to reduce the variance of estimating \(\mu_L\) some \(L \le K\) . The resulting estimator accelerates convergence to OCV-K , and L provides a degree of freedom for targeting a control variate level that contributes the greatest to the estimator variance.

Parameters

covnp.ndarray (nmodels,nmodels)

The estimated covariance between each model.

nsample_ratiositerable (nmodels-1)

The sample ratioss \(r_\alpha>1\) for each low-fidelity model

Kinteger (K<=nmodels-1)

The number of effective control variates.

Linteger (1<=L<=K+1)

The id of the models whose mean is being targeted by the remaining nmodels-K low fidelity models.

pkgpackage (optional)

A python package (numpy or torch) used to store the covariances.