How to set a 'condition' in a model like WebPPL?

[Flawless1202]

I have read the tutorial called Probabilistic Models of Cognition. And I have read an example in Section Causal and statistical dependence as follows:

var marg = Infer({method: 'enumerate'}, function() {
  var smokes = flip(0.2)
  var lungDisease = (smokes && flip(0.1)) || flip(0.001)
  var cold = flip(0.02)
  var cough = (cold && flip(0.5)) || (lungDisease && flip(0.5)) || flip(0.001)
  var fever = (cold && flip(0.3)) || flip(0.01)
  var chestPain = (lungDisease && flip(0.2)) || flip(0.01)
  var shortnessOfBreath = (lungDisease && flip(0.2)) || flip(0.01)

  condition(cough)
  return {cold: cold, lungDisease: lungDisease}
})

viz.marginals(marg)

I try to realize the condition function in RxInfer.jl. I follow the example in this tutorial. Here is my code:

using RxInfer, Distributions

struct Cond end
@node Cond Stochastic [out, in]
@rule Cond(:in, Marginalisation) (q_out::PointMass,) = begin
    return Bernoulli(mean(q_out))
end

@model function f(cond)
    smokes ~ Bernoulli(0.2)
    lung_disease ~ (smokes && Bernoulli(0.1)) || Bernoulli(0.001)
    cold ~ Bernoulli(0.02)
    cough ~ (cold && Bernoulli(0.5)) || (lung_disease && Bernoulli(0.5)) || Bernoulli(0.001)
    cond .~ Cond(cough)
end

result = infer(model = f(), data = (cond = [true],))

And I get the true answer. But in my implementation, the input of Cond must be a distribution. When I use a Bool expression such as cond .~ Cond(cough == true), I get the error as follows:

Delta node `==` requires meta specification with the `where { meta = ... }` in the `@model` macro or with the separate `@meta` specification. See documentation for the `DeltaMeta`.

Is there any way to fix this error and make the Cond function work well? @ThijsvdLaar @bvdmitri Thanks for your reply!

[albertpod]

Hi @Flawless1202! Thanks for trying out RxInfer.jl!

I’m not entirely sure I understand your question. The variable “cough” is a random variable drawn from the lengthy expression. You then pass this random variable to a Cond node (not a function in Julia sense). Could you elaborate a bit more on what you’re trying to achieve?

[Nimrais]

yes, we can, but I am not sure that I understood what model is doing. The links does not open for me.

Can @Flawless1202 you drop graphical representation of the model here?

[Nimrais]

mainly what are we observing and what are we inferring?

[wouterwln]

It looks to me that we need the Transition node for this problem. I'm interpreting (smokes && Bernoulli(0.1)) || Bernoulli(0.001) as "If you smoke, there's a 10% chance on lung disease, otherwise there is 0.1% chance" You'd realize that with

@model function f(cough)
    smokes ~ Bernoulli(0.2)
    lung_disease ~ Transition(smokes, [0.1 0.001; 0.9 0.999])
    cold ~ Bernoulli(0.2)
    ...
end

I've deliberately put 3 dots for the rest of the model, because the expression for cond is a Contingency table between 3 Bernoulli random variables. We can implement this with the TransitionMixture node in (ReactiveBayes/ReactiveMP.jl#407) this PR, but this example warrants from a general Contingency node that takes N nonparametric discrete distributions.

[albertpod]

@Flawless1202, essentially what you’re saying is that you want to sum three Bernoulli random variables, then apply a condition (sum > 2), and observe the outcome. Therefore, your inference problem becomes: given the outcome, what is the posterior distribution over those three Bernoulli random variables?

[Nimrais]

@Flawless1202 Regarding your question about RxInfer implementation of this model

var model = function () {
  var A = flip()
  var B = flip()
  var C = flip()
  var D = A + B + C
  //add the desired assumption:
  condition(D >= 2)
  return {'A': A}
};
var dist = Infer(model)

It can be almost one-to-one translated into RxInfer like this

using RxInfer, Distributions
using ExponentialFamilyProjection
using Manopt

struct Cond end

@node Cond Stochastic [out, in]

@rule Cond(:in, Marginalisation) (q_out::PointMass,) = begin
    return Bernoulli(mean(q_out))
end

function f(x, y, z)
    return x + y + z >= 2
end

@model function model(cond)
    A ~ Bernoulli(0.5)
    B ~ Bernoulli(0.5)
    C ~ Bernoulli(0.5)
    cond .~ Cond(f(A, B, C))
end

delta_meta = @meta begin
    f() -> CVIProjection()
end

result = infer(model = model(), data = (cond = [0.999],), meta = delta_meta)

If you're wondering why we need @meta, you can check how to implement inference around deterministic nodes here. Generally, when you have a deterministic relationship in your model, you need to specify how to run inference around it. CVIProjection() is the most generic approach that will work in almost all scenarios.

The only tricky part here is setting cond = [0.999]. We have only one observation, and to avoid problems with hard constraints, I softened it slightly.