Graphical Models and Algebraic Statistics

So most people who know me in an academic setting know that I have a thing for algebraic statistics. I'm kind of like a cheerleader for it than an expert in it. I know some algebra and have read a few chapters of various books on the subject of algebraic statistics but I certainly have never grasped it enough to do anything meaningful. I wonder though if there is any cool relationship potentially between graphical models and algebraic statistics. My basis for this, absolutely nothing but that I like both of these objects and it would be neat for them to have cool intertwining properties.

I wish that algebraic statistics had more clear uses to it that would make the large amount of time I'd have to invest in it worthwhile but if someday these two things have cool properties, well I called it here first!