`ArgumentError: Union{} does not have elements` when trying to run a state space model

[sjwild]

I am trying to run a state space model, and I keep encountering the error in the subject line when using ReverseDiff. I found a previous issue raising it, but it was with Julia 1.4. (EDIT: link)

Here is a minimum reproducible example with Julia 1.10.0 and Turing 0.30.0

#Julia 1.10

using Plots, StatsPlots
using Turing, ReverseDiff, Memoization 
using LinearAlgebra


# build data
t = [1:.05:8;]
σ = .3
y = @. rand(sin(t) + Normal(0, σ))

scatter(t, y)

@model function state_space(y, 
    TT,
    ::Type{T}=Float64) where {T}

    # Priors 
    α ~ Normal(y[1], 0.001)
    τ ~ Exponential(1)
    η ~ filldist(Normal(0, 1), TT-1)
    σ ~ Exponential(1)

    # create latent variable
    x = Vector{T}(undef, TT)

    x[1] = α

    for t in 2:TT
        x[t] = x[t-1] + η[t-1] * τ
    end

    # measurement model
    y ~ MvNormal(x, σ * I)

    return x

end

n_iter = 1500
model = state_space(y, length(t))
chns = sample(model, NUTS(n_iter * 2, 0.8; adtype = AutoReverseDiff(true)), n_iter);

And here is the stacktrace

ERROR: ArgumentError: Union{} does not have elements
Stacktrace:
  [1] eltype(::Type{Union{}})
    @ Base ./abstractarray.jl:237
  [2] eltype(vi::DynamicPPL.ThreadSafeVarInfo{DynamicPPL.TypedVarInfo{…}, Vector{…}}, spl::DynamicPPL.Sampler{NUTS{…}})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/abstract_varinfo.jl:366
  [3] get_matching_type(spl::DynamicPPL.Sampler{…}, vi::DynamicPPL.ThreadSafeVarInfo{…}, ::Type{…})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/compiler.jl:722
  [4] matchingvalue(sampler::DynamicPPL.Sampler{…}, vi::DynamicPPL.ThreadSafeVarInfo{…}, value::Type{…})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/compiler.jl:693
  [5] matchingvalue(context::DynamicPPL.SamplingContext{…}, vi::DynamicPPL.ThreadSafeVarInfo{…}, value::Type)
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/compiler.jl:706
  [6] macro expansion
    @ ~/.julia/packages/DynamicPPL/YWihz/src/model.jl:993 [inlined]
  [7] make_evaluate_args_and_kwargs
    @ ~/.julia/packages/DynamicPPL/YWihz/src/model.jl:971 [inlined]
  [8] _evaluate!!(model::DynamicPPL.Model{…}, varinfo::DynamicPPL.ThreadSafeVarInfo{…}, context::DynamicPPL.SamplingContext{…})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/model.jl:962
  [9] evaluate_threadsafe!!
    @ ~/.julia/packages/DynamicPPL/YWihz/src/model.jl:952 [inlined]
 [10] evaluate!!
    @ ~/.julia/packages/DynamicPPL/YWihz/src/model.jl:887 [inlined]
 [11] logdensity(f::LogDensityFunction{…}, θ::ReverseDiff.TrackedArray{…})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/logdensityfunction.jl:94
 [12] Fix1
    @ Base ./operators.jl:1118 [inlined]
 [13] ReverseDiff.GradientTape(f::Base.Fix1{…}, input::Vector{…}, cfg::ReverseDiff.GradientConfig{…})
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/api/tape.jl:199
 [14] ReverseDiff.GradientTape(f::Function, input::Vector{Float64})
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/api/tape.jl:198
 [15] _compiledtape
    @ LogDensityProblemsADReverseDiffExt ~/.julia/packages/LogDensityProblemsAD/OQ0BL/ext/LogDensityProblemsADReverseDiffExt.jl:56 [inlined]
 [16] #ADgradient#1
    @ LogDensityProblemsADReverseDiffExt ~/.julia/packages/LogDensityProblemsAD/OQ0BL/ext/LogDensityProblemsADReverseDiffExt.jl:50 [inlined]
 [17] ADgradient(ad::AutoReverseDiff, ℓ::LogDensityFunction{…})
    @ Turing.Essential ~/.julia/packages/Turing/tdsVz/src/essential/ad.jl:44
 [18] ADgradient(ad::AutoReverseDiff, ℓ::LogDensityFunction)
    @ Turing.Essential ~/.julia/packages/Turing/tdsVz/src/essential/ad.jl:20 [inlined]
 [19] initialstep(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, spl::DynamicPPL.Sampler{…}, vi::DynamicPPL.TypedVarInfo{…}; init_params::Nothing, nadapts::Int64, kwargs::@Kwargs{…})
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/hmc.jl:148
 [20] step(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, spl::DynamicPPL.Sampler{…}; initial_params::Nothing, kwargs::@Kwargs{…})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/YWihz/src/sampler.jl:116
 [21] step
    @ ~/.julia/packages/DynamicPPL/YWihz/src/sampler.jl:99 [inlined]
 [22] macro expansion
    @ ~/.julia/packages/AbstractMCMC/Es490/src/sample.jl:127 [inlined]
 [23] macro expansion
    @ ~/.julia/packages/ProgressLogging/6KXlp/src/ProgressLogging.jl:328 [inlined]
 [24] macro expansion
    @ ~/.julia/packages/AbstractMCMC/Es490/src/logging.jl:9 [inlined]
 [25] mcmcsample(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, sampler::DynamicPPL.Sampler{…}, N::Int64; progress::Bool, progressname::String, callback::Nothing, discard_initial::Int64, thinning::Int64, chain_type::Type, initial_state::Nothing, kwargs::@Kwargs{…})
    @ AbstractMCMC ~/.julia/packages/AbstractMCMC/Es490/src/sample.jl:117
 [26] sample(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, sampler::DynamicPPL.Sampler{…}, N::Int64; chain_type::Type, resume_from::Nothing, initial_state::Nothing, progress::Bool, nadapts::Int64, discard_adapt::Bool, discard_initial::Int64, kwargs::@Kwargs{})
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/hmc.jl:117
 [27] sample
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/hmc.jl:86 [inlined]
 [28] #sample#2
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:190 [inlined]
 [29] sample
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:183 [inlined]
 [30] #sample#1
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:180 [inlined]
 [31] sample(model::DynamicPPL.Model{…}, alg::NUTS{…}, N::Int64)
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:174
 [32] top-level scope
    @ REPL[11]:1
Some type information was truncated. Use `show(err)` to see complete types.

