Support for Multivariate distributions is not implemented

[Nimrais]

Right now, if someone will try to run an EM like inference on an edge with multivariate incoming messages in RxInfer he will obtain an error like this

MethodError: no method matching support(::MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}})
Closest candidates are:
  support(!Matched::Type{NegativeBinomial})
   @ ExponentialFamily [~/.julia/packages/ExponentialFamily/QIygk/src/distributions/negative_binomial.jl:10](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/.julia/packages/ExponentialFamily/QIygk/src/distributions/negative_binomial.jl:10)
  support(!Matched::Type{NormalGamma})
   @ ExponentialFamily [~/.julia/packages/ExponentialFamily/QIygk/src/distributions/normal_gamma.jl:102](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/.julia/packages/ExponentialFamily/QIygk/src/distributions/normal_gamma.jl:102)
  support(!Matched::ContinuousMultivariateLogPdf)
   @ BayesBase [~/.julia/packages/BayesBase/ZObVB/src/densities/function.jl:191](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/.julia/packages/BayesBase/ZObVB/src/densities/function.jl:191)
  ...
Stacktrace:
  [1] support(product::ProductOf{MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}}, LinearizedProductOf{ContinuousMultivariateLogPdf{UnspecifiedDomain}}})
    @ BayesBase [~/.julia/packages/BayesBase/ZObVB/src/prod.jl:182](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/.julia/packages/BayesBase/ZObVB/src/prod.jl:182)
  [2] logpdf(product::ProductOf{MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}}, LinearizedProductOf{ContinuousMultivariateLogPdf{UnspecifiedDomain}}}, x::Vector{Float64})
    @ BayesBase [~/.julia/packages/BayesBase/ZObVB/src/prod.jl:188](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/.julia/packages/BayesBase/ZObVB/src/prod.jl:188)
  [3] (::var"#158#159"{ProductOf{MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}}, LinearizedProductOf{ContinuousMultivariateLogPdf{UnspecifiedDomain}}}})(x::Vector{Float64})
    @ Main [~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:30](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:30)
  [4] myADAMoptimizer(func::var"#158#159"{ProductOf{MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}}, LinearizedProductOf{ContinuousMultivariateLogPdf{UnspecifiedDomain}}}}, init_value::Vector{Float64}, η::Float64; β1::Float64, β2::Float64, ϵ::Float64, niter::Int64)
    @ Main [~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:9](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:9)
  [5] myADAMoptimizer(func::Function, init_value::Vector{Float64}, η::Float64)
    @ Main [~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:1](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:1)
  [6] default_point_mass_form_constraint_optimizer(::Type{Multivariate}, ::Type{Continuous}, constraint::PointMassFormConstraint{typeof(RxInfer.default_point_mass_form_constraint_optimizer), var"#151#152", typeof(RxInfer.default_point_mass_form_constraint_boundaries)}, distribution::ProductOf{MvNormalMeanCovariance{Float64, Vector{Float64}, Matrix{Float64}}, LinearizedProductOf{ContinuousMultivariateLogPdf{UnspecifiedDomain}}})
    @ Main [~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:32](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/GaussianProcessNode/newconfig_gpnode.ipynb:32)
...
    @ RxInfer [~/PhD/RxInfer.jl/src/inference/batch.jl:300](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/RxInfer.jl/src/inference/batch.jl:300)
 [71] batch_inference
    @ RxInfer [~/PhD/RxInfer.jl/src/inference/batch.jl:94](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/RxInfer.jl/src/inference/batch.jl:94) [inlined]
 [72] #infer#230
    @ RxInfer [~/PhD/RxInfer.jl/src/inference/inference.jl:306](https://file+.vscode-resource.vscode-cdn.net/Users/nguyenhuuminhhoang/PhD/GaussianProcessNode/~/PhD/RxInfer.jl/src/inference/inference.jl:306) [inlined]

[Nimrais]

Before we had smt like UndefinedSupport if I am not wrong.

[bvdmitri]

Good catch, it should really use insupport(product, x) instead of x ∈ support(product). The reason for this change was due to the fact its not always possible to create a support object (legacy from Distribuitions.jl, where they don't support infinite discrete ranges). So whenever possible, we should use insupport(distribution, x) instead. insupport should be properly defined for all members in ExponentialFamily.jl.

we probably overlooked this place when the change was introduced

[bvdmitri]

Fixed in #14