Distance Metrics Enhancement: New metrics, 3-way-comparisons, Bootstrapping

[eroell]

Description of feature

The part of interest here is pertpy’s Distance metrics.
The main file to be worked on is https://github.com/theislab/pertpy/tree/main/pertpy/tools/_distances

This description is updated from a description in an older PR, but here should be all relevant information in one place, split into 4 packages:

1) Add new metrics to Distance

• mean_var_distn
• Mahalanobis
• (ilisi, not important since doesnt work well)

For these, here is already draft implementations on the hackathon branch which you might want to copy or look into.

2) Add “three-way comparison option”

• Basically compute (with the metrics from Distance) prediction vs true perturbed, and prediction vs true unperturbed, and report the ratio

For this, here is already a draft implementation from the hackathon branch which you might want to copy or look into.

3) Bootstrapping

• Add “bootstrap” option which reports mean+stdev instead of just a point distance estimate

For this, here is already a draft PR which you might want to continue using or look into :)

4) General TODOs

• All metrics should be further tested for edge cases and sparse/non-sparse inputs.
• Some metrics would need to be inverted as they currently measure similarity not distance.
• Some metrics require a specific order of what is x,y,z input (control, perturbed, predicted perturbed) so that needs to be clear in the documentation.