Accept LogDensityProblems objects

[sethaxen]

This PR removes the methods of pathfinder and multipathfinder that accepted both a function and its gradient and instead has a single method that takes either a function or an object implementing the LogDensityProblems interface.

It also moves away from using AbstractDifferentiation for ad backends (development seems to have stalled) in favor of using LogDensityProblemsAD. This should enable better compatibility with PPLs; Turing, Soss, and Tilde models all implement this interface.

Fixed #115

[codecov-commenter]

Codecov Report

Base: 92.69% // Head: 92.64% // Decreases project coverage by -0.06% ⚠️

Coverage data is based on head (367fec7) compared to base (9e6bf45).
Patch coverage: 100.00% of modified lines in pull request are covered.

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Additional details and impacted files

@@            Coverage Diff             @@
##             main     #122      +/-   ##
==========================================
- Coverage   92.69%   92.64%   -0.06%     
==========================================
  Files          13       13              
  Lines         575      571       -4     
==========================================
- Hits          533      529       -4     
  Misses         42       42              

Impacted Files	Coverage Δ
src/Pathfinder.jl	100.00% <ø> (ø)
src/transducers.jl	100.00% <ø> (ø)
src/multipath.jl	67.27% <100.00%> (+0.60%)	⬆️
src/optimize.jl	93.33% <100.00%> (-0.79%)	⬇️
src/singlepath.jl	88.63% <100.00%> (+1.13%)	⬆️

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[sethaxen]

For some reason, these changes break reproducibility when parallelizing with multithreading. Strange.

[sethaxen]

For some reason, these changes break reproducibility when parallelizing with multithreading. Strange.

Seems to be due to tpapp/LogDensityProblemsAD.jl#6, relates JuliaDiff/ForwardDiff.jl#573

[sethaxen]

On further thought, I think I will go the way of AdvancedHMC and DynamicHMC and completely remove the option where a user passes a function. This simplifies the code. Pathfinder should probably be used most as a backend, and regardless, it's easy to construct LogDensityProblems from models in the major PPLs.