From what I understand the Tree-Structured Parzen Estimator (TPE) creates two probability models based on hyperparameters that exceed the performance of some threshold and hyperparameters that don't.
What I don't fully understand is why TPE is "tree-structured." Is the simple clustering of y > thresh and y < thresh sufficient to call it a "tree?" When I envision a "tree structure" I usually think of many different "forks," perhaps some that are not binary and some that are forks of forks. Although a tree with just one fork is still technically a tree, the name "Tree-Structured Parzen Estimator" seems like it would describe something much more complex.
My question is whether or not I am missing some other deeper conceptual "forks" inherent in TPE that would turn it into a "tree" when you look at the bigger picture.