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AD fails for MixtureModel #722

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cpfiffer opened this issue Mar 20, 2019 · 14 comments
Closed

AD fails for MixtureModel #722

cpfiffer opened this issue Mar 20, 2019 · 14 comments
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@KDr2

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@cpfiffer
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AD fails through the MixtureModels function. This is related to #674, should I move this over there?

MWE:

using Turing

@model MarginalizedGMM(x, K) = begin
    N = length(x)

    # Draw the paramters
    μ = Vector(undef, K)
    τ = Vector(undef, K)
    for i in 1:K
        μ[i] ~ Normal()
        τ[i] ~ Gamma()
    end

    # Set the Dirichlet prior.
    α = 1.0
    w ~ Dirichlet(K, α)

    # Calculate weighted Normals.
    for i in 1:N
      x[i] ~ MixtureModel(Normal, [(μ[i], τ[i]) for i = 1:K], w)
    end
end

val = rand(10)
chn = sample(MarginalizedGMM(val, 3), NUTS(1000, 0.65))

Error:

ERROR: LoadError: MethodError: no method matching MixtureModel(::Type{Normal}, ::Array{Tuple{ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#413#61")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9},ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#413#61")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Float64,9}},1}, ::Array{ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#413#61")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9},1})
Closest candidates are:
  MixtureModel(::Type{C<:Distribution}, ::AbstractArray) where C<:Distribution at /home/cameron/.julia/packages/Distributions/WHjOk/src/mixtures/mixturemodel.jl:122
  MixtureModel(::Type{C<:Distribution}, ::AbstractArray, ::Array{Float64,1}) where C<:Distribution at /home/cameron/.julia/packages/Distributions/WHjOk/src/mixtures/mixturemodel.jl:139
Stacktrace:
 [1] macro expansion at /home/cameron/.julia/dev/Turing/src/core/compiler.jl:44 [inlined]
 [2] macro expansion at /home/cameron/code/julia/misc.jl:20 [inlined]
 [3] (::getfield(Main, Symbol("###inner_function#413#61")){Int64})(::Turing.Core.VarReplay.VarInfo, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}, ::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#413#61")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}) at /home/cameron/.julia/dev/Turing/src/core/compiler.jl:388
 [4] #call#3 at /home/cameron/.julia/dev/Turing/src/Turing.jl:62 [inlined]
 [5] Model at /home/cameron/.julia/dev/Turing/src/Turing.jl:62 [inlined]
 [6] macro expansion at /home/cameron/.julia/dev/Turing/src/core/VarReplay.jl:112 [inlined]
 [7] runmodel!(::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#413#61")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::Turing.Core.VarReplay.VarInfo, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}) at /home/cameron/.julia/dev/Turing/src/core/VarReplay.jl:107
@xukai92
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xukai92 commented Mar 20, 2019

Which Distributions.jl version is the error from? We used to host a customised version of GMM which supports AD but we removed it in some time. However, this PR JuliaStats/Distributions.jl#615 is recently merged so I'm not sure if it's not testing with the newest Distributions or that PR doesn't solve the problem.

@yebai
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yebai commented Mar 20, 2019

Related: #266

@cpfiffer
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This fails on Distributions v0.17.0. I also ran it on the master branch, and now I've got this error:

ERROR: LoadError: TypeError: in typeassert, expected Float64, got ForwardDiff.Dual{Nothing,Float64,9}
Stacktrace:
 [1] setindex!(::Array{Float64,1}, ::ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#369#29")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Float64,9}, ::Int64) at ./array.jl:767
 [2] _mixlogpdf1(::MixtureModel{Univariate,Continuous,Normal,ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#369#29")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9}}, ::Float64) at /home/cameron/.julia/packages/Distributions/fMt8c/src/mixtures/mixturemodel.jl:369
 [3] observe at /home/cameron/.julia/packages/Distributions/fMt8c/src/mixtures/mixturemodel.jl:433 [inlined]
 [4] observe at /home/cameron/.julia/dev/Turing/src/inference/Inference.jl:179 [inlined]
 [5] observe(::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}, ::MixtureModel{Univariate,Continuous,Normal,ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#369#29")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9}}, ::Float64, ::Turing.Core.VarReplay.VarInfo) at /home/cameron/.julia/dev/Turing/src/inference/hmc.jl:311

