VonMises failed to find valid initial parameters in 1000 tries.

[yakir12]

Minimal working example

using Turing
@model function bmodel(αs)
    μ ~ Uniform(-π, π)
    κ ~ InverseGamma(2, 3)
    for i in eachindex(αs)
        αs[i] ~ VonMises(μ, κ) # doesn't work
        # αs[i] ~ Normal(μ, κ) # works
    end
end
x = rand(VonMises(0.3, 3), 100)
model = bmodel(x)
chain = sample(model, NUTS(), 1000)

Description

When trying to fit the model above to the data using a Normal distribution, I get no issues, but if I switch that distribution to VonMises, it errors.

Julia version info

versioninfo()

Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × AMD Ryzen 5 PRO 8540U w/ Radeon 740M Graphics
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 12 virtual cores)

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]st --manifest

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[yakir12]

I'll add that I've simplified the MWE even further by replacing the multiple observations with a single observation:

using Turing
@model function bmodel(α)
    μ ~ Uniform(-π, π)
    κ ~ InverseGamma(2, 3)
    α ~ VonMises(μ, κ) # doesn't work
    # α ~ Normal(μ, κ) # works
end
x = rand(VonMises(0.3, 3))
model = bmodel(x)
chain = sample(model, NUTS(), 1000)

It still errors with the same error:

┌ Warning: failed to find valid initial parameters in 10 tries; consider providing explicit initial parameters using the `initial_params` keyword
└ @ Turing.Inference ~/.julia/packages/Turing/GS2NO/src/mcmc/hmc.jl:160
Sampling 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:00
ERROR: failed to find valid initial parameters in 1000 tries. This may indicate an error with the model or AD backend; please open an issue at https://github.com/TuringLang/Turing.jl/issues
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] find_initial_params(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, varinfo::DynamicPPL.VarInfo{…}, hamiltonian::AdvancedHMC.Hamiltonian{…}; max_attempts::Int64)
    @ Turing.Inference ~/.julia/packages/Turing/GS2NO/src/mcmc/hmc.jl:170
  [3] find_initial_params(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, varinfo::DynamicPPL.VarInfo{…}, hamiltonian::AdvancedHMC.Hamiltonian{…})
    @ Turing.Inference ~/.julia/packages/Turing/GS2NO/src/mcmc/hmc.jl:145
  [4] initialstep(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, spl::DynamicPPL.Sampler{…}, vi_original::DynamicPPL.VarInfo{…}; initial_params::Nothing, nadapts::Int64, kwargs::@Kwargs{})
    @ Turing.Inference ~/.julia/packages/Turing/GS2NO/src/mcmc/hmc.jl:210
  [5] step(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, spl::DynamicPPL.Sampler{…}; initial_params::Nothing, kwargs::@Kwargs{…})
    @ DynamicPPL ~/.julia/packages/DynamicPPL/I9lST/src/sampler.jl:125
  [6] step
    @ ~/.julia/packages/DynamicPPL/I9lST/src/sampler.jl:108 [inlined]
  [7] macro expansion
    @ ~/.julia/packages/AbstractMCMC/kwj9g/src/sample.jl:161 [inlined]
  [8] macro expansion
    @ ~/.julia/packages/ProgressLogging/6KXlp/src/ProgressLogging.jl:328 [inlined]
  [9] (::AbstractMCMC.var"#25#26"{Bool, String, Nothing, Int64, Int64, Int64, Nothing, @Kwargs{…}, Random.TaskLocalRNG, DynamicPPL.Model{…}, DynamicPPL.Sampler{…}, Int64, Int64, Int64})()
    @ AbstractMCMC ~/.julia/packages/AbstractMCMC/kwj9g/src/logging.jl:12
 [10] with_logstate(f::AbstractMCMC.var"#25#26"{…}, logstate::Base.CoreLogging.LogState)
    @ Base.CoreLogging ./logging/logging.jl:522
 [11] with_logger(f::Function, logger::LoggingExtras.TeeLogger{Tuple{LoggingExtras.EarlyFilteredLogger{…}, LoggingExtras.EarlyFilteredLogger{…}}})
    @ Base.CoreLogging ./logging/logging.jl:632
 [12] with_progresslogger(f::Function, _module::Module, logger::Base.CoreLogging.ConsoleLogger)
    @ AbstractMCMC ~/.julia/packages/AbstractMCMC/kwj9g/src/logging.jl:36
 [13] macro expansion
    @ ~/.julia/packages/AbstractMCMC/kwj9g/src/logging.jl:11 [inlined]
 [14] mcmcsample(rng::Random.TaskLocalRNG, model::DynamicPPL.Model{…}, sampler::DynamicPPL.Sampler{…}, N::Int64; progress::Bool, progressname::String, callback::Nothing, num_warmup::Int64, discard_initial::Int64, thinning::Int64, chain_type::Type, initial_state::Nothing, kwargs::@Kwargs{…})
    @ AbstractMCMC ~/.julia/packages/AbstractMCMC/kwj9g/src/sample.jl:144
 [15] 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/GS2NO/src/mcmc/hmc.jl:117
 [16] sample
    @ ~/.julia/packages/Turing/GS2NO/src/mcmc/hmc.jl:86 [inlined]
 [17] #sample#100
    @ ~/.julia/packages/Turing/GS2NO/src/mcmc/abstractmcmc.jl:29 [inlined]
 [18] sample
    @ ~/.julia/packages/Turing/GS2NO/src/mcmc/abstractmcmc.jl:20 [inlined]
 [19] #sample#99
    @ ~/.julia/packages/Turing/GS2NO/src/mcmc/abstractmcmc.jl:17 [inlined]
 [20] sample(model::DynamicPPL.Model{typeof(bmodel), (:α,), (), (), Tuple{Float64}, Tuple{}, DynamicPPL.DefaultContext}, alg::NUTS{AutoForwardDiff{nothing, Nothing}, AdvancedHMC.DiagEuclideanMetric}, N::Int64)
    @ Turing.Inference ~/.julia/packages/Turing/GS2NO/src/mcmc/abstractmcmc.jl:14
 [21] top-level scope
    @ REPL[11]:1
Some type information was truncated. Use `show(err)` to see complete types.

