Help with Turing.jl: BetaBinomial ArgumentError: BetaBinomial: the condition n >= zero(n) && (α >= zero(α) && β >= zero(β)) is not satisfied

Specific Domains Probabilistic programming
1

New to Julia, but have had my looks on it for a while now and finally got a bit of extra time during the Summer the play around with it, wuhuu!

My goal is to implement a small program that I already have running in Python which uses Numpyro and Jax to improve its speed.

I am trying to use a BetaBinomial model with Turing.

using Turing
using Turing: Variational

N = [7642688, 7609177, 8992872, 8679915, 8877887, 8669401]
k = [2036195, 745632, 279947, 200865, 106383, 150621]
z = collect(1:length(N))

@model function betabin_model(z, k, N)
    q ~ Beta(2, 3)
    A ~ Beta(2, 3)
    c ~ Beta(1, 9)

    ϕ ~ Exponential(1000)
    θ = ϕ + 2

    for i in eachindex(z)
        μ = clamp(A * (1-q)^(z[i]-1) + c, 0, 1)
        α = μ * θ
        β = (1-μ) * θ
        k[i] ~ BetaBinomial(N[i], α, β)
    end
end

model = betabin_model(z, k, N);
chains = sample(model, NUTS(), 1000);

I get a warning, but it seems to run anyways:

Warning: The current proposal will be rejected due to numerical error(s).
│   isfinite.((θ, r, ℓπ, ℓκ)) = (true, false, false, false)
└ @ AdvancedHMC ~/.julia/packages/AdvancedHMC/bv9VV/src/hamiltonian.jl:47

However, sometimes when I run it, I run into a specific error. I can reproduce the error when I try to use ADVI:

advi = ADVI(10, 1000)
q = vi(model, advi);

which gives the following error:

ERROR: LoadError: ArgumentError: BetaBinomial: the condition n >= zero(n) && (α >= zero(α) && β >= zero(β)) is not satisfied.

This I cannot understand, at least from a mathematical standpoint. All of the elements in N are positive, θ is > 2, and I am even clipping μ to be between 0 and 1; how can either α or β (or n) then be negative?

Does anyone have any explanations? Also, please, feel free to comment on the quality of the code as this is my first julia code and I am here to learn :slight_smile:

1 Like
2

Numerical error warnings during warm-up are normal and expected. If they persist past the warm-up, they generally indicate a problem with the model or its implementation.

Do you see this error when sampling with NUTS?

3

As far as I know, I should be sampling with NUTS?

chains = sample(model, NUTS(), 1000);
4

Ah, I misunderstood you. Yeah, when sampling with ADVI it happens every time, but I have experienced it other times, although now that I think about it, it might have been when using:


using Optim

# Generate a MLE estimate.
mle_estimate = optimize(model, MLE())

# Generate a MAP estimate.
map_estimate = optimize(model, MAP())
5

I sampled your model with NUTS and also estimated the modes with MLE and MAP and did not see these errors. For NUTS, I drew 1000 samples from 16 chains and only found one transition with numerical error, which is quite good. rhat and ess both look good, so there aren’t any obvious issues here.

I’d chalk this up as an issue specific to ADVI, which unfortunately I can’t help with.

6

Okay, I’ve managed to narrow it down to the following.

If I change k to the following:

k = [2042914, 745828, 277760, 205701, 97427, 152673]

and then generate the MAP estimate with a specific set of initial parameters:

map_estimate = optimize(model, MAP(), [0.1, 0.1, 0.01, 100])

(with everything else kept the same) I run into the previously mentioned error:

ERROR: LoadError: ArgumentError: BetaBinomial: the condition n >= zero(n) && (α >= zero(α) && β >= zero(β)) is not satisfied.

I have tried adding @info N[i], α, β inside the model. With this, I find the following lines just before the error is called:

