Implement Latent Dirichlet Allocation (LDA) Example

[albertpod]

I'd like to propose adding a Latent Dirichlet Allocation (LDA) example to the codebase. Looking at the current functionality, it seems we already have all the necessary building blocks in place - specifically the DirichletCollection and MultinomialPolya nodes!

LDA would make an excellent addition to our examples for several reasons:

1. It's a fundamental topic model widely used in text analysis and machine learning
2. It would demonstrate RxInfer's capability with hierarchical Bayesian models
3. It exercises multiple probability distributions in combination
4. The results are intuitive and visually presentable

The generative model is straightforward:

• Topic-word distributions: φₖ ~ Dirichlet(β)
• Document-topic distributions: θₗ ~ Dirichlet(α)
• Topic assignments: zₗₙ ~ Multinomial(θₗ)
• Words: wₗₙ ~ Multinomial(φzₗₙ)

This seems like a relatively easy yet powerful example to implement that would showcase RxInfer.jl's strengths. It could also serve as a benchmark against other probabilistic programming frameworks.

[divital-coder]

Hi LazyDynamics,
I have been passively engaging with the LazyDynamics packages when it was the "center" of attention at linkedin :) (pretty amazing launch of the RxInfer.jl")

I would love to work on this, and was wondering If I can actively engage and provide high quality research examples

[albertpod]

Hi @divital-coder!

Just for clarity, RxInfer.jl is not a property of Lazy Dynamics, nor any other package in this repository (ReactiveBayes). ReactiveBayes is an open source initiative supported by different parties, including Lazy Dynamics.
If you want to support RxInferExamples, we will be grateful! The LDA example is a good start, but if you want to contribute something else related to RxInfer, please feel free to do so!

[divital-coder]

Thanks for the distinction @albertpod, I found a listing under LazyDynamics for developing models, so sort of correlated that with the experimental research models under the RxInfer.jl examples. Reactivebayes is a great organisation, would love to provide an example soon.