[Updated] Likelihood-informed processors

[odunbar]

Co-authored by @ArneBouillon

Purpose

• Derived from the LIS work of Add likelihood-informed data processors #376
• Closes Add new utilities for the likelihood-informed DataProcessor #370

Content

• Migration of the LIS from Add likelihood-informed data processors #376 under the following simplifications/changes:
  • [change] encoder_kwargs for structure vectors now keep samples_in and samples_out in their respective distributions, and also contain the algorithm time values dt corresponding to the distributions
  • [simplification] we no longer provide the dim_criterion, only a threshold for doing dimension reduction
  • [change] the user provides iters (Vector{Int}) not alphas (Vector{FT}) to indicate which dt values they would like to use for dimension reduction. A message reports the dt of the requested iterations
  • [change] if multiple iters are requested, by default we compute the LIS for each iter, then use a trapezoidal rule to create the final subspace.
  • [simplified] Reduced the complexity of the DimReduction example
  • [change] added a shift by the data mean
  • [change] Use a more robust information measure f(k) = log(1+k)^2 and truncate based on cumsum(f(k))/sum(f(k)) > eps. Leads to cutoff eps that is not "0.99999"
• Extended encoder_kwargs_from(eki,prior; g_final=...) to obtain all kwargs for encoding a typical problem. Additionally, we provide a convenience where the user can provide the "g" ensemble for a final evaluation of "u" in from the eki
• Recreated the DimensionReduction example for a linear problem to assess performance

MISC

• Refactor the boundary between public/private encode/decode functions.
  • API (to Utilities): encode_data, encode_structure_matrix, encode_with_schedule applied to encoder_schedule. NOT applicable to processors.
  • Private: _encode_data _encode_structure_matrix only applicable to exact processors etc.
  • API (to Emulators): encode_data and encode_structure_matrix (and decode counterparts) allow application to emulator in place of encoder_schedule
• add small check for error message

Example DimensionReduction

We just try the DR methods (using the forward map wrapper in place of an emulator) for a linear example in 100D->100D: the following is output

┌ Info: (reduced_dim, error) of posterior mean to whitened "reference" solution,
└  when using the truncation ({for PCA}, {for LI})
5×4 DataFrame
 Row │ truncation         PCA-in          LI-in 1:1       LI-in 1:5      
     │ Tuple…             Tuple…          Tuple…          Tuple…         
─────┼───────────────────────────────────────────────────────────────────
   1 │ (0.995, 0.999999)  (55, 0.165108)  (74, 0.155773)  (55, 0.157305)
   2 │ (0.99, 0.9999)     (38, 0.128842)  (45, 0.137292)  (29, 0.133462)
   3 │ (0.98, 0.999)      (23, 0.216203)  (30, 0.154637)  (21, 0.136362)
   4 │ (0.94, 0.94)       (9, 0.540077)   (11, 0.316728)  (10, 0.128643)
   5 │ (0.9, 0.88)        (6, 0.514944)   (9, 0.42256)    (8, 0.294448)

We see that as you increase truncation, our new LI 1:5 method reduces errors much more slowly than PCA. Meanwhile LI 1:1 is similar

[codecov]

Codecov Report

❌ Patch coverage is 92.41379% with 22 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.03%. Comparing base (6341ca2) to head (7134a07).

Files with missing lines	Patch %	Lines
src/Utilities.jl	81.81%	18 Missing ⚠️
src/Utilities/likelihood_informed.jl	97.70%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #410      +/-   ##
==========================================
- Coverage   94.18%   94.03%   -0.15%     
==========================================
  Files          10       11       +1     
  Lines        1977     2214     +237     
==========================================
+ Hits         1862     2082     +220     
- Misses        115      132      +17     

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