[yebai]

This is not a Turing bug, likely a misspecified model, or simply that the posterior is difficult for HMC.

[yebai]

This may indicate an error with the model or AD backend; please open an issue at https://github.com/TuringLang/Turing.jl/issues

@penelopeysm, let's rephrase this message and replace the word "error" with something similar to my above comment. Also, let's redirect users to Julia discourse instead of opening issues here.

[penelopeysm]

let's rephrase this message and replace the word "error"

This is not a Turing bug

The message doesn't claim that there's an error with Turing; it just says it's an error, which could well be a user error.

Would you like to write something that is closer to what you intend?

Also, let's redirect users to Julia discourse instead of opening issues here.

I personally like having people open issues. I don't think that GitHub issues should only be used for bugs with the libraries, I think it's perfectly fine for users to ask for help here.

[penelopeysm]

@yakir12 On the topic of the model: A couple of days ago I actually wrote up a page to help debug this exact error :)

https://turinglang.org/docs/usage/troubleshooting/#initial-parameters

If you try out the first step:

using Turing
using DynamicPPL.TestUtils.AD: run_ad

@model function bmodel(α)
    μ ~ Uniform(-π, π)
    κ ~ InverseGamma(2, 3)
    α ~ VonMises(μ, κ)
end

x = rand(VonMises(0.3, 3))
model = bmodel(x)
adtype = AutoForwardDiff()
result = run_ad(model, adtype; test=false, benchmark=false)
result.grad_actual

You'll find that ForwardDiff is returning NaNs:

2-element Vector{Float64}:
 NaN
 NaN

I also tried ReverseDiff (returns one NaN instead of two), Mooncake (errors), and Enzyme (errors) so the root issue seems to be that Julia's AD packages don't handle VonMises well.

[yebai]

It's likely not a user error either. Some models are difficult for MCMC. Thus, HMC could fail. A better message could look like

"This may indicate a misspecification of the model, or the posterior is difficult for the specified HMC sampler. "

I personally like having people open issues. I don't think that GitHub issues should only be used for bugs with the libraries, I think it's perfectly fine for users to ask for help here.

These issues are more likely modelling-oriented than Turing-specific. Another reason for using Julia's discourse is that more people there can help, and the discussions are more discoverable than here.

[penelopeysm]

I see that, but this error happens even before HMC starts sampling, it's simply trying to find an initial starting point with valid logp and valid gradients.

This code path has been reported 5 times, and 3 of those times, it's an AD problem, and would have been trivially caught by run_ad:

#2584
#2526
#2389 -- Not the same error message, but it used to hang, and I fixed it by making it error instead.

1 time, it was probably a modelling problem, but ultimately boiled down to AD, and would also have been caught by run_ad:

#2559

1 time, it was the model being a problem (although arguably our initialisation also isn't flexible enough):

#2476

[yebai]

@penelopeysm the above errors are indeed about HMC initialisation, but they are for different models.

Briefly, the VonMises distribution has support depending on its parameters (i.e., mu and kappa). This will instruct Turing to construct a TruncatedBijector, which will change when mu and kappa change. This canonical example breaks NUTS because its warmup procedure assumes constant support for RVs.

[penelopeysm]

I posted a comment above (maybe it got lost!) that this issue is also about AD: #2584 (comment)

[yebai]

I did see your comment. It is a numerical edge case for AD, which is likely still caused by model misspecification. So, I suggested rephrasing the warning message above.

More generally, even with great effort, making AD or bijectors consistently numerically stable is impossible due to constraints inherited from the finite precision assumption of numerical computing.

[yebai]

@yakir12, for your example, you could try slice sampling instead of HMC, which works quite well for low-dimensional posterior distributions (up to a few tens of parameters):

using Turing, SliceSampling

@model function bmodel(αs)
    μ ~ Uniform(-π, π)
    κ ~ InverseGamma(2, 3)
    for i in eachindex(αs)
        αs[i] ~ VonMises(μ, κ) # doesn't work
        # αs[i] ~ Normal(μ, κ) # works
    end
end
x = rand(VonMises(0.3, 3), 100)
model = bmodel(x)

chain = sample(model, externalsampler(RandPermGibbs(SliceSteppingOut(2.))), 1000)

Random walk MH might also work well, but slightly less user-friendly than slice sampling because you need to tune the proposal to get good convergence.

[penelopeysm]

@yebai I am sorry but I am struggling to understand -- if the problem is a model misspecification, surely the solution is to change the model?

As I see it, it's an AD issue, and using another sampler like slice sampling or MH works precisely because it sidesteps the use of AD entirely. So, to me, it seems that the error message is quite accurate, and the only thing I would change about the error message is to add a link to the docs.

I see the point about Discourse being more widely seen, though I must mention that GitHub is a much better place for us developers. For example, the fact that people open issues here is precisely what helps us see the typical underlying causes of this error. If an issue was better solved on Discourse, I wouldn't have any qualms with closing an issue and asking people to post on Discourse. I would rather have it this way, instead of people posting bugs on Discourse and me having to look on there to find out.