Support for Parameterized SPNs

[byzakyz]

Describe your request

SPNs with some probabilities left undefined as parameters (e.g., p, 1-p). This would allow for the creation of SPNs where nodes are defined with parameters instead of fixed probabilities, like so:
X0 = Categorical(p=p1, scope=0) # p1 is the parameter name

Parameterized log_likelihood Function:
Enhancing the log_likelihood function to operate on parameterized SPNs. The function should be able to return inference results as a function of the parameters (f(p1, ..., pk))

Method for Parameterizing Probabilities in SPNs:
A method that takes an existing SPN and allows users to set some of the probabilities of its nodes as parameters. This would be particularly useful for parameterizing SPNs that have been learned from data.

Briefly explain its use-case

To learn spn from data and paremeterize some of the nodes to create large parameterized networks for benchmarking the computational efficiency and time required for inference across different methods. I am particularly interested in comparing the results for the transformed Markov Chain from the parameterized SPN and how they differ with increased number of parameters.