Is there any way to compute the Bethe Free Energy of a given model?

[Flawless1202]

I want to compute the Bethe Free Energy like follows:

@model function coin_model(y, a, b)
    θ ~ Beta(a, b)
    for i in eachindex(y)
        y[i] ~ Bernoulli(θ)
    end
end

result = infer(
    model = coin_model(a = 4.0, b = 8.0), 
    data  = (y = dataset,)
)

free_energy = compute_free_energy(result.model)

How to implement the compute_free_energy function? @ThijsvdLaar @bvdmitri @alstat @wmkouw @kobus78 Thanks a lot!

[Nimrais]

Hi, I may not fully understand your question, but in most cases, the local free energy is defined per node. RxInfer will produce this as an output - you just need to specify it through a keyword argument in the infer function.

If you're asking about implementing free energy for a model with a custom node, you can look at how it's implemented in the ReactiveMP source code, specifically at the implementation of the Beta distribution here https://github.com/ReactiveBayes/ReactiveMP.jl/blob/main/src/nodes/predefined/beta.jl#L6.

result = infer(
           model = coin_model(a = 4.0, b = 8.0),
           data  = (y = dataset,),
           free_energy=true,
       )
Inference results:
  Posteriors       | available for (θ)
  Free Energy:     | Real[696.125]

[bvdmitri]

As @Nimrais pointed out you simply need to set free_energy flag to true and it will setup the inference function to also compute Bethe Free Energy with every iteration. See an example here.
Note, however, that it is not always possible to compute BFE for all models because sometimes its way too challenging.