The graphical model Represents probabilistic independence. Given a set of conditional independence assumptions, how to find the probabilistic graphical model that maximizes some metrics (e.g, minimum size)? I'm somehow new to this topic and wonder what are the topics called that solve this problem?
I think the keyword you are looking for is Structure Learning. You might start by looking at this review Structure learning in graphical modeling.
The review mentions several context where you try to estimate a graphical model from your data given a set of constraints on its structure, such as conditional independences as you mention.
Another case which can be seen as structure learning which I know of and that does not appear explicitly in the review, is the case of Gaussian Markov Random Field (GMRF) fitting to general Gaussian Random Field (GRF). Given fixed a neighborhood structure, or conditional independence properties which induce a GMRF, you want to approximate the correlations that appear in a GRF (in which there is no conditional independence property). Fitting Gaussian Markov Random Fields to Gaussian Fields is a famous article on the topic.