I am working on a phylogenetic tree inference model using Pyro (Bayesian inference in phylogeny - Wikipedia). The problem involves constructing a tree from a set of leaf nodes by recursively merging them and assigning a likelihood to the resulting tree. The leaf nodes are selected randomly, requiring discrete sampling.
However, the tree topology is discrete and cannot be enumerated and it needs to be inferred. Given this, is it possible to make Variational Inference in Pyro work with such a model?