How to mimick a Discrete Bayes Net in Turing.jl?

Specific Domains Probabilistic Programming
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1

Hi,

I’ve been using Turing.jl for various purposes, and recently I thought it might be easy to mimick inference from a basic discrete bayesian network like I could do with BayesNets.jl like this for example:

bn = DiscreteBayesNet()
push!(
    bn, 
    DiscreteCPD(
        :a, # our root node
        [0.6, 0.4], # prior
    )
)
push!(
    bn,
    DiscreteCPD(
        :b,
        [:a], # :a is :b's parent node
        [2],
        [
            Categorical([0.9, 0.1]),
            Categorical([0.1, 0.9]),
        ],
    )
)

infer_df = DataFrame(infer(
    bn,
    :a,
    evidence = Assignment(
        :b => 1, # observing a specific state of :b, infer :a's new distribution
    ),
))

Which gives updated probabilities for :a:

2×2 DataFrame
 Row │ a      potential 
     │ Int64  Float64   
─────┼──────────────────
   1 │     1  0.931034
   2 │     2  0.0689655

I’ve been toying around with a Turing model for a while now, trying to combine Dirichlet and Categorical distributions etc, but I can’t seem to figure out a way to infer the correct posterior probabilities from some evidence (here, a single observation of :b). I’ve been able to get the probabilities to go in the correct direction, but not to approximate the exact inference result through sampling with Turing.

I guess I’m going at it wrong, probably. I’m not an expert with probabilistic programming. On the other hand, Turing seems so flexible that I guess it should be possible, though I’m not sure. Would you have an example of how to do something like this in Turing?

2

Welcome to the forum! This is an interesting question, I’ve been thinking about a similar thing. Could you share your attempts?

3

Most contemporary PPLs are developed with continuous variables in mind. Therefore, for pure Bayesian networks, it’s best to use frameworks specialized to those.

4

Are there any Discrete Bayesian network frameworks in Julia?

5

I think so? A quick google search revaled BayesNets.jl. I am sure there is more, but I am more of a general PPL man myself, so not much experience with Bayesian networks.

6

Also see the RxInfer.jl tutorial on Bayesian networks.