@ritesh99rakesh ritesh99rakesh mentioned this issue Mar 24, 2019
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@yebai
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yebai commented Mar 27, 2019 •
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Which Distributions.jl version is the error from? We used to host a customised version of GMM which supports AD but we removed it in some time. However, this PR JuliaStats/Distributions.jl#615 is recently merged so I'm not sure if it's not testing with the newest Distributions or that PR doesn't solve the problem.

@xukai92
There seem to be some leftover issues with JuliaStats/Distributions.jl#615. The same model still doesn't work even after changing MixtureModel to UnivariateGMM.

using Turing

@model MarginalizedGMM(x, K) = begin
    N = length(x)

    # Draw the paramters
    μ = Vector{Real}(undef, K)
    τ = Vector{Real}(undef, K)
    for i in 1:K
        μ[i] ~ Normal()
        τ[i] ~ Gamma()
    end

    # Set the Dirichlet prior.
    α = 1.0
    w ~ Dirichlet(K, α)

    # Calculate weighted Normals.
    for i in 1:N
      x[i] ~ Distributions.UnivariateGMM(μ,τ, Categorical(w))
    end
end

val = rand(10)
chn = sample(MarginalizedGMM(val, 3), NUTS(1000, 0.65))

Output:

julia> chn = sample(MarginalizedGMM(val, 3), NUTS(1000, 0.65))
[ Info: [Turing] looking for good initial eps...
ERROR: TypeError: in typeassert, expected Float64, got ForwardDiff.Dual{Nothing,Float64,9}
Stacktrace:
 [1] setindex!(::Array{Float64,1}, ::ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Float64,9}, ::Int64) at ./array.jl:767
 [2] _mixlogpdf1(::UnivariateGMM{Array{Real,1},Array{Real,1}}, ::Float64) at /Users/hg344/.julia/packages/Distributions/fMt8c/src/mixtures/mixturemodel.jl:369
 [3] logpdf at /Users/hg344/.julia/packages/Distributions/fMt8c/src/mixtures/mixturemodel.jl:433 [inlined]
 [4] observe at /Users/hg344/.julia/dev/Turing/src/inference/Inference.jl:192 [inlined]
 [5] observe at /Users/hg344/.julia/dev/Turing/src/inference/Inference.jl:180 [inlined]
 [6] observe at /Users/hg344/.julia/dev/Turing/src/inference/hmc.jl:308 [inlined]
 [7] macro expansion at /Users/hg344/.julia/dev/Turing/src/core/compiler.jl:52 [inlined]
 [8] macro expansion at ./REPL[39]:18 [inlined]
 [9] (::getfield(Main, Symbol("###inner_function#457#33")){Int64})(::Turing.Core.VarReplay.VarInfo, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}, ::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}) at /Users/hg344/.julia/dev/Turing/src/core/compiler.jl:388
 [10] #call#3 at /Users/hg344/.julia/dev/Turing/src/Turing.jl:62 [inlined]
 [11] Model at /Users/hg344/.julia/dev/Turing/src/Turing.jl:62 [inlined]
 [12] macro expansion at /Users/hg344/.julia/dev/Turing/src/core/VarReplay.jl:110 [inlined]
 [13] runmodel!(::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::Turing.Core.VarReplay.VarInfo, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}) at /Users/hg344/.julia/dev/Turing/src/core/VarReplay.jl:105
 [14] f at /Users/hg344/.julia/dev/Turing/src/core/ad.jl:109 [inlined]
 [15] vector_mode_dual_eval(::getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}}, ::Array{Real,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9,Array{ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9},1}}) at /Users/hg344/.julia/packages/ForwardDiff/N0wMF/src/apiutils.jl:37
