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Which open-source software (toolbox) do you think is the best for modelling graphical models (e.g. factor graphs), and doing inference on them? (the language doesn't matter)

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Another is the gRain package in R.

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I found LibDai very useful: http://staff.science.uva.nl/~jmooij1/libDAI/

Also Factorie is very easy to use.

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I recently had written PyGModels in Python capable of doing inference over LWF Chain Graphs:

It is quite lightweight as it depends only on standard library. However for heavy lifting, I suggest:

The development on PyGModels is very active and documentation severely lags.

However there is a stable release which had appeared in JOSS:

Eraslan, D. K. (2021) ‘PyGModels: A python package for exploring probabilistic graphical models with graph theoretical structures’, Journal of Open Source Software, 6(61). doi: 10.21105/joss.03115.

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