Add conditional_bdm to compute BDM(x|y)

[nodtem66]

• add conditional_bdm(X,Y) and test_conditional_bdm based on supplementary from Hernández-Orozco S, Zenil H, (2021)
• add compute_f_of_intersect used in Coarse Conditional BDM to compute
• add pytest mark for slow in tox.ini

[codecov[bot]]

Codecov Report

Merging #16 (71461aa) into master (4bedea1) will decrease coverage by 1.86%. The diff coverage is 89.36%.

@@            Coverage Diff             @@
##           master      #16      +/-   ##
==========================================
- Coverage   92.93%   91.07%   -1.87%     
==========================================
  Files          16       16              
  Lines         863      896      +33     
==========================================
+ Hits          802      816      +14     
- Misses         61       80      +19     

Impacted Files	Coverage Δ
pybdm/options.py	40.00% <0.00%> (ø)
pybdm/utils.py	91.30% <0.00%> (-2.18%)	:arrow_down:
pybdm/bdm.py	94.00% <94.11%> (-0.19%)	:arrow_down:
pybdm/algorithms.py	89.25% <100.00%> (-0.83%)	:arrow_down:
tests/conftest.py	70.96% <100.00%> (+2.00%)	:arrow_up:
tests/test_bdm.py	100.00% <100.00%> (ø)
tests/test_partitions.py	100.00% <100.00%> (ø)
tests/test_perturbation.py	100.00% <100.00%> (ø)
pybdm/encoding.py	72.00% <0.00%> (-20.00%)	:arrow_down:

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[sztal]

Hi @nodtem66 and thanks for this contribution! I will merge it in the upcoming new release (hopefully around June/July this year). In the meantime I have an important question.

I see that in some of the tests you added you use PartitionCorrelated. Is this necessary, that is, is correlated partition somehow instrumental for this new method you implemented (I have not yet read the paper)? I am asking because I plan to remove or at least deprecate the correlated partition from the next release as it is not really feasible to define normalized BDM properly in this case.

[nodtem66]

Thanks, @sztal. I look forward to seeing the next upcoming release.

For your question, I used the PartitionCorrelated in testing because it looks similar to the result from supplementary. The author used StringPartition which is like the correlated partition, as shown in the following figure from the Wolfram notebook: "StringConditionalExperimentsV6.nb". The two test cases in test_bdm.py actually came from this script.

So, I suggest either mark it deprecated or throw the exception when using with normalized BDM.