Robustness and Conditional Independence Ideals

Johannes Rauh and Nihat Ay

Contact the author: Please use for correspondence this email.
Submission date: 29. Sep. 2011
Bibtex
MSC-Numbers: 13P25, 13P10, 62H20
Download full preprint: PDF (156 kB), PS ziped (163 kB)

Abstract:
We study notions of robustness of Markov kernels and probability distribution of a system that is described by n input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to describe the system’s behaviour after knockouts. Robustness imposes structural constraints on these potentials.

Robustness of probability distributions is defined via conditional independence statements. These statements can be studied algebraically. The corresponding conditional independence ideals are related to binary edge ideals. The set of robust probability distributions lies on an algebraic variety. We compute a Gröbner basis of this ideal and study the irreducible decomposition of the variety. These algebraic results allow to parametrize the set of all robust probability distributions.