I still have yet to use graphical models (in the traditional sense, not including the new age variational inference style neural networks as graphical models) in real life. Am I just completely missing something? Where do people generally find compelling uses for graphical models?
I use graphical models all over the place, typically for problems that have more structure than simple statistics calculations, but don't need the huge capacity of machine learning models. For example I work with bio folks measuring "EC50" values, basically parameters of titration curves in a wet lab. It seems like a simple curve fitting problem with say 5 parameters. But then these wet lab scientists measure hundreds of curves at once, so we want to put hierarchical structure among the curves -- that is all the curves should look pretty similar with only a few degrees of freedom. Graphical models are a great framework for expressing prior knowledge about the dependencies between these curve parameters. But yeah I then do inference in graphical models using variational inference in PyTorch.
Is there a resource you would recommend for learning about applying GM and related techniques to data like those you described (similar structures with N DoF)? As a hobbyist I've been toying with symbolic regression and this feels like a wall I've been running up against
They are used quite a bit in computational genomics. Indeed, genomics is full of latent variable problems where one has a good model for the underlying phenomena but often not a lot of labeled data.