optim.jl

# Collect all sum nodes.
snodes = filter(n -> isa(n, SumNode), values(spn))

# option 1

# Create an initial values.
q1 = mapreduce(n -> n.logweights[:], vcat, snodes)

# Helper function used by ForwardDiff.
function f1(θ)

    N, D = size(x)
    c = 1
    for i in 1:length(snodes)
        K = length(snodes[i])

        # Extraction of parameters.
        ϕ = θ[c:(c+K-1)]

        # Copy parameters to SPN node.
        snodes[i].logweights[:] = ϕ

        c += length(snodes[i])
    end

    # Return llh.
    return mean(logpdf(spn.root, x) .- logpdf(spn.root, ones(1,D) * NaN))
end

# option 2

# Create an initial values.
q2 = mapreduce(n -> exp.(n.logweights[:]), vcat, snodes)

# Helper function used by ForwardDiff.
function f1(θ)

    N, D = size(x)
    c = 1
    for i in 1:length(snodes)
        K = length(snodes[i])

        # Extraction of parameters.
        ϕ = θ[c:(c+K-1)]

        # Copy parameters to SPN node.
        snodes[i].logweights[:] = log.(projectToPositiveSimplex!(ϕ))

        c += length(snodes[i])
    end

    # Return llh.
    return mean(logpdf(spn.root, x))
end