Hello Ricardo,
I checked out the Logistic Normal Distribution. I understand that there is some additive logistic transformation that could be done on my probability vector, which should be represented by a multivariate normal?
Citing from wikipedia.org:
This follows from applying the additive logistic transformation to map a multivariate normal random variable y ∼ N ( μ , Σ ) , y ∈ R D − 1 to the simplex…
Although the connection between the two nodes (category and material) is not in fact a random variable. That connection is known and static. I know how materials relate to categories (if it’s made of glass, it’s probably a wineglass or sunglasses) and how category relates to material (if its a wineglass its probably made of: glass - 80% or out of plastic 20% e.g.). I just need to connect two probability vectors, one for category and one for material (currently represented by the Dirichlet distributions) together in such a way, that if on any vector an observation is done, the new updated information would flow through the connections to other nodes. The values in the vectors of the nodes would change, although the values of the connections would not.
Question 1)
Is the probability matrix T1 (`T2’ respectively) just a representation of the Σ in the multivariate normal random variable in the wikipedia entry cited above?
Question 2)
I could not find any direct implementation of such logits in PyMC3 documentation. Would I need to create custom distributions for that? Regarding transformations there is this scarce entry in the docs. Could perhaps the pymc3.DirichletMultinomial be the distribution I am looking for? (link here).
Thank you.