 [16] vector_mode_gradient!(::Array{Real,1}, ::getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}}, ::Array{Real,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9,Array{ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9},1}}) at /Users/hg344/.julia/packages/ForwardDiff/N0wMF/src/gradient.jl:103
 [17] gradient! at /Users/hg344/.julia/packages/ForwardDiff/N0wMF/src/gradient.jl:35 [inlined]
 [18] gradient!(::Array{Real,1}, ::getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}}, ::Array{Real,1}, ::ForwardDiff.GradientConfig{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9,Array{ForwardDiff.Dual{ForwardDiff.Tag{getfield(Turing.Core, Symbol("#f#26")){Turing.Core.VarReplay.VarInfo,Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}},Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}},Real},Real,9},1}}) at /Users/hg344/.julia/packages/ForwardDiff/N0wMF/src/gradient.jl:33
 [19] gradient_logp_forward(::Array{Real,1}, ::Turing.Core.VarReplay.VarInfo, ::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}) at /Users/hg344/.julia/dev/Turing/src/core/ad.jl:116
 [20] gradient_logp at /Users/hg344/.julia/dev/Turing/src/core/ad.jl:80 [inlined]
 [21] #2 at /Users/hg344/.julia/dev/Turing/src/inference/support/hmc_core.jl:12 [inlined]
 [22] #_leapfrog#26(::Nothing, ::Nothing, ::Function, ::Array{Real,1}, ::Array{Float64,1}, ::Int64, ::Float64, ::getfield(Turing.Inference, Symbol("##2#3")){Turing.Core.VarReplay.VarInfo,Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}},Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}}) at /Users/hg344/.julia/dev/Turing/src/inference/support/hmc_core.jl:147
 [23] _leapfrog(::Array{Real,1}, ::Array{Float64,1}, ::Int64, ::Float64, ::Function) at /Users/hg344/.julia/dev/Turing/src/inference/support/hmc_core.jl:147
 [24] #_find_good_eps#29(::Int64, ::Function, ::Array{Real,1}, ::getfield(Turing.Inference, Symbol("##4#5")){Turing.Core.VarReplay.VarInfo,Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}},Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}}, ::Function, ::getfield(Turing.Inference, Symbol("##12#13")), ::getfield(Turing.Inference, Symbol("##10#11")){Int64}) at /Users/hg344/.julia/dev/Turing/src/inference/support/hmc_core.jl:253
 [25] _find_good_eps(::Array{Real,1}, ::Function, ::Function, ::Function, ::Function) at /Users/hg344/.julia/dev/Turing/src/inference/support/hmc_core.jl:245
 [26] find_good_eps(::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}, ::Turing.Core.VarReplay.VarInfo) at /Users/hg344/.julia/dev/Turing/src/inference/support/hmc_core.jl:236
 [27] step(::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::Turing.Sampler{NUTS{Turing.Core.ForwardDiffAD{40},Any}}, ::Turing.Core.VarReplay.VarInfo, ::Val{true}) at /Users/hg344/.julia/dev/Turing/src/inference/hmc.jl:202
 [28] macro expansion at ./util.jl:213 [inlined]
 [29] #sample#37(::Bool, ::Nothing, ::Int64, ::Nothing, ::Function, ::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::NUTS{Turing.Core.ForwardDiffAD{40},Any}) at /Users/hg344/.julia/dev/Turing/src/inference/hmc.jl:150
 [30] sample(::Turing.Model{Tuple{:μ,:τ,:w},Tuple{:x},getfield(Main, Symbol("###inner_function#457#33")){Int64},NamedTuple{(:x,),Tuple{Array{Float64,1}}},NamedTuple{(:x,),Tuple{Symbol}}}, ::NUTS{Turing.Core.ForwardDiffAD{40},Any}) at /Users/hg344/.julia/dev/Turing/src/inference/hmc.jl:102
 [31] top-level scope at none:0