[devmotion]

As the stacktrace states, the problem is that in Julia 1.10 the call to return_type in https://github.com/TuringLang/DynamicPPL.jl/blob/11a75fffe3737a5ce06407444a81d588c3b4e188/src/abstract_varinfo.jl#L366 returns a Union{} but eltype(Union{}) throws an error.

A few comments:

• It might be better to use Base.promote_op (see https://docs.julialang.org/en/v1/manual/methods/#Output-type-computation)
• The Union{} indicates that getindex(vi, spl) throws an error
• It might be good to catch the Union{} return value nevertheless and throw a more descriptive error message

Regarding the second point, adding print statements such as @show vi[spl] right before the failing code reveals the underlying problem:

ERROR: MethodError: vcat(::ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}, ::ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}, ::ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}, ::ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{Float64}, Vector{Float64}}) is ambiguous.

Candidates:
  vcat(var"376"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, var"377"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(X1::Union{Number, AbstractVecOrMat{<:Number}}, X::Union{Number, AbstractVecOrMat{<:Number}}...)
    @ SparseArrays ~/.asdf/installs/julia/1.10.0/share/julia/stdlib/v1.10/SparseArrays/src/sparsevector.jl:1235
  vcat(var"376"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, var"377"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"376"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, var"377"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"339"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"348"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, var"349"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"339"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"339"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"348"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, var"349"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"348"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, var"349"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"372"::AbstractVector, var"373"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"372"::AbstractVector, var"373"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"372"::AbstractVector, var"373"::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"337"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"344"::AbstractVector, var"345"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVector...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"337"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"337"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"344"::AbstractVector, var"345"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::AbstractVecOrMat...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52
  vcat(var"344"::AbstractVector, var"345"::AbstractVector, x::ReverseDiff.TrackedArray{V, D, 1} where {V, D}, xs::Union{Number, AbstractVector}...)
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/derivatives/arrays.jl:52

Possible fix, define
  vcat(::ReverseDiff.TrackedArray{…} where {…}, ::ReverseDiff.TrackedArray{…} where {…}, ::ReverseDiff.TrackedArray{…} where {…}, ::Vararg{…})

