Bound error when trying to provide initial parameters for optimization in a model with LKJCholesky

[touste]

Minimal working example

using Turing
using LinearAlgebra

@model function random_intercept_slope_LKJ(X, g, y;
    n_groups=maximum(g),
    predictors=size(X, 2)
)
    # Population-level means
    μ ~ MvNormal(zeros(predictors), 5.0)

    # Correlation structure among random effects
    Ω ~ LKJCholesky(predictors, 2.0)   # correlation matrix L

    # Group-level scales
    τ ~ filldist(Exponential(1.0), predictors)

    # Random effects in std-normal space
    γ ~ filldist(Normal(0, 1), predictors, n_groups)

    # Reconstruct group-level coefficients
    Σ_L = Diagonal(τ) * Ω.L
    β = μ .+ Σ_L * γ

    # Observation noise
    σ ~ Exponential(1)

    # Likelihood
    for i in eachindex(y)
        y[i] ~ Normal(X[i, :]' * β[:, g[i]], σ)
    end
end


N = 300
n_groups = 6
predictors = 2

X = hcat(ones(N), randn(N))
g = rand(1:n_groups, N)

# True parameters
true_μ = [1.0, 2.0]

# True correlation matrix
true_R = [1.0 0.6;
    0.6 1.0]
true_L = cholesky(Symmetric(true_R)).L

# True scales
true_τ = [0.7, 0.8]

# Full covariance Cholesky
Σ_L = Diagonal(true_τ) * true_L

# Random group effects
true_γ = randn(predictors, n_groups)

# Group-level coefficients
β = true_μ .+ Σ_L * true_γ

# Noise
true_σ = 0.3

# Generate y
y = similar(X[:, 1])
for i in 1:N
    y[i] = X[i, :]' * β[:, g[i]] + true_σ * randn()
end

model = random_intercept_slope_LKJ(X, g, y)

map = maximum_a_posteriori(model) #OK, returns a solution vector of length 20


true_param_vec = Float64[]
append!(true_param_vec, true_μ)
append!(true_param_vec, [true_L[1, 1], true_L[2, 1], true_L[2, 2]])
append!(true_param_vec, true_τ)
for g in 1:n_groups
    append!(true_param_vec, true_γ[:, g])
end
push!(true_param_vec, true_σ)
# true_param_vec has length 20


map = maximum_a_posteriori(model; initial_params=true_param_vec) # Bounds error

Description

See the example.

initial_params expects a vector of length 21. It looks like the confusion comes from the fact that Ω has 4 components but the map estimates only returns Ω.L, so 3 components. This is also inconsistent with how initial parameters are defined for sampling, where Turing expects a vector of length 20 and not 21 here.

Julia version info

versioninfo()

versioninfo()
Julia Version 1.12.2
Commit ca9b6662be4 (2025-11-20 16:25 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 20 × 13th Gen Intel(R) Core(TM) i9-13900H
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, alderlake)
  GC: Built with stock GC
Threads: 10 default, 1 interactive, 10 GC (on 20 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1
  JULIA_NUM_THREADS = 10

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[penelopeysm]

Hello - thanks for reporting! Yes, this is quite ugly unfortunately.

As you identified the output of the moderesult is generated via

julia> using AbstractPPL; collect(AbstractPPL.varname_and_value_leaves(@varname(x), rand(LKJCholesky(2, 1.0))))
3-element Vector{Tuple{VarName{:x, ComposedFunction{Accessors.IndexLens{Tuple{Int64, Int64}}, Accessors.PropertyLens{:L}}}, Float64}}:
 (x.L[1, 1], 1.0)
 (x.L[2, 1], 0.5057385879036544)
 (x.L[2, 2], 0.8626867801845682)

but the input to initial_params expects the full matrix because

julia> using DynamicPPL; @model f() = x ~ LKJCholesky(2, 1.0); VarInfo(f())[:]
4-element Vector{Float64}:
 1.0
 0.14727480025638529
 0.0
 0.9890956137853619

In the short term I would suggest to just use the full matrix i.e. you will need to include true_L[1,2].

Long term, vectors are just not the correct format to provide values in (it is honestly a bit silly the way you are forced to reconstruct the vector for initial inputs with the chain of append!).

This is also inconsistent with how initial parameters are defined for sampling, where Turing expects a vector of length 20 and not 21 here.

Since v0.41 MCMC sampling no longer accepts vectors for initial_params and the reason for removing that is precisely because it leads to quite meaningless code, as well as ambiguities over which elements need to be provided and in what order. A similar change will be made to optimisation (in the near future) so that you instead pass parameters as a NamedTuple or a Dict, like:

true_params = (; Ω = true_L, ...)
maximum_a_posteriori(model; initial_params=InitFromParams(true_params))

[touste]

Thanks for the detailed answer! Yes having a NamedTuple for providing initial parameters for optimization would be ideal, I'm glad that's planned!