[WIP] CES implementation for CATKE

[odunbar]

Purpose

Runs a CES configuration on a large dataset

• this problem isn't really a good Bayesian one, as we only have inputs & a loss function. Therefore we must estimate the noise level of the problem over the ensemble, and solve with respect to this, the noise level will dictate the posterior.

To-do

• requires the 1GB data file catke-parameters.jld2

Content

• script to run GP (slow) and scalar-RF (faster)-based CES algorithms. rather than emulating the forward map, here we emulate the loss function directly with a 23D->1D map.
• plotting prior, posterior, and also before & after mlt hyperparameter training to see if it acheives benefit. (prior/untuned in grey on plots)
• some L^2 errors also computed on a chunk of validation data (compared to an untuned fit) to assess the hyperparameter training

Current result: train with data from iterations 51:20:251, estimating noise from final 50 iterations

These are still rough-and-ready, and may be improved by further looking at the choice of kernel structure for the RF maps. Current finding increasing rank shrinks posterior spread before stabilizing (below = rank 7 kernel).
(Right: Zoom-in of Left, red bar = final EKI mean, grey bars, min/max of training data)

Grey bars indicate that some parameters: C^WwDelta, C^{hi}C, C^{hi}D, C^{hi}e, C^{lo}e, C^ec may accelerate EKI convergence and emulator sample production with more biased priors toward the respective min/max of the current training data

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