How can Gröbner bases used to describe discrete probability? I am working in the field of machine learning, and I have come across a few papers that show relationships between Gröbner bases and discrete probability. So I come here for help.
Can you please explain how can Gröbner bases be used to describe discrete probability?
I have looked at Gröbner bases and I understand the general concepts (and used Maple to calculate a few examples). So it is the link that is missing for me.

You can find a nice introduction here: Pistone, Giovanni and Riccomagno, Eva and Wynn, Henry, Pistone, 
Pistone, Giovanni; Riccomagno, Eva; Wynn, Henry
Computational commutative algebra in discrete statistics