Stacktrace:
  [1] getindex(vi::TypedVarInfo{@NamedTuple{…}, ReverseDiff.TrackedReal{…}}, spl::Sampler{NUTS{…}})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/varinfo.jl:1447
  [2] macro expansion
    @ ./show.jl:1181 [inlined]
  [3] eltype(vi::TypedVarInfo{@NamedTuple{…}, ReverseDiff.TrackedReal{…}}, spl::Sampler{NUTS{…}})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/abstract_varinfo.jl:368
  [4] get_matching_type(spl::Sampler{NUTS{…}}, vi::TypedVarInfo{@NamedTuple{…}, ReverseDiff.TrackedReal{…}}, ::Type{Float64})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/compiler.jl:722
  [5] matchingvalue(sampler::Sampler{NUTS{…}}, vi::TypedVarInfo{@NamedTuple{…}, ReverseDiff.TrackedReal{…}}, value::Type{Float64})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/compiler.jl:693
  [6] matchingvalue(context::SamplingContext{Sampler{…}, DefaultContext, Random.TaskLocalRNG}, vi::TypedVarInfo{@NamedTuple{…}, ReverseDiff.TrackedReal{…}}, value::Type)
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/compiler.jl:706
  [7] macro expansion
    @ ~/.julia/dev/DynamicPPL/src/model.jl:993 [inlined]
  [8] make_evaluate_args_and_kwargs
    @ ~/.julia/dev/DynamicPPL/src/model.jl:971 [inlined]
  [9] _evaluate!!(model::Model{…}, varinfo::TypedVarInfo{…}, context::SamplingContext{…})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/model.jl:962
 [10] evaluate_threadunsafe!!
    @ ~/.julia/dev/DynamicPPL/src/model.jl:936 [inlined]
 [11] evaluate!!
    @ ~/.julia/dev/DynamicPPL/src/model.jl:889 [inlined]
 [12] logdensity(f::LogDensityFunction{TypedVarInfo{…}, Model{…}, SamplingContext{…}}, θ::ReverseDiff.TrackedArray{Float64, Float64, 1, Vector{…}, Vector{…}})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/logdensityfunction.jl:94
 [13] Fix1
    @ Base ./operators.jl:1118 [inlined]
 [14] ReverseDiff.GradientTape(f::Base.Fix1{…}, input::Vector{…}, cfg::ReverseDiff.GradientConfig{…})
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/api/tape.jl:199
 [15] ReverseDiff.GradientTape(f::Function, input::Vector{Float64})
    @ ReverseDiff ~/.julia/packages/ReverseDiff/UJhiD/src/api/tape.jl:198
 [16] _compiledtape
    @ LogDensityProblemsADReverseDiffExt ~/.julia/packages/LogDensityProblemsAD/OQ0BL/ext/LogDensityProblemsADReverseDiffExt.jl:56 [inlined]
 [17] #ADgradient#1
    @ LogDensityProblemsADReverseDiffExt ~/.julia/packages/LogDensityProblemsAD/OQ0BL/ext/LogDensityProblemsADReverseDiffExt.jl:50 [inlined]
 [18] ADgradient(ad::AutoReverseDiff, ℓ::LogDensityFunction{TypedVarInfo{…}, Model{…}, SamplingContext{…}})
    @ Turing.Essential ~/.julia/packages/Turing/tdsVz/src/essential/ad.jl:44
 [19] ADgradient(ad::AutoReverseDiff, ℓ::LogDensityFunction{TypedVarInfo{…}, Model{…}, SamplingContext{…}})
    @ Turing.Essential ~/.julia/packages/Turing/tdsVz/src/essential/ad.jl:20 [inlined]
 [20] initialstep(rng::Random.TaskLocalRNG, model::Model{…}, spl::Sampler{…}, vi::TypedVarInfo{…}; init_params::Nothing, nadapts::Int64, kwargs::@Kwargs{…})
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/hmc.jl:148
 [21] step(rng::Random.TaskLocalRNG, model::Model{…}, spl::Sampler{…}; initial_params::Nothing, kwargs::@Kwargs{…})
    @ DynamicPPL ~/.julia/dev/DynamicPPL/src/sampler.jl:116
 [22] step
    @ ~/.julia/dev/DynamicPPL/src/sampler.jl:99 [inlined]
 [23] macro expansion
    @ ~/.julia/packages/AbstractMCMC/Es490/src/sample.jl:127 [inlined]
 [24] macro expansion
    @ ~/.julia/packages/ProgressLogging/6KXlp/src/ProgressLogging.jl:328 [inlined]
 [25] macro expansion
    @ ~/.julia/packages/AbstractMCMC/Es490/src/logging.jl:9 [inlined]
 [26] mcmcsample(rng::Random.TaskLocalRNG, model::Model{…}, sampler::Sampler{…}, N::Int64; progress::Bool, progressname::String, callback::Nothing, discard_initial::Int64, thinning::Int64, chain_type::Type, initial_state::Nothing, kwargs::@Kwargs{…})
    @ AbstractMCMC ~/.julia/packages/AbstractMCMC/Es490/src/sample.jl:117
 [27] sample(rng::Random.TaskLocalRNG, model::Model{…}, sampler::Sampler{…}, N::Int64; chain_type::Type, resume_from::Nothing, initial_state::Nothing, progress::Bool, nadapts::Int64, discard_adapt::Bool, discard_initial::Int64, kwargs::@Kwargs{})
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/hmc.jl:117
 [28] sample
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/hmc.jl:86 [inlined]
 [29] #sample#2
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:190 [inlined]
 [30] sample
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:183 [inlined]
 [31] #sample#1
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:180 [inlined]
 [32] sample(model::Model{…}, alg::NUTS{…}, N::Int64)
    @ Turing.Inference ~/.julia/packages/Turing/tdsVz/src/mcmc/Inference.jl:174
 [33] top-level scope
    @ REPL[18]:1
Some type information was truncated. Use `show(err)` to see complete types.

[sjwild]

Thanks for the quick response! I'll have a look at the resources you posted.

[ElOceanografo]

+1 on this issue, I just ran into the same thing with my own state space model.

[devmotion]

The problem should be fixed by TuringLang/DynamicPPL.jl#568 (but tests currently fail due to an issue with LinearAlgebra on Julia 1.10 and a seemingly unrelated problem with Turing 0.30.2).

[devmotion]

Fixed by TuringLang/DynamicPPL.jl#568 which will be available in the next DynamicPPL release: JuliaRegistries/General#99754