The Algebraic Limits of Polynomial Information Measures (opens in new tab)

The paper studies the existence of \emph{polynomial} measures of dependence between two random variables: polynomial functions of the joint distribution that (i) vanish on independence and (ii) cannot increase under post-processing of either variable (the data processing inequality, DPI). Mutual information satisfies both properties but is transcendental in the joint distribution, making it impossible to estimate without bias from finitely many ...