# Turing: "no method matching cholenksy"

**URL:** <https://discourse.julialang.org/t/turing-no-method-matching-cholenksy/29287>\
**Category:** Probabilistic Programming\
**Created:** [September 29, 2019, 8:59am UTC](https://discourse.julialang.org/t/turing-no-method-matching-cholenksy/29287 "2019-09-29T08:59:26Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![jdhooghe](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jdhooghe/32/9976_2.png) [@jdhooghe](https://discourse.julialang.org/u/jdhooghe)\
**Post date:** [September 29, 2019, 8:59am UTC](https://discourse.julialang.org/t/turing-no-method-matching-cholenksy/29287/1 "2019-09-29T08:59:26Z")

</div>

Good morning,

I am doing a Bayesian logistic regression with correlated logit regression co-efficients. Here is the model I am working with:

’  
Turing.setadbackend(:reverse\_diff)  
@model BayesLogisticRegression(y, X) = begin  
N\_Observations = size(X)[1]  
N\_Features = size(X)[2]

```
Sigma ~ InverseWishart(N_Features+2, Matrix{Float32}(I, N_Features+1, N_Features+1))
Mu ~ MvNormal(zeros(N_Features+1), Matrix{Float32}(I, N_Features+1, N_Features+1) )
Coefficients ~ MvNormal(Mu, Sigma)

Logit = X[:, 1]*Coefficients[2] .+ Coefficients[1]

Probability = Sigmoid.(Logit)
for i = 1:N_Observations
    y[i] ~ Bernoulli(Probability[i])
end

```

end;

```
Model = BayesLogisticRegression(y, X)
Chain = sample(Model, NUTS(10, 100, 0.65))

```

’

I am currently getting the error: "Method error: no method matching cholesky(::TrackedArray{…,Array{Float64, 2}}; check = false).  
It highlights Sigma in the error. I used [https://discourse.julialang.org/t/hyper-priors-in-turing/20752](https://discourse.julialang.org/t/hyper-priors-in-turing/20752) as a template so Im not sure why I’m getting this error. Thank you!

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**Author:** ![trappmartin](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/trappmartin/32/1165_2.png) [@trappmartin](https://discourse.julialang.org/u/trappmartin)\
**Post date:** [September 29, 2019, 10:47am UTC](https://discourse.julialang.org/t/turing-no-method-matching-cholenksy/29287/2 "2019-09-29T10:47:56Z")

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Hi,  
The following minor modification of your code runs fine on the current #master branch of Turing using Julia 1.1.0.

```julia
using Turing, FillArrays, LinearAlgebra

# Sigmoid function (numerically stable)
sigmoid(x::T) where {T<:Real} = x >= zero(x) ? inv(exp(-x) + one(x)) : exp(x) / (exp(x) + one(x))

@model BayesLogisticRegression(y, X) = begin
       N,D = size(X)

       Sigma ~ InverseWishart(D+2, Matrix{Float64}(I, D+1, D+1))
       Mu ~ MvNormal(Fill(0.0, D+1), 1.0 )
       Coefficients ~ MvNormal(Mu, Sigma)

       Logit = X[:, 1]*Coefficients[2] .+ Coefficients[1]

       Probability = sigmoid.(Logit)
       for i = 1:N
           y[i] ~ Bernoulli(Probability[i])
       end
end

# initialize model with some dummy data
Model = BayesLogisticRegression(rand(0:1, 100), randn(100, 10));

# NUTS sampling for 10 iterations
Turing.setadbackend(:reverse_diff)
sample(Model, NUTS(0.65), 10);

```

However, if the initial values for `Sigma` are such that the matrix is not positive-definite & symmetric the sampling will break in the first iteration. Which means you have to be lucky or better set some reasonable initial values for `Sigma`.

Note: Unfortunately, we have to provid tailored gradients in Turing using our own DistributionsAD package for some distributions (including MvNormal) as not all distributions from the Distributions package allow for proper AD.

@cpfiffer is it possible to set initial values for `Sigma` using the new interface? If so, how would you do it?

– EDIT –  
I seemed to have been lucky and cannot reproduce it anymore. I think you will have to set appropriate initial values.

@Kai_Xu Do you think we might have to change the initialisation procedure for such cases?

```julia
Stacktrace:
 [1] checkpositivedefinite(::Int64) at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/factorization.jl:11
 [2] #cholesky!#97(::Bool, ::Function, ::Array{Float64,2}, ::Val{false}) at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/cholesky.jl:182
 [3] #cholesky#101 at ./none:0 [inlined]
 [4] cholesky at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/cholesky.jl:275 [inlined] (repeats 2 times)
 [5] logpdf_with_trans(::InverseWishart{Float64,PDMats.PDMat{Float64,Array{Float64,2}}}, ::Array{Float64,2}, ::Bool) at /Users/martin/.julia/packages/Bijectors/hFDmJ/src/Bijectors.jl:365
 [6] assume(::Turing.SampleFromUniform, ::InverseWishart{Float64,PDMats.PDMat{Float64,Array{Float64,2}}}, ::Turing.Core.RandomVariables.VarName{:Sigma}, ::Turing.Core.RandomVariables.VarInfo{Turing.Core.RandomVariables.Metadata{Dict{Turing.Core.RandomVariables.VarName,Int64},Array{Distribution,1},Array{Turing.Core.RandomVariables.VarName,1},Array{Real,1},Array{Set{Turing.Selector},1}},Real}) at /Users/martin/.julia/dev/Turing/src/inference/Inference.jl:519

```

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<div class="post-metadata">

**Author:** ![cpfiffer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cpfiffer/32/208747_2.png) [@cpfiffer](https://discourse.julialang.org/u/cpfiffer)\
**Post date:** [September 29, 2019, 2:30pm UTC](https://discourse.julialang.org/t/turing-no-method-matching-cholenksy/29287/3 "2019-09-29T14:30:17Z")

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> [@trappmartin](#):
>
> @cpfiffer is it possible to set initial values for `Sigma` using the new interface? If so, how would you do it?

It is possible, but it’s super user-unfriendly. Basically you have to pass in all parameters in a single vector, so this model would require you to unwrap all the elements of `Sigma`, `Mu`, and `Coefficients`. I’m hoping sometime that we can overhaul this to allow the passing in of a `NamedTuple`, but for right now it’s really primitive.