have non-root removal be done in src/inference/cudd/compile.jl

[github-actions]

https://github.com/Juice-jl/Dice.jl/blob/d80e01a7dd7019eb8daa543199b6276e7682dbc8/src/autodiff_pr/train.jl#L39

# The bridge between autodiff and cudd
export LogPr, compute_mixed, train!, pr_mixed, support_mixed, with_concrete_ad_flips

mutable struct LogPr <: ADNode
    bool::Dist{Bool}
end
NodeType(::Type{LogPr}) = Leaf()
compute_leaf(::LogPr) = error("LogPr must be expanded")
backward(::LogPr, _, _) = error("LogPr must be expanded")

mutable struct LogPrExpander
    w::WMC
    cache::Dict{ADNode, ADNode}
    function LogPrExpander(w)
        new(w, Dict{ADNode, ADNode}())
    end
end

function expand_logprs(l::LogPrExpander, root::ADNode)::ADNode
    fl(x::LogPr) = expand_logprs(l, logprob(l.w, x.bool))
    fl(x::Var) = x
    fl(x::Constant) = x
    fi(x::Add, call) = Add(call(x.x), call(x.y))
    fi(x::Mul, call) = Mul(call(x.x), call(x.y))
    fi(x::Pow, call) = Pow(call(x.x), call(x.y))
    fi(x::Sin, call) = Sin(call(x.x))
    fi(x::Cos, call) = Cos(call(x.x))
    fi(x::Log, call) = Log(call(x.x))
    fi(x::ADMatrix, call) = ADMatrix(map(call, x.x))
    fi(x::GetIndex, call) = GetIndex(call(x.x), x.i)
    fi(x::Map, call) = Map(x.f, x.f′, call(x.x))
    fi(x::Transpose, call) = Transpose(call(x.x))
    fi(x::NodeLogPr, call) = NodeLogPr(call(x.pr), call(x.hi), call(x.lo))
    foldup(root, fl, fi, ADNode, l.cache)
end

# Within roots' LogPrs there are Dist{Bool} DAGs. Collect minimal roots all DAGs
function bool_roots(roots)
    # TODO: have non-root removal be done in src/inference/cudd/compile.jl
    seen_adnodes = Dict{ADNode, Nothing}()
    seen_bools = Dict{AnyBool, Nothing}()
    non_roots = Set{AnyBool}()
    to_visit = Vector{ADNode}(roots)
    while !isempty(to_visit)
        x = pop!(to_visit)
        foreach(x, seen_adnodes) do y
            if y isa LogPr
                foreach(y.bool, seen_bools) do bool
                    union!(non_roots, children(bool))
                    if bool isa Flip && bool.prob isa ADNode && !haskey(seen_adnodes, bool.prob)
                        push!(to_visit, bool.prob)
                    end
                end
            end
        end
    end
    setdiff(keys(seen_bools), non_roots)
end

function compute_mixed(var_vals::Valuation, root::ADNode)
    compute_mixed(var_vals, [root])[root]
end

function compute_mixed(var_vals::Valuation, roots)
    l = LogPrExpander(WMC(BDDCompiler(bool_roots(roots))))
    expanded_roots = [expand_logprs(l, x) for x in roots]
    vals = compute(var_vals, expanded_roots)
    Dict(root => vals[l.cache[root]] for root in roots)
end

function train!(
    var_vals::Valuation,
    loss::ADNode;
    epochs::Integer,
    learning_rate::Real,
)
    losses = []
    l = LogPrExpander(WMC(BDDCompiler(bool_roots([loss]))))
    loss = expand_logprs(l, loss)
    for _ in 1:epochs
        vals, derivs = differentiate(var_vals, Derivs(loss => 1))

        # update vars
        for (adnode, d) in derivs
            if adnode isa Var
                var_vals[adnode] -= d * learning_rate
            end
        end

        push!(losses, vals[loss])
    end
    push!(losses, compute_mixed(var_vals, loss))
    losses
end

function collect_flips(bools)
    flips = Vector{Flip}()
    foreach_down(bools) do x
        x isa Flip && push!(flips, x)
    end
    flips
end

function with_concrete_ad_flips(f, var_vals, dist)
    flip_to_original_prob = Dict()
    a = ADComputer(var_vals)
    l = LogPrExpander(WMC(BDDCompiler()))
    for x in collect_flips(tobits(dist))
        if x.prob isa ADNode
            flip_to_original_prob[x] = x.prob
            x.prob = compute(a, expand_logprs(l, x.prob))
        end
    end
    res = f()
    for (x, prob) in flip_to_original_prob
        x.prob = prob
    end
    res
end

function pr_mixed(var_vals)
    (args...; kwargs...) -> with_concrete_ad_flips(var_vals, args...) do
        pr(args...; kwargs...)
    end
end

function support_mixed(dist)
    flip_to_original_prob = Dict()
    for x in collect_flips(tobits(dist))
        if x.prob isa ADNode
            flip_to_original_prob[x] = x.prob
            x.prob = 0.5
        end
    end
    res = keys(pr(dist))
    for (x, prob) in flip_to_original_prob
        x.prob = prob
    end
    res
end