Feature: aliases and keyword distribution specification in the model macro

[bvdmitri]

This PR adds aliases feature to model specification (@model macro):

See ReactiveBayes/ReactiveMP.jl#1 and #17

In the first version the following aliases are available:

a || b: alias for OR(a, b) node
a && b: alias for AND(a, b) node
a -> b: alias for IMPLY(a, b) node
¬a or !a: alias for NOT(a) node
a + b + c: alias for (a + b) + c
Normal(μ|m|mean = ..., σ²|τ⁻¹|v|var|variance = ...) alias for NormalMeanVariance(..., ...) node
Normal(μ|m|mean = ..., τ|σ⁻²|w|p|prec|precision = ...) alias for NormalMeanVariance(..., ...) node
MvNormal(μ|m|mean = ..., Σ|V|Λ⁻¹|cov|covariance = ...) alias for MvNormalMeanCovariance(..., ...) node
MvNormal(μ|m|mean = ..., Λ|W|Σ⁻¹|prec|precision = ...) alias for MvNormalMeanPrecision(..., ...) node

Example

@model function mymodel()
    
    
    x1 ~ MvNormal(μ = zeros(2), Σ⁻¹ = diageye(2))
    x2 ~ MvNormal(μ = zeros(2), Λ = diageye(2))
    x3 ~ MvNormal(mean = zeros(2), W = diageye(2))
    x4 ~ MvNormal(μ = zeros(2), prec = diageye(2))
    x5 ~ MvNormal(m = zeros(2), precision = diageye(2))
    
    y1 ~ MvNormal(mean = zeros(2), Σ = diageye(2))
    y2 ~ MvNormal(m = zeros(2), Λ⁻¹ = diageye(2))
    y3 ~ MvNormal(μ = zeros(2), V = diageye(2))
    y4 ~ MvNormal(mean = zeros(2), cov = diageye(2))
    y5 ~ MvNormal(mean = zeros(2), covariance = diageye(2))

    x ~ x1 + x2 + x3 + x4 + x5
    y ~ y1 + y2 + y3 + y4 + y5
    
    d = datavar(Vector{Float64})
    d ~ MvNormal(μ = x + y, covariance = diageye(2))
end

@model function mycoolmodel()
    a ~ Bernoulli(0.5)
    b ~ Bernoulli(0.5)
    c ~ Bernoulli(0.5)
    
    y = datavar(Float64)
    
    o ~ ¬a || b && !c
    o ~ Bernoulli(y)
    
end

TODO:

• add Gamma distributions aliases

Update:

• a * b * c: alias for (a * b) * c
• Gamma(α|a|shape = ..., θ|β⁻¹|scale = ...) alias for GammaShapeScale(..., ...) node.
• Gamma(α|a|shape = ..., β|θ⁻¹|rate = ...) alias for GammaShapeRate(..., ...) node.

[bartvanerp]

Looks great!
Perhaps we could also add γ for the univariate precision parameter, and ∨ and ∧ for and and or (or the other way around)?

[bvdmitri]

Thanks @bartvanerp ! I will add γ.

Initially this PR implemented ∨ and ∧ for or and and respectively. However, it turned out, that Julia does not have any precedence priority for those. In contrast, && and || have the correct precedence (&& exectues first then ||). I decided not to use ∨ and ∧ because it might be confusing for a user and may potentially create wrong models. We could add only if we explicitly state that these do not have precedence and a user must use brackets. But that is not that natural as && and ||.

[bvdmitri]

@wmkouw This feature also enables this

y ~ x1 + x2 + x3 + x4

But only static sum can be unrolled at a parse time, e.g. this is still not possible

y ~ ∑(x) # not possible
# or 
y ~ +(x...) # not possible

[wmkouw]

I am happy with these aliases: I think they really add to the user-friendliness of RMP. But the feature to add multiple variables at once, i.e.,

y ~ x1 + x2 + x3 + x4

does not solve the issue with unnecessary loops being constructed.

Perhaps I just need a custom node that implements a linear combination. Something along the lines of:

y ~ lincomb(A, x1, x2, ...)

which implements y = A'x. I'll work on a PR for RMP.