Sinusoidal example

[lm2612]

Purpose

This will close #247

To-do

• Copy sinusoidal example from EnsembleKalmanProcesses.jl for the calibration step
• Create two emulators (Gaussian process, scalar random feature) and compare performance
• Demonstrate sampling code and plot samples to show how to do uncertainty quantification
• Documentation

Content

---

• I have read and checked the items on the review checklist.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (a621a04) 88.09% compared to head (ab5a875) 88.16%.
Report is 8 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #248      +/-   ##
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+ Coverage   88.09%   88.16%   +0.07%     
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  Files           7        7              
  Lines        1134     1124      -10     
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- Hits          999      991       -8     
+ Misses        135      133       -2     

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[odunbar]

Hi @lm2612 This looks really good so far. I have focussed just on the Docs for now, I'll take a peak at the RF setup etc. in a bit. It's mostly minor comments, although there is one larger comment.

• I find the marginal GP/RF validation plots quite opaque. It's very hard to interpret how far the data is from the training points etc. as only ordering in one axis is not very clear.

[odunbar]

Hi @lm2612

A review on the example itself:

• The difference in performance is due to it not being a fair experiment, I have detailed the small fix, and I observe this balances out the behaviour significantly. though the RF still has a heavier tail for theta_1 (Note RF still learns the noise where GP doesnt)

[odunbar]

Another Kernel that performs very similarly to GP is the following vector-RF case without decorrelation:

kernel_structure = NonseparableKernel(LowRankFactor(2,nugget))
optimizer_options = Dict(
    "scheduler" => EKP.DataMisfitController(on_terminate = "continue"),
   "n_iteration" => 50,
    "rng" => rng,
)
random_features = VectorRandomFeatureInterface(
    n_features,
    input_dim,
    output_dim,
    rng = rng,
    kernel_structure = kernel_structure,
    optimizer_options = optimizer_options,
)
emulator_random_features = Emulator(random_features, input_output_pairs, normalize_inputs = true, obs_noise_cov=Γ, decorrelate=false)

[odunbar]

LGTM - this is a fantastic example! Please run the julia formatter - otherwise my comments are very minor.

Then we can squash&merge