Tutorial 2: Unsupervised Learning using Bayesian Mixture Models

Hi,
I wanted to generalize the tutorial's code a bit so that cluster 2D-cluster centroids could possess unconstrained components. In the tutorial the x- and y- components are constrained to be equal. In the tutorial this is achieved by using only a 1D-parameter vector $\mu = [-3.5, 0.5]$. I rewrote the code only a tiny bit so that these equality constraints are avoided. Now, I have replaced the 1D-vector $\mu = [-3.5, 0.5]$ by one DxK array with cluster centroids as column vectors. Despite all my code tinkering I were not successful in the identification of the two clusters. Now I want to ask you whether you could modify your tutorial code so that the equality constraint in $\mu-$components is avoided. Then it would be possible to run the algorithm with the Old Faitful data set so that a comparison with results of EM algorithm (cf. Bishop, 2006, p.437, Fig 9.8) is possible.

A second issue is that I cannot install Turing.jl v0.30.5. My configuration is Win11 and

[31c24e10] Distributions v0.25.107
[7876af07] Example v0.5.3
[1a297f60] FillArrays v1.9.3
[c3e4b0f8] Pluto v0.19.38
[f3b207a7] StatsPlots v0.15.7
[fce5fe82] Turing v0.30.4

Thanks in advance, Claus Möbus

Start with Tutorial 2: Unsupervised Learning using Bayesian Mixture Models and inspect how the centroid parameter μ is represented. Reproduce the current tutorial, then compare its clustering behavior on the Old Faithful data with the requested unconstrained components and the EM results referenced from Bishop (2006, Fig. 9.8); document the Turing.jl v0.30.5 installation issue separately if it remains reproducible.