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Loopy belief propagation for factor graphs on discrete variables, in JAX!

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updates: - [github.com/PyCQA/isort: 5.10.1 → 5.13.2](https://github.com/PyCQA/isort/compare/5.10.1...5.13.2) - [github.com/psf/black: 22.3.0 → 24.8.0](https://github.com/psf/black/compare/22.3.0...24.8.0) - [github.com/pre-commit/pre-commit-hooks: v4.1.0 → v5.0.0](https://github.com/pre-commit/pre-commit-hooks/compare/v4.1.0...v5.0.0) - [github.com/PyCQA/flake8: 4.0.1 → 7.1.1](https://github.com/PyCQA/flake8/compare/4.0.1...7.1.1) - [github.com/pre-commit/mirrors-mypy: v0.942 → v1.11.2](https://github.com/pre-commit/mirrors-mypy/compare/v0.942...v1.11.2)

One of the speed bottleneck in creating a `FactorGraph` is the time to create the `variables_for_factors` list, which is currently slow as we loop through the individual variables. However, in...

Creating the `vars_to_starts` as a dictionnary mapping variable to int is expensive in the case where we have a lot of variables. Instead it could map a variable group to...

_Originally posted by @wlehrach in https://github.com/vicariousinc/PGMax/pull/136#discussion_r860084436_

_Originally posted by @antoine-dedieu in https://github.com/vicariousinc/PGMax/pull/136#discussion_r860284075_

See @StannisZhou in https://github.com/vicariousinc/PGMax/pull/129#discussion_r841420714_

See https://github.com/vicariousinc/PGMax/pull/80

Currently it's not clear what names PGMax assigns to different variables (e.g. https://github.com/vicariousinc/PGMax/issues/115). Add documentation to make this clearer.

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