[...] a lot of [ Info: ] above here

[ Info: (8877887, Dual{ForwardDiff.Tag{Turing.Core.var"#f#3"{DynamicPPL.TypedVarInfo{NamedTuple{(:q, :A, :c, :ϕ), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:q, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:q, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:A, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:A, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:c, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:c, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:ϕ, Tuple{}}, Int64}, Vector{Exponential{Float64}}, Vector{AbstractPPL.VarName{:ϕ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{var"#24#25", (:z, :k, :N), (), (), Tuple{Vector{Int64}, Vector{Int64}, Vector{Int64}}, Tuple{}}, DynamicPPL.SampleFromPrior, Turing.OptimizationContext{DynamicPPL.DefaultContext}}, Float64}}(7.453710778999033,-1.1633888898325928,0.29162337763363744,6.945280851663119,7.417474913162984), Dual{ForwardDiff.Tag{Turing.Core.var"#f#3"{DynamicPPL.TypedVarInfo{NamedTuple{(:q, :A, :c, :ϕ), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:q, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:q, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:A, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:A, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:c, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:c, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:ϕ, Tuple{}}, Int64}, Vector{Exponential{Float64}}, Vector{AbstractPPL.VarName{:ϕ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{var"#24#25", (:z, :k, :N), (), (), Tuple{Vector{Int64}, Vector{Int64}, Vector{Int64}}, Tuple{}}, DynamicPPL.SampleFromPrior, Turing.OptimizationContext{DynamicPPL.DefaultContext}}, Float64}}(403.94591260649196,1.1633888898325928,-0.29162337763363744,-6.945280851663119,401.98214847232805))
[ Info: (8669401, Dual{ForwardDiff.Tag{Turing.Core.var"#f#3"{DynamicPPL.TypedVarInfo{NamedTuple{(:q, :A, :c, :ϕ), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:q, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:q, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:A, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:A, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:c, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:c, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:ϕ, Tuple{}}, Int64}, Vector{Exponential{Float64}}, Vector{AbstractPPL.VarName{:ϕ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{var"#24#25", (:z, :k, :N), (), (), Tuple{Vector{Int64}, Vector{Int64}, Vector{Int64}}, Tuple{}}, DynamicPPL.SampleFromPrior, Turing.OptimizationContext{DynamicPPL.DefaultContext}}, Float64}}(7.162863556540884,-0.3614415363041935,0.07248121590660006,6.945280851663119,7.128041630854146), Dual{ForwardDiff.Tag{Turing.Core.var"#f#3"{DynamicPPL.TypedVarInfo{NamedTuple{(:q, :A, :c, :ϕ), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:q, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:q, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:A, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:A, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:c, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:c, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:ϕ, Tuple{}}, Int64}, Vector{Exponential{Float64}}, Vector{AbstractPPL.VarName{:ϕ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{var"#24#25", (:z, :k, :N), (), (), Tuple{Vector{Int64}, Vector{Int64}, Vector{Int64}}, Tuple{}}, DynamicPPL.SampleFromPrior, Turing.OptimizationContext{DynamicPPL.DefaultContext}}, Float64}}(404.2367598289501,0.3614415363041935,-0.07248121590660006,-6.945280851663119,402.2715817546368))
[ Info: (7642688, Dual{ForwardDiff.Tag{Turing.Core.var"#f#3"{DynamicPPL.TypedVarInfo{NamedTuple{(:q, :A, :c, :ϕ), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:q, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:q, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:A, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:A, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:c, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:c, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:ϕ, Tuple{}}, Int64}, Vector{Exponential{Float64}}, Vector{AbstractPPL.VarName{:ϕ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{var"#24#25", (:z, :k, :N), (), (), Tuple{Vector{Int64}, Vector{Int64}, Vector{Int64}}, Tuple{}}, DynamicPPL.SampleFromPrior, Turing.OptimizationContext{DynamicPPL.DefaultContext}}, Float64}}(NaN,NaN,NaN,NaN,NaN), Dual{ForwardDiff.Tag{Turing.Core.var"#f#3"{DynamicPPL.TypedVarInfo{NamedTuple{(:q, :A, :c, :ϕ), Tuple{DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:q, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:q, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:A, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:A, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:c, Tuple{}}, Int64}, Vector{Beta{Float64}}, Vector{AbstractPPL.VarName{:c, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}, DynamicPPL.Metadata{Dict{AbstractPPL.VarName{:ϕ, Tuple{}}, Int64}, Vector{Exponential{Float64}}, Vector{AbstractPPL.VarName{:ϕ, Tuple{}}}, Vector{Float64}, Vector{Set{DynamicPPL.Selector}}}}}, Float64}, DynamicPPL.Model{var"#24#25", (:z, :k, :N), (), (), Tuple{Vector{Int64}, Vector{Int64}, Vector{Int64}}, Tuple{}}, DynamicPPL.SampleFromPrior, Turing.OptimizationContext{DynamicPPL.DefaultContext}}, Float64}}(Inf,NaN,NaN,NaN,NaN))
ERROR: LoadError: ArgumentError: BetaBinomial: the condition n >= zero(n) && (α >= zero(α) && β >= zero(β)) is not satisfied.
Stacktrace:
  [1] macro expansion
    @ ~/.julia/packages/Distributions/fXTVC/src/utils.jl:6 [inlined]
  [2] #BetaBinomial#42
    @ ~/.julia/packages/Distributions/fXTVC/src/univariate/discrete/betabinomial.jl:30 [inlined]
  [3] BetaBinomial
    @ ~/.julia/packages/Distributions/fXTVC/src/univariate/discrete/betabinomial.jl:30 [inlined]
  [4] #24
    @ ~/work/julia_metaDMG/metaDMG/fit.jl:91 [inlined]

[...] continues with long error messages here

I do not know if this error is reproducible, but I can at least recreate it now.

7

I was able to reproduce this error with these values of k. Since there aren’t any obvious issues with your model or implementation, I’d recommend opening an issue on the Turing repo.

8

Okay, thanks a lot, @sethaxen!