@yebai yebai mentioned this issue Mar 28, 2019
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@yebai yebai mentioned this issue Mar 28, 2019
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@xukai92
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xukai92 commented Mar 28, 2019

I see. This is from this line: https://github.com/JuliaStats/Distributions.jl/blob/master/src/mixtures/mixturemodel.jl#L369, which basically constraints the return log-pdf to be the same type as the observed variable (in our case it's Float64).

The following hack works:

    for i in 1:N
      _x = eltype(μ)(x[i])
      _x ~ Distributions.UnivariateGMM(μ,τ, Categorical(w))
    end

but I will try to resolve the in Distributions.jl soon.

@xukai92
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xukai92 commented Mar 28, 2019

but I will try to resolve the in Distributions.jl soon.

By making the returned log-pdf same as the type of parameters.

@xukai92
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xukai92 commented Mar 28, 2019

Submitted JuliaStats/Distributions.jl#853

@yebai
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yebai commented Mar 28, 2019

@xukai92 can you test against both ForwardDiff and Flux.Tracker?

@xukai92
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xukai92 commented Mar 28, 2019

OK you mean added a test in Turing or locally just.

@yebai
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yebai commented Mar 28, 2019

a local test would be fine for now; we can add UniveriateGMM to #712 later.

@xukai92
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xukai92 commented Mar 28, 2019

Just checked with JuliaStats/Distributions.jl#853 it works with both forward and reverse mode.

@yebai
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yebai commented Apr 11, 2019 •
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@cpfiffer could you give this another try, since a fix has been merged into Distributions.jl?

BTW: we need to use UniveriateGMM instead of MixtureModel (see here); and Distributions > v0.18.0.

Ps: this is the output when using Distributions.jl#master

julia> chn = sample(MarginalizedGMM(val, 3), NUTS(1000, 0.65))
[ Info: [Turing] looking for good initial eps...
[ Info: [Turing] found initial ϵ: 0.534375
[ Info:  Adapted ϵ = 0.0580430187561183, std = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]; 500 iterations is used for adaption.
[NUTS] Sampling...100% Time: 0:00:46
[NUTS] Finished with
  Running time        = 45.401994264000045;
  #lf / sample        = 0.0;
  #evals / sample     = 159.324;
  pre-cond. metric    = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0,....
Object of type Chains, with data of type 1000×15×1 Array{Union{Missing, Float64},3}

Log evidence      = 0.0
Iterations        = 1:1000
Thinning interval = 1
Chains            = 1
Samples per chain = 1000
internals         = elapsed, epsilon, eval_num, lf_eps, lf_num, lp
parameters        = τ[3], μ[2], τ[1], τ[2], μ[3], w[1], w[3], w[2], μ[1]

parameters
      Mean    SD   Naive SE  MCSE     ESS   
w[1] 0.3611 0.3097   0.0098 0.0364   72.2558
w[2] 0.3682 0.2954   0.0093 0.0321   84.8491
w[3] 0.2707 0.2831   0.0090 0.0184  236.6837
μ[1] 0.2623 0.6867   0.0217 0.0334  422.6678
μ[2] 0.3501 0.6140   0.0194 0.0251  598.7659
μ[3] 0.1939 0.8178   0.0259 0.0150 1000.0000
τ[1] 0.5724 0.6730   0.0213 0.0417  260.2737
τ[2] 0.5381 0.6824   0.0216 0.0586  135.4392
τ[3] 0.7176 0.8237   0.0260 0.0389  447.9841

@cpfiffer
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I'll run it through today or tomorrow to see if the results look good.

@mohamed82008
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This seems to be working now. I will close the issue.

@ForceBru ForceBru mentioned this issue Jun 8, 2021
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