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| function coreVIdiag(logp::Function, μ₀::AbstractArray{T, 1}, Σ₀diag::AbstractArray{T, 1}; gradlogp = gradlogp, seed = seed, S = S, test_every = test_every, optimiser = optimiser, iterations = iterations, numerical_verification = numerical_verification, Stest = Stest, show_every = show_every) where T | ||
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| D = length(μ₀) | ||
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| #---------------------------------------------------- | ||
| # generate latent variables | ||
| #---------------------------------------------------- | ||
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| Ztrain = generatelatentZ(S = S, D = D, seed = seed) | ||
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| #---------------------------------------------------- | ||
| # Auxiliar function for handling parameters | ||
| #---------------------------------------------------- | ||
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| function unpack(param) | ||
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| @assert(length(param) == D+D) | ||
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| local μ = param[1:D] | ||
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| local Cdiag = reshape(param[D+1:D+D], D) | ||
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| return μ, Cdiag | ||
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| end | ||
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| #---------------------------------------------------- | ||
| # Objective and gradient functions for Optim.optimize | ||
| #---------------------------------------------------- | ||
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| function minauxiliary(param) | ||
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| local μ, Cdiag = unpack(param) | ||
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| local ℓ = elbo(μ, Cdiag, Ztrain) | ||
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| update!(trackELBO; newelbo = ℓ, μ = μ, C = Cdiag) | ||
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| return -1.0 * ℓ # Optim.optimise is minimising | ||
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| end | ||
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| function minauxiliary_grad(param) | ||
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| local μ, Cdiag = unpack(param) | ||
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| return -1.0 * elbo_grad(μ, Cdiag, Ztrain) # Optim.optimise is minimising | ||
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| end | ||
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| #---------------------------------------------------- | ||
| # Functions for covariance and covariance root | ||
| #---------------------------------------------------- | ||
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| function getcov(Cdiag) | ||
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| Diagonal(Cdiag.^2) | ||
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| end | ||
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| function getcovroot(Cdiag) | ||
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| return Cdiag | ||
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| end | ||
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| #---------------------------------------------------- | ||
| # Approximate evidence lower bound and its gradient | ||
| #---------------------------------------------------- | ||
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| function elbo(μ, Cdiag, Z) | ||
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| local aux = z -> logp(μ .+ Cdiag.*z) | ||
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| Transducers.foldxt(+, Map(aux), Z) / length(Z) + GaussianVariationalInference.entropy(Cdiag) | ||
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| end | ||
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| function partial_elbo_grad(μ, Cdiag, z) | ||
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| local g = gradlogp(μ .+ Cdiag.*z) | ||
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| [g; vec(g.*z)] | ||
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| end | ||
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| function elbo_grad(μ, Cdiag, Z) | ||
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| local aux = z -> partial_elbo_grad(μ, Cdiag, z) | ||
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| local gradμCdiag = Transducers.foldxt(+, Map(aux), Z) / length(Z) | ||
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| # entropy contribution to covariance | ||
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| gradμCdiag[D+1:end] .+= vec(1.0 ./ Cdiag) | ||
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| return gradμCdiag | ||
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| end | ||
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| # Package Optim requires that function for gradient has following signature | ||
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| gradhelper(storage, param) = copyto!(storage, minauxiliary_grad(param)) | ||
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| #---------------------------------------------------- | ||
| # Numerically verify gradient | ||
| #---------------------------------------------------- | ||
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| numerical_verification ? verifygradient(μ₀, Σ₀diag, elbo, minauxiliary_grad, unpack, Ztrain) : nothing | ||
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| #---------------------------------------------------- | ||
| # Define callback function called at each iteration | ||
| #---------------------------------------------------- | ||
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| # We want to keep track of the best variational | ||
| # parameters encountered during the optimisation of | ||
| # the elbo. Unfortunately, the otherwise superb | ||
| # package Optim.jl does not provide a consistent way | ||
| # accross different optimisers to do this. | ||
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| trackELBO = RecordELBOProgress(; μ = zeros(D), C = zeros(D), | ||
| Stest = Stest, | ||
| show_every = show_every, | ||
| test_every = test_every, | ||
| elbo = elbo, seed = seed) | ||
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| #---------------------------------------------------- | ||
| # Call optimiser to minimise *negative* elbo | ||
| #---------------------------------------------------- | ||
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| options = Optim.Options(extended_trace = false, store_trace = false, show_every = 1, show_trace = false, iterations = iterations, g_tol = 1e-6, callback = trackELBO) | ||
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| result = Optim.optimize(minauxiliary, gradhelper, [μ₀; vec(sqrt.(Σ₀diag))], optimiser, options) | ||
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| μopt, Copt = unpack(result.minimizer) | ||
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| #---------------------------------------------------- | ||
| # Return results | ||
| #---------------------------------------------------- | ||
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| Σopt = getcov(Copt) | ||
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| return MvNormal(μopt, Σopt), elbo(μopt, Copt, Ztrain), Copt | ||
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| end |
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