Conditional Independence and Toric Fiber Products

Conditional Independence(CI) models allow to represent sophisticated relations between random variables. Understanding their geometrical poperties gives insights into the boundary structure, i.e. distributions with limited support.

In this talk we show how to decompose complicated CI-models into simpler ones using an algebraic technique called the toric fiber product. We also discuss differences between the classical CI-inference, using the 'axioms' of conditional independence, and algebraic CI-inference using containment of ideals in polynomial rings.