Efficient weighted sum over an array of independent Normal distributions

[kainbr]

Hey! I try to implement the TrueSkill model [1] using RxInfer. Based on the overall factor graph (Figure 1 in the paper), there is a deterministic node in the center that aggregates (sums) the individual performances of a team's players into a single Normal distribution, $t_*$.

The corresponding message-passing equations for this node are shown in Table 1.

Essentially, this aggregation requires a weighted sum (or dot product) of independent univariate Normal distributions. Starting with just the unweighted case, my main hurdle is applying a sum function over an array of independent random variables:

@model function model(y)
    local x

    for i in 1:3
        x[i] ~ Normal(mean=1.0, variance=1.0)
    end

    # y := (x[1] + x[2]) + x[3] # This works, but doesn't scale to an arbitrary number of entries in x
    y := sum(x) # This fails: no method matching sum(::Float64, ::Float64, ::Float64)
end

meta = @meta(begin
    sum() -> Linearization()
end)

result = infer(
    model=model(),
    meta=meta,
    data=(y=UnfactorizedData(missing),),
)

result.predictions[:y]

I also experimented with a reduce logic and constraining the covariance matrix of a MvNormalDistribution but was unsuccessful. My current workaround idea is to implement a custom node that takes an array of distributions as input (similar to the interface of the Mixture node).

However, building a custom node feels like a bit of overkill for what seems like a standard operation. Am I missing a built-in feature, or is there a more idiomatic way to handle this in RxInfer?

Thanks in advance!

[1] TrueSkill: A Bayesian Skill Rating System (https://www.microsoft.com/en-us/research/wp-content/uploads/2007/01/NIPS2006_0688.pdf)