Inference with the SampleListFormConstraint

[ThijsvdLaar]

Hi, I'm trying to do inference in a continuous multivariate model. I want to estimate a parameter belief from a Gaussian prior and log-pdfs for the likelihood. I want to approximate the posterior by a SampleList. However, I'm getting an error in the approximation that I don't know how to resolve. A minimal example that reproduces the error (with Julia 1.10.4 and RxInfer 3.5.0):

using RxInfer

struct Observation end

@node Observation Stochastic [ out, x ]

@rule Observation(:x, Marginalisation) (q_out::PointMass,) = begin
    y = mean(q_out)

    log_mu(x) = -0.5*(y - x)'*(y - x)  # Some function
    
    return ContinuousMultivariateLogPdf(UnspecifiedDomain(), log_mu)
end

@model function mwe(y)
    x ~ MvNormalMeanCovariance(zeros(2), diageye(2))  # Parameter prior
    for i in eachindex(y)
        y[i] ~ Observation(x)
    end
end

constraints = @constraints begin
    q(x) :: SampleListFormConstraint(20)
end

# Generate some data
Y_hat = rand(MvNormalMeanPrecision(zeros(2), diageye(2)), 20)
y_hat = [y_i for y_i in eachcol(Y_hat)]

result = infer(
    model       = mwe(), 
    data        = (y = y_hat,),
    constraints = constraints
)

gives

MethodError: no method matching __approximate(::SampleListFormConstraint{20, Random._GLOBAL_RNG, AutoProposal, BayesBase.BootstrapImportanceSampling}, ::MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}}, ::LinearizedProductOf{ContinuousMultivariateLogPdf{UnspecifiedDomain}})

Closest candidates are:
  __approximate(!Matched::SampleListFormConstraint{N, R, S, M}, ::Any, ::Any) where {N, R, S<:RightProposal, M}
   @ RxInfer C:\Users\tvdlaar\.julia\packages\RxInfer\iG4wU\src\constraints\form\form_sample_list.jl:44
  __approximate(::SampleListFormConstraint{N, R, S, M}, ::Any, !Matched::BayesBase.AbstractContinuousGenericLogPdf) where {N, R, S<:AutoProposal, M}
   @ RxInfer C:\Users\tvdlaar\.julia\packages\RxInfer\iG4wU\src\constraints\form\form_sample_list.jl:56
  __approximate(::SampleListFormConstraint{N, R, S, M}, !Matched::BayesBase.AbstractContinuousGenericLogPdf, ::Any) where {N, R, S<:AutoProposal, M}
   @ RxInfer C:\Users\tvdlaar\.julia\packages\RxInfer\iG4wU\src\constraints\form\form_sample_list.jl:52
  ...

[wouterwln]

An implicit optimization of RxInfer seems to be causing a bug here. What happens is the following: RxInfer is trying to multiply all incoming messages to x before approximating with a sample list. The problem is that RxInfer first tries to multiply all ContinuousMultivariateLogPdf's (storing them in a LinearizedProductOf) and tries to multiply this result with a MvNormalMeanCovariance. This is a problem because according to RxInfer, a LinearizedProductOf is not an AbstractContinuousGenericLogPdf, so we do not know which distribution to use as a reference distribution. Let's first propose to RxInfer to use the MvNormalMeanCovariance as it's reference distribution:

constraints = @constraints begin
   q(x) :: SampleListFormConstraint(20, LeftProposal())
end

Now if you rerun you'll still run into an error, but this is in the actual sampling, so we're further down the line. The problem is that the domain of ContinuousMultivariateLogPdf is not known, so it defaults to Any. We can fix this by specifying the domain in the rule as $\mathbb{R}^n$:

@rule Observation(:x, Marginalisation) (q_out::PointMass,) = begin
           y = mean(q_out)

           log_mu(x) = -0.5*(y - x)'*(y - x)  # Some function

           return ContinuousMultivariateLogPdf(RxInfer.BayesBase.DomainSets.RealNumbers() ^ length(y), log_mu)
end

With this rule, inference runs for me. Still we should fix the bug where LinearizedProductOf is not seen as a distribution. Thanks for the catch ;)

[ThijsvdLaar]

Brilliant, that did the trick. Thanks @wouterwln !