add method for iid-batched conditioning.

[janfb]

• introduce condition_on method for likelihood-estimator-based potential to condition on a batch of theta values (experimental conditions) that match the current batch of iid x_o.
• deprecate MNLE-based potential (can be nle-based)
• adapt tests for conditioned mnle.

[codecov]

Codecov Report

Attention: Patch coverage is 26.08696% with 17 lines in your changes missing coverage. Please review.

Project coverage is 78.30%. Comparing base (06890eb) to head (074efa0).

Files with missing lines	Patch %	Lines
...inference/potentials/likelihood_based_potential.py	19.04%	17 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1331       +/-   ##
===========================================
- Coverage   89.39%   78.30%   -11.09%     
===========================================
  Files         118      118               
  Lines        8709     8736       +27     
===========================================
- Hits         7785     6841      -944     
- Misses        924     1895      +971     

Flag	Coverage Δ
unittests	78.30% <26.08%> (-11.09%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
sbi/inference/trainers/nle/mnle.py	85.36% <100.00%> (-7.32%)	⬇️
sbi/utils/conditional_density_utils.py	73.46% <100.00%> (-21.09%)	⬇️
sbi/utils/sbiutils.py	78.11% <ø> (-8.68%)	⬇️
...inference/potentials/likelihood_based_potential.py	60.00% <19.04%> (-40.00%)	⬇️

... and 29 files with indirect coverage changes

[michaeldeistler]

I am not sure I fully understand tbh.

IIUC, then there are four different dimensions across which we could vectorize:

1. Across the x batch-dimension, in case we want to amortize.
2. Across the x iid-dimension, in case we have iid samples.
3. Across a batch of theta conditions which act as different experimental conditions
4. Across thetas, in case we want to run multi-chain.

Which one of these does this PR solve? And which ones does it not yet solve?

Can we maybe somewhere define names for each of these four dimensions above and specify which ones are handled by which function (or which ones are currently assumed to be the same dimension and therefore do not have a cartesian product applied to them)?

[michaeldeistler]

The condition is in theta space, right?

[michaeldeistler]

iid_dim is the same as for x, right?

[michaeldeistler]

Would be useful to define event_shape more explicitly here.

[michaeldeistler]

rename event_shape to x_event_shape.

[michaeldeistler]

Please specify shape.

[michaeldeistler]

Should the condition be the full theta or only the ones that are not part of dims_to_sample?

[michaeldeistler]

The sentence above implies that it is only "a part of theta"

[michaeldeistler]

So the batch_shape of condition must match the batch_shape of x later on?

[michaeldeistler]

this is nasty, but I also don't think that there is another way to do this.

[janfb]

As discussed in the call, the plan is to

• introduce (sample, batch, *event) for the theta_condition at inference time
• this will enable sampling for multiple xs (batched x) multiple iid observations (for each x) and simultaneously passing a corresponding batch of conditions for each x. For example, for a decision-making use-case, it will be possible to sample in one call: multiple subject (batch of xs) where each subject performed N trials with N (different) experimental conditions. N needs to be the same for all subjects though.
• improve naming and docs to avoid confusion between condition and experimental_condition, e.g., use theta_condition
• add tests for new conditioning functions