# MAP Optimization and RAM usage related to autodiff

Hi there probabilistic programming folks - I’ve enjoyed reading the posts here and now have one of my own. I am trying to estimate the MAP of a multivariate linear model with a mixture model component using Turing (will be made clear in the example code). Optimization with LBFGS / ConjugateGradient works (in the sense of getting a reasonable result), but uses a tremendous amount of RAM usage (~5 Gb for the small example below). If I rerun in the same session, RAM usage continues to climb. If I use an optimization method that does not require gradients (e.g,. NelderMead()), the heavy RAM usage isn’t issue, I so presume this is related to autodiff.

Would be grateful for any thoughts here on what is going on. I suspect much of it is due to the line that increments the joint model lob probability due to the mixture model aspect. Running @code_warntype on the model does result in some red (type unstable) text, though I am not entirely sure how to modify the code to reduce the type instability.

``````using Turing
using Distributions
using ReverseDiff
using Memoization
using LinearAlgebra
using StatsFuns
using Optim

function simulate()
N_SAMPLES = 100
N_GENES = 100
N_DONORS = 3
N_INTERVENTIONS = 10

α = .5
G = rand(Bernoulli(.3), N_GENES, N_GENE_MASK)
dists = [MvNormal(zeros(N_GENES), α .* G[:, i]) for i in 1:N_GENE_MASK]

β = zeros(N_INTERVENTIONS, N_GENES)
for i in 1:N_INTERVENTIONS
β[i, :] = rand(dists[z])
end

D = rand(Bernoulli(.2), N_SAMPLES, N_DONORS)
ψ = rand(Normal(0, .3), N_DONORS)
X = rand(Bernoulli(.1), N_SAMPLES, N_INTERVENTIONS)
ϵ = rand(Normal(0, 0.1), N_SAMPLES, N_GENES)
Y = rand(X * β .+ D * ψ .+ ϵ, N_SAMPLES, N_GENES)

return Y, Int8.(D), Int8.(X), Int8.(G)
end

function logpMGaussianMixture(x, dists, w::AbstractVector)
logw = log.(w)
K = length(logw)
N = size(x, 1)
sum(logsumexp(logw[k] + logpdf(dists[k], x) for k in 1:K))
end
@model function marginalized_bipartite_model(
Y,
D,
X,
G,
::Type{T} = Float64) where {T}

N_GENES::Int64 = size(Y, 2)
N_INTERVENTIONS::Int64 = (size(X, 2))
N_DONORS::Int64 = size(D, 2)
N_SAMPLES::Int64 = size(Y, 1)
N_MASKS::Int64 = size(G, 2)

w ~ Dirichlet(N_MASKS, 1.0)
α ~ Normal(-1, 1)
covs = [sqrt(.1) .+ exp(α) .* G[:, z] for z in 1:N_MASKS]
μ = zeros(N_GENES)
dists = [MvNormal(μ, covs[k]) for k in 1:N_MASKS]

β ~ filldist(Normal(0, 1.0), N_INTERVENTIONS, N_GENES)

Turing.@addlogprob! sum([logpMGaussianMixture(view(β, i, :), dists, w) for i in 1:N_INTERVENTIONS])

ψ ~ filldist(Normal(2, 3), N_DONORS)
σ ~ Exponential(0.2)

d = D * ψ
for j in 1:N_GENES
Y[:, j] ~ MvNormal(view(X * β, :, j) .+ d, σ)
end

end

function run_model(counts_mat::Matrix{Float64}, donors_mat::Matrix{Int8}, interventions_mat::Matrix{Int8}, gene_mat::Matrix{Int8})

Turing.emptyrdcache()
Turing.setrdcache(:true)

model = marginalized_bipartite_model(
view(counts_mat, :, 1:100),
view(donors_mat, :, :),
view(interventions_mat, :, :),
view(gene_mat, 1:100, 1:5)
)

map_estimate = optimize(
model,
MAP(),
# LBFGS(;m = 3),
# SimulatedAnnealing(),
Optim.Options(
f_tol = 1e-3,
g_tol = 1e-2,
iterations = 50,
store_trace = false,
show_trace = true,
show_every = 3
)
)

return map_estimate, model
end

sims = simulate()
@time result, model = run_model(sims...)

``````

Thanks very much